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docs/g12/chy4uz.md

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+# HL History - 2
+
+The course code for this page is **CHY4UZ**.
+
+o7

docs/g12/eng4uz.md

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+# HL English - 2
+
+The course code for this page is **ENG4UZ**.

docs/g12/fsf3uz.md

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+# SL French - 2
+
+The course code for this page is **FSF3UZ**.
+
+o7
+
+## Resources
+
+ - [Textbook: Oxford IB French B Course Companion](/resources/g11/textbook-french-b-second-edition.pdf) ([Answers](/resources/g11/textbook-french-b-second-edition-answers.pdf))

docs/g12/sch4uz.md

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+# HL Chemistry - 2
+
+The course code for this page is **SCH4UZ**.
+
+## Thermal concepts
+
+!!! definition
+    - A **system** consists of reactants and products being studied, often represented as a chemical equation.
+    - The **surroundings**/**environment** are all matter outside of the system capable of absorbing or releasing energy.
+
+ - **Open** systems allow **energy and matter** to move in and out of the system.
+ - **Closed** systems allow only **energy** to move in and out of the system.
+ - **Isolated** systems do not allow energy or matter to move in and out of the system. This is an ideal but unrealistic scenario.
+
+### Changes
+
+As **breaking bonds requires energy** and **forming bonds releases energy**:
+
+!!! definition
+    - An **endothermic** reaction overall requires energy.
+    - An **exothermic** reaction overall releases energy.
+
+**Physical** changes such as state changes or dissolving substances may release or require energy depending on the energy of intermolecular bonds being broken and formed.
+
+!!! example
+    - Ice melting requires energy to break the stronger bonds in a solid.
+    - Dissolving salt in water breaks the intermolecular bonds holding the salt together but regains it all by forming new bonds with the water.
+
+**Chemical** changes all involve breaking old bonds to form new bonds. Depending on the energy required/released in breaking/forming those bonds, the reaction may end up endothermic or exothermic. Regardless, all reactions need a small initial **activation energy** to begin.
+
+!!! info
+    Acid-base reactions are always exothermic.
+
+### Specific heat capacity
+
+Please see [SL Physics 1#3.1 - Thermal concepts](/sph3u7/#31-thermal-concepts) for more information.
+
+## Enthalpy
+
+Represented as $H$ in joules, enthalpy represents the total energy in a system. Absolute enthalpy is not measurable, so change in enthalpy ($\Delta H$) is often used instead. The magnitude of enthalpy change is dependent on the type of change and quantity of substance that is changing.
+
+A **negative** $\Delta H$ indicates that energy has left the system and so is an **exothermic** reaction.
+
+In a balanced chemical equation, change in enthalpy is written to the right after the product.
+$$
+a + b \to c\ \ \Delta H = x\text{ kJ}
+$$
+
+!!! example
+    Energy is required for the decomposition of water so its enthalpy is positive.
+    $$\ce{H2O_{(l)} -> H2_{(g)} + 1/2 O2_{(g)}\ \ \Delta H = +280 kJ}$$
+
+$\Delta H$ can also be included in a balanced thermochemical equation as a reactant or product instead of listed at the end. In this case, it is always positive and its sign determines whether it is a reactant or product.
+$$
+a + b + x\text{ kJ} \to c
+$$
+
+!!! example
+    Using the same formula as in the previous example:
+    $$\ce{H2O_{(l)} + 285.5 kJ -> H2_{(g)} + 1/2 O2_{(g)}}$$
+
+### (Standard) Molar enthalpy of reaction
+
+The **molar enthalpy of reaction** $\Delta H_x$ expresses the change in enthalpy when exactly one mole of the substance is involved in the reaction.
+
+!!! example
+    The molar enthalpy of combustion (also known as the **heat of combustion**) of ethanol is $\pu{-1367 kJ/mol}$, indicating that every one mole of ethanol combusted releases 1367 kilojoules of energy.  
+    $\Delta H_\text{combustion} = \ce{-1367 kJ/mol C2H6O}$
+
+The **standard molar enthalpy of reaction** $\Delta H^\theta_x$ is the molar enthalpy of reaction when initial and final conditions of the reaction are at standard atmospheric temperature and pressure (SATP, 25°C @ 100 kPA). Therefore, the activation energy, energy released/required during the reaction, and energy released/required following the reaction to return to SATP are all included.
+
+!!! warning
+    This includes energy required for some substances to change state, such as water vapour from combustion cooling to 25°C.
+
+### Energy profiles
+
+Also known as **reaction profiles**, energy profiles are a visual representation of the change in chemical potential energy of the system.
+
+ - Absolute enthalpy ($H$) is placed on the y-axis while the reaction progress (time, sort of) is placed on the x-axis.
+ - A horizontal line representing the enthalpy before the change is placed at the beginning labelled with the reactants.
+ - A horizontal line representing the enthalpy after the change is placed at the end labelled with the products.
+ - The change in enthalpy is labelled with an arrow in the direction of the change with its value if known.
+ - A hump shows the reaction in progress (even exothermic reactions require some activation energy).
+
+### Bond enthalpies
+
+$\Delta H_B$, also known as **bond association energies**, the enthalpy of a bond type (e.g., $\ce{C-H}$) is the energy required to break **1 mol** of that bond type when the reactants and products are **gaseous** so energy is not lost from state changes. Compared of other methods of determining reaction enthalpy, this method is less accurate due to the other compounds affecting bond strength and thus enthalpy on a per-molecule basis.
+
+The change in enthalpy of a reaction can be approximated by considering the bonds broken and formed:
+$$\Delta H = \sum n\Delta H_B\text{reactants} - \sum n\Delta H_B\text{products}$$
+
+## Calorimetry
+
+!!! definition
+    - A **calorimeter** measures changes in energy.
+
+A basic calorimeter uses a lid and insulation to keep matter in and minimise energy changes with its surroundings. A thermometer is used to measure the temperature change of the water, and a stirrer is common to ensure accurate thermometer readings. The reactants are placed in water to react.
+
+<img src="/resources/images/basic-calorimeter.png" width=700>(Source: Kognity)</img>
+
+It is assumed that all the heat lost/gained by the reaction is gained/lost from the water.
+
+$$-q_\ce{H2O}=\Delta H_\text{reaction}$$
+
+In the event that reactants cannot be placed in water to react (e.g., combustion), a **bomb calorimeter** is used, which contains a metal sealed box submerged in the waterfilled with reactant and oxygen. A circuit leads into the box to start the reaction with a spark.
+
+!!! warning
+    Assumptions in calorimetry:
+    
+    - All energy released/absorbed from the system goes to/from the surroundings of the calorimeter (water). This usually needs to be corrected for in bomb calorimeters by measuring the heat capacity and mass of the metal box inside the calorimeter as well.
+    - No energy is transferred outside the calorimeter — the insulation should work properly.
+    - The calorimeter itself does not absorb or release energy — this is not a good assumption but can be compensated for.
+    - A dilute aqueous solution is assumed to have the same density and specific heat capacity as water — this assumption is best when the solute is diluted close to 1 mol/L.
+
+### Measuring calorimeters
+
+Instead of recording the temperature of the calorimeter at any one point, a range of temperatures over time per trial should be plotted to obtain a curve. As calorimeters are not perfect and absorb/release energy, it will generate a graph that peaks and slowly returns to ambient temperature. To remedy this, the line returning the temperature to normal should be **linearly regressed** and extrapolated to the reaction start time to obtain a more accurate peak temperature.
+
+## Hess's law
+
+Hess's law asserts that the change in enthalpy works like displacement - so long as the products and reactants are the same, any reaction with any number of intermediate steps will result in the same change in enthalpy.
+$$\Delta H = \sum \Delta H \text{ of intermediate reactions}$$
+
+### Formation equations
+
+A **formation equation** is a balanced chemical equation where exactly one mole of product and its reactants in **elemental form** are in their standard state — -gens are diatomic, phosphorus is $\ce{P4}$, sulfur is $\ce{S8}$, and at SATP (25°C, 100 kPa).
+
+!!! info
+    Fractions are permitted as coefficients on the reactant side to get exactly one mole of product.
+
+!!! example
+    $$\ce{6C_{(s)} + 6H2_{(g)} + 3O2_{(g)} -> C6H12O6}$$
+    $$\ce{2C_{(s)} + 3/2 H2_{(g)} + 1/2 Cl2_{(g)} -> C2H3Cl_{(g)}}$$
+
+The **standard enthalpy of formation** $\Delta H^\theta_f$ is the energy change from the formation of one mole of its substance from its elements in their standard states. It can be determined by subtracting the sum of the enthalpy of each element/compound on the reactant side and adding those on the product side.
+$$\Delta H = \sum n\Delta H\text{ products} - \sum n\Delta H\text{ reactants}$$
+
+!!! warning
+    It is assumed that there is no state change that would affect enthalpy when calculating *standard* enthalpy of formation.
+
+### Enthalpy cycles
+
+Enthalpy cycles are a visual representation of Hess's law. It is used to show that the energy is the same from initial reactants to a product regardless of any intermediate steps.
+
+!!! example
+    $\Delta H_1 = \Delta H_2 + \Delta H_3$. Note that both arrows point to the intermediate product.
+    <img src="/resources/images/enthalpy-cycles.png" width=700>(Source: Kognity)</img>
+
+## Born-Haber cycles
+
+!!! definition
+    - The **standard enthalpy of atomisation** $\Delta H^\theta_{atm}$ is the energy required to change 1 mol of an element at SATP in its standard state to 1 mol of atoms of that element in its gaseous state.
+
+To form an ionic compound from elements in their standard states:
+
+ - the elements must be converted into gaseous atoms, (enthalpy of atomisation)
+ - the atoms must lose or gain electrons to form ions, (electron affinity/ionisation energy)
+ - and then the gaseous ions must bond to form an ionic compound.
+
+The products should be listed on each level of a Born-Haber cycle, and relatively to-scale arrows should point in the direction of enthalpy change, where upwards increases enthalpy.
+
+<img src="/resources/images/born-haber-simple.png" width=700>(Source: Kognity)</img>
+
+Second ionisation energy may increase the peak enthalpy after it has lowered from first ionisation energy. In this case, unlike the below figure, the first and second ionisation energies can be combined into a single arrow representing the sum of both.
+
+<img src="/resources/images/born-haber-ionisation.png" width=700>(Source: Kognity)</img>
+
+### Lattice enthalpy
+
+The lattice enthalpy of an ionic compound is the energy required to dissociate 1 mol of an ionic solid to its gaseous ions.
+
+ - It decreases as ionic radius increases due to greater distance and charge separation
+ - It increases as difference in charge increases because the greater charges are more strongly attracted
+ - The above only apply if the other (ionic radius/charge) is the same or similar
+ - Difference in charge has a much greater effect than ionic radius as it is multiplicative while the effect of increasing radius is additive
+
+### Enthalpy of solution and hydration
+
+The enthalpy of hydration is the enthalpy change when 1 mol of a gaseous ion is dissolved in water to make an infinitely dilute solution such that it is unaffected by attraction or repulsion from other ions.
+
+!!! example
+    The enthalpy of $\ce{Na+_{(g)} -> Na+_{(aq)}}$ is the enthalpy of hydration of $\ce{Na+}$.
+
+The enthalpy of solution is the enthalpy change when 1 mol of a substance dissolves in water. It is equal to the sum of the enthalpy of hydration and lattice enthalpy.
+
+$$\Delta H_{sol}=\Delta H_{hy} + \Delta H_{latt}$$
+
+!!! example
+    The enthalpy change of $\ce{NaCl_{(s)} -> Na+_{(aq)} + Cl-_{(aq)}}$ is the enthalpy of solution of $\ce{NaCl}$.
+
+## Entropy
+
+**Entropy**, $S$, is a measure of structural disorder in a system in $\pu{J/K/mol}$. Absolute enthalpy is always positive, similar to enthalpy. An increase in disorder results in more entropy which results in a greater chance that a system will be in a certain state.
+
+A reaction that increases entropy can continue even in the absence of extra energy, which results in endothermic reactions.
+
+Reactions that would increase entropy are **entropically favoured**, so entropy will work to make it happen.
+
+The following changes increase entropy:
+
+ - changes in state of one substance to a more disordered state, i.e., solid → liquid → gas,
+ - mixing particles of different types, e.g., solid to aqueous,
+ - increasing the number of moles of total gas or decreasing the number of moles of a solid,
+ - and increasing the number of moles of gas on the product side compared to the reactant side, which has the greatest effect.
+
+### Spontaneity
+
+The **spontaneity** of a reaction is its tendency to continue without extra energy input after its initial activation energy.
+
+Gibbs free energy or **standard free energy** ($\Delta G$/$\Delta G^\theta$, $\pu{kJ}$ or $\pu{kJ/mol}$) is a measure of the sponetaneity of a chemical change. Spontaneous reactions must have a negative $\Delta G$, while those that are positive will require more energy to continue.
+$$\Delta G^\theta = \Delta H^\theta - T\Delta S^\theta$$
+
+## Chemical kinetics
+
+The **rate of a reaction** is the change of reactant to product per unit of time. The following are all viable methods of measuring rate of reaction:
+
+ - change in gas volume via gas collection,
+ - change in mass,
+ - change in light absorption,
+ - titration,
+ - and change in conductivity.
+
+In an ideal gas, the kinetic energy of particles is spread in a **Maxwell-Boltzmann distribution**, where the total area under the curve is equal to the total number of particles in the sample.
+
+<img src="/resources/images/maxwell-boltzmann.png" width=700>(Source: Kognity)</img>
+
+As temperature increases, the distribution's total area *does not change* but the overall spread moves to the right as more particles have higher kinetic energies.
+
+<img src="/resources/images/mbdist-temperature.png" width=700>(Source: Kognity)</img>
+
+### Collision theory
+
+Collision theory states that for a chemical reaction to take place between two particles:
+
+ - they must collide,
+ - they must have proper **collision geometry** or **collision orientation** — similar to viruses bumping into cells, the "keys" must hit "locks" — in this case usually they must strike the bond,
+ - they must collide with enough energy to break the initial bond.
+
+If all of these conditions are met, the collision is an **effective collision** — a collision that results in a chemical reaction.
+
+The rate of a reaction increases with:
+
+ - the frequency of collisions,
+ - and the proportion of collisions that are effective collisions
+
+Over time, the rate generally decreases because initially the highest concentration of reactants results in the highest collision frequency, which goes down as reactants are consumed. The proportion of effective collisions will also decrease as reactants also collide with product. Eventually, the reaction will stop or be so slow it appears to have stopped.
+
+<img src="/resources/images/change-of-rate-over-time.jpg" width=700>(Source: Kognity)</img>
+
+The following factors affect the rate of reaction:
+
+ - **Surface area/particle size of a solid:** as only particles on the surface of a solid can be collided with, smaller solid particles have greater surface area where more collisions can happen, leading to greater collision frequency.
+ - **Concentration/pressure of reactant**: A greater concentration leads to more reactant particles to collide in a given volume, increasing collision frequency.
+ - **Temperature**:
+    - Increasing temperature increases reactant particles' kinetic energy, increasing collision frequency,
+    - however it primarily increases the chance of particles having sufficient activation when they do collide, changing the proportion of effective collisions.
+
+### Activation energy
+
+Because electron clouds repel reach other, without extra energy, particles would not get close enough to break bonds. This energy required for particles to become closer is known as the **activation energy** of a reaction. All chemical reactions have an activation energy requirement.
+
+### Catalysts
+
+A catalyst is a substance that increases the rate of a reaction without being consumed. Not all reactions have catalysts, and increasing catalyst quantity does not necessarily always increase the rate of reaction.
+
+Catalysts operate by reducing the activation energy needed by creating an **alternative reaction pathway** with a lower activation energy, so a larger proportion of particles are able to reach that lower energy requirement.
+
+<img src="/resources/images/catalyst-energy.png" width=700>(Source: Kognity)</img>
+
+Visualised with a Maxwell-Boltzmann distribution:
+
+<img src="/resources/images/mbdist-catalyst.png" width=700>(Source: Kognity)</img>
+
+Catalysts can also improve the chances of correct collision geometry by encouraging certain orientations.
+
+## Rates of reaction
+
+The **law of mass action** states that the rate of any reaction is directly proportional to the product of each reactant **concentration**. For a reaction of the form $\ce{aA + bB -> products}$, the rate law holds that:
+
+$$r=k[A]^a [B]^b$$
+
+where $k$ is the **rate constant**, an empirically determined value that is only valid for one reaction at one temperature. Its units are equal to whatever balances out the equation — where $n$ is the order of reaction, it is equal to $\ce{dm^{3(n-1)}} / \pu{mol}^{n-1} / \pu{s}$.
+
+!!! warning
+    Solids and liquids have constant concentrations, so their factor is incorporated as part of $k$ and **not included** as a separate factor (e.g., not as $[C]^c$).
+
+The **individual order of reaction** is the value of the exponent of a specific reactant in the rate law. It must be a real positive number.
+
+!!! example
+    The individual order of the reaction with respect to $A$ is $a$, and the order of reaction is $a+b$.
+
+To determine the individual order of reaction of a reactant, two identical experiments with equal quantities of the **other** reactants are needed. Where $c$ is the concentration of the reactant between the two trials, $r$ is the rate, and $n$ is the individual order of that reactant:
+
+$$\biggr(\frac{c_2}{c_1}\biggr)^n = \frac{r_2}{r_1}$$
+
+!!! example
+    For the following data, changing the concentration of $\ce{OCl-}$ by a factor of 3 causes a rate change by a factor of 9, therefore the individual order of $\ce{OCl-}$ is 2.
+    
+    | Initial $\ce{[OCl-]}$ | Initial $\ce{[I-]}$ | Initial rate |
+    | --- | --- | --- |
+    | $1.0\times10^{-3}$ | $4.0\times10^{-3}$ | $1.0\times10^{-3}$ |
+    | $3.0\times10^{-3}$ | $4.0\times10^{-3}$ | $9.0\times10^{-3}$ |
+
+### Integrated rate laws
+
+Throughout the course of one trial of one reaction, a **concentration-time graph** can be used to find details about its rate. Where concentration is the concentration of the reactant in question over time:
+
+<img src="/resources/images/concentration-time.png" width=700>(Source: Kognity)</img>
+
+A reactant with an individual order of
+
+ - **zero** shows a negative linear line, and $k=-\text{slope}$.
+ - **one** shows exponential decay, and $k=-\text{slope}$ of a graph of $\ln(\text{concentration})$ against time, which should be linear.
+ - **two** shows a *deeper* exponential decay, and $k=\text{slope}$ of a graph of $\frac{1}{\text{concentration}}$ against time, which should be linear.
+
+Additionally, a **concentration-rate graph** can be used.
+
+<img src="/resources/images/concentration-rate.png" width=700>(Source: Kognity)</img>
+
+A reactant with an individual order of
+
+ - **zero** shows a horizontal line.
+ - **one** shows a positive linear line that passes through the origin.
+ - **two** shows the right side of a positive quadratic that passes through the origin.
+
+### Half-life
+
+The half-life ($t_{1/2}$) of a reaction represents the time required for half of the sample to be used.
+
+In the context of radiation, it is the time for half of the nuclei in a radioactive sample to decay.
+
+In a **zero-order** reaction, each half-life is half of the previous.
+
+In a **first-order** reaction, it is constant regardless of concentration, and can the concentration can be expressed with an equation, where $[A]$ is the concentration of a wanted substance, $k$ is the rate constant, and $[A_0]$ is the initial concentration.
+
+$$\ln[A]=\ln[A_0]-kt_{1/2}$$
+
+In a **second-order** reaction, each half-life is double the previous.
+
+### Reaction mechanisms
+
+!!! definition
+    - A **multi-step reaction** consists of more than one reaction as intermediate steps.
+    - An **elementary step** is the basic step of a multi-step reaction, usually involving one or two molecules but never more than three.
+    - A **reactant** is present initially but not at the end of a reaction unless in excess.
+    - A **product** is not present initially but appears at the end of a reaction.
+    - A **catalyst** is present both at the start and end of a reaction. It may be consumed and regenerated in intermediate steps.
+    - A **reaction intermediate** is not present at the start or end of a reaction as it is generated and consumed in the intermediate steps.
+    - The **molecularity** of a reaction represents the number of molecules that react in an elementary reaction from uni- to termolecular.
+    - An **activated complex** or **transition state** is the point where new bonds are being formed at the same time bonds are being broken.
+
+A reaction involving any more than three particles will always take place under **multiple steps** because of the near-impossibility of such a perfect collision. Even reactions with three particles are often **multi-step**.
+
+The **reaction mechanism** is the step-by-step sequence of all elementary steps of a reaction. An elementary step that is repeated consecutively should be surrounded with square brackets and a coefficient.
+
+!!! example
+    $$\ce{2\times\big[HOBr + HBr -> Br2 + H2O\big]}$$
+
+!!! example
+    The reaction $\ce{NO2_{(g)} + CO_{(g)} -> NO_{(g)} + CO2_{(g)}}$ has a theoretical reaction mechanism of:
+    $$
+    \begin{align*}
+    \ce{
+    NO2_{(g)} + NO2_{(g)} &-> NO3_{(g)} + NO_{(g)} \\
+    NO3_{(g)} + CO_{(g)} &-> NO2_{(g)} + CO2_{(g)}
+    }
+    \end{align*}
+    $$
+    $\ce{NO3_{(g)}}$ is a reaction intermediate.
+
+Multi-step reactions will have a **rate-determining step**, which is the slowest step and so is responsible for the rate law of the reaction, acting as a bottleneck. If reaction intermediates are present, the **original** reactants or catalysts that form that intermediate are still used in the rate law.
+
+!!! example
+    The reaction $\ce{H2_{(g)} + Q2_{(g)} + 2Z2_{(g)} -> 2HZ_{(g)} + 2QZ_{(g)}}$ has the following reaction mechanism:
+    $$
+    \begin{align*}
+    \ce{
+    H2_{(g)} + Q2_{(g)} &-> 2HQ_{(g)} \\
+    2\times\big[HQ_{(g)} + Z2_{(g)} &-> HZ_{(g)} + QZ_{(g)}\big]\ \text{ (slow)}
+    }
+    \end{align*}
+    $$
+    As normally for this reaction $\ce{r=k[HQ][Z2]}$, because $\ce{HQ}$ is a reaction intermediate, it is instead $\ce{r=k[H2][Q2][Z2]}$ after substituting in the first step, **ignoring product coefficients**.
+
+Often, the step with the highest activation energy is the slowest because of collision theory. Alternatively, the one with the least favourable collision geometry, such as if there are more particles that have to collide, may be the slowest.
+
+If a reactant doesn't appear in the rate-limiting step (including via intermediates), changing its concentration will not affect the rate of reaction and so it will have an individual order of 0 in the final rate law.
+
+A reaction mechanism is only plausible if:
+
+ - each elementary reaction has **three** or less reactant particles,
+ - the rate-determining step is consistent with the rate law provided, and
+ - the elementary steps add up to the overall equation.
+
+### Arrhenius equation
+
+The Arrhenius equation relates the temperature to the rate of a reaction.
+
+Where:
+
+ - $k$ is the rate constant,
+ - $R$ is the ideal gas constant,
+ - $E_a$ is the activation energy for the reaction,
+ - $A$ is the proportionality/Arrhenius constant for the reaction,
+ - and $e$ is Euler's number
+
+$$k=Ae^\frac{-E_a}{RT}$$
+
+Graphing $\ln k$ against $\frac{1}{T}$ forms the linear relation:
+$$\ln k = \frac{-E_a}{R}\frac{1}{T}+\ln A$$
+
+where the slope of the graph is $\frac{-E_a}{R}$ and the y-intercept is $\ln A$.
+
+The number of moles of gas particles that are above the activation energy threshold is expressed in the second term of the equation: $e^\frac{-E_a}{RT}$.
+
+## Equilibrium
+
+!!! definition
+    - A reaction is at **dynamic equilibrium** if both the forward and reverse reaction continue at **equal and constant** rates, and there are no **macroscopic** changes such as temperature, colour, mass, or concentration.
+
+A chemical equation at equilibrium is represented with two single-headed arrows, indicating that a reaction has proceeded to the point that concentrations are constant, and rates are equal and constant.
+$$\ce{A + B <=> C}$$
+
+<img src="/resources/images/equilibrium-rate.png" width=700>(Source: Kognity)</img>
+
+In order for a system to eventually tend to equilibrium, the system must:
+
+ - be closed, with constant concentrations of reactant and product,
+ - maintain a constant temperature, and
+ - maintain a constant pressure if the reactant or product is a gas.
+
+For a given reaction, as long as the reactants and products are stoichiometrically matched, any combination will tend to the same equilibrium.
+
+!!! example
+    The following initital concentrations for the reaction $\ce{C + O2 -> CO2}$ will all tend to the same equilibrium.
+    
+    - 2 mol $\ce{C}$ and 2 mol $\ce{O2}$
+    - 2 mol $\ce{CO2}$
+    - 1 mol $\ce{C}$, 1 mol $\ce{O2}$, and 1 mol $\ce{CO2}$
+
+At equilibrium, the concentrations of the reactants and products must end up constant (but **not necessarily equal**).
+
+!!! example
+    <img src="/resources/images/equilibrium-concentration.jpeg" width=700>(Source: Kognity)</img>
+
+**Phase equilibrium** is when two or more states of exactly one pure substance are in dynamic equilibrium.
+
+!!! warning
+    A solution or an aqueous compound cannot be in phase equilibrium because it is not a pure substance.
+
+!!! example
+    Water constantly evaporates and condenses. Because the rate of evaporation is only dependent on the surface area of the water, the rate of condensation increases until the two are equal and constant at phase equilibrium.
+
+A **solubility equilibrium** requires at least two substances — a solute and a solvent.
+
+### Equilibrium constant
+
+!!! definition
+    - The **position of equilibrium** is the concentration of reactants and products at dynamic equilibrium.
+
+The equilibrium constant $K_c$ or $K_eq$ is related to the concentration of reactants and products in a given system at equilibrium at a given temperature. It is equal to the product of all products divided by the product of all reactants.
+$$
+\ce{aA + bB + cC <=> fF + gG + hH} \\
+\begin{align*}
+K_c &= \ce{\frac{[F]^f [G]^g [H]^h}{[A]^a [B]^b [C]^c}} \\
+&= \frac{\Pi[\text{products}]^p}{\Pi[\text{reactants}]^r}
+\end{align*}
+$$
+
+The units of $K_c$ varies similar to the rate constant so they are often omitted.
+
+!!! warning
+    Only concentrations that change during the course of the reaction should appear in $K_c$, so solids and liquid water should not be included. 
+
+If $K_c$ is greater than 1000, the reaction is **product-favoured**, meaning that there will be a greater concentration of products at equilibrium. If $K_c$ is less than 0.001, the reaction is **reactant-favoured**.
+
+Contrary to the house of cards of lies told to you in lower grades, all reactions are equilibrium reactions, but some have $K_c$s that are so large or small that they effectively occur to completion or don't occur at all.
+
+#### ICE tables
+
+An initial-change-equilibrium (ICE) table is used to work with equilibrium concentrations and **only contains concentrations**.
+
+It consists of:
+
+ - the original concentrations of each compound in the "initial" row,
+ - the change in concentration in the form of a variable of each compound after one "iteration" of the reaction in the "change" row, and
+ - the end equilibrium concentration of each compound in the "equilibrium" row. The "initial" and "change" rows should sum to the "equilibrium" row.
+
+!!! example
+    An ICE table with 1 mole each of $\ce{H2}$ and $\ce{I2}$ in $\pu{2.00 dm3}$ of water that eventually ends up with an equilibrium concentration of $\ce{[H2]}=\pu{0.11 mol/dm3}$ will form the following ICE table.
+    
+    | | $\ce{H2_{(g)}}$ | $\ce{I2_{(g)}}$ | $\ce{2HI_{(g)}}$ |
+    | --- | --- | --- | --- |
+    | Initial | 0.50 | 0.50 | 0 |
+    | Change | $-y$ | $-y$ | $+2y$ |
+    | Equilibrium | 0.11 | 0.50$-y$ | $+2y$ |
+
+When working with values involving $K_c$, if the initial concentration of a chemical is much bigger than $K_c$ ($[A]/K_c > 500$), it is possible to assume that it will not change at all.
+
+This assumption is valid if the impact of the calculated shift is less than 5%.
+
+!!! example
+    If the equilibrium concenration is equal to $0.250-2y$, and the initial concentration is very big, assume that the equilibrium concentration is $0.250$, removing the $-2y$ from the equation.
+    
+    As long as $2y$ is less than 5% of 0.250, the assumption is valid.
+
+!!! info
+    In this course, when working with $K_c$ and ICE tables, only three things should be possible when solving for concentrations: you can get a perfect square, you can use the quadratic equation, or you can use the approximation rule.
+
+### Le Chatelier's principle
+
+Le Chatelier's principle states that: If there is a change in a system at equilibrium, the position of equilibrium will readjust to minimise the effect of the change.
+
+The changes that this principle affects — and therefore affect equilibrium — include changes in temperature, concentration, and pressure. These changes are assumed to occur instantaneously, which may result in sudden theoretical spikes in concentration-time graphs.
+
+The initial rate of the change will start **fast** and then slow down, appearing as a sharp change instead into a curve in a concentration-time/reaction progress graph that **never return to its original value**.
+
+!!! tip
+    Drawing horizontal dotted lines that represent the original position of equilibrium and vertical lines to represent the moment of system change makes it clearer to read.
+
+Increasing the **temperature** of a system causes it to shift in favour of the **endothermic** side, and vice versa. 
+
+Of the three changes, this is the only one that would change $K_c$ as it changes the rate constants, which are temperature-specific ($K_c\propto\frac{r_\text{reverse}}{r_\text{forward}}$). Therefore, as temperature **increases**, $K_c$ also **increases**, and vice versa.
+
+!!! example
+    If heat is added to a solution of KCl, more KCl will dissolve to minimise the change in temperature as it is an endothermic process.
+
+Increasing the **concentration** of a reactant or product will cause the position to shift **away** from the increased side, and vice versa.
+
+??? example
+    If there is an **instantaneous** spike of $\ce{N2}$ to a system at equilibrium, it will be consumed along with $\ce{H2}$ to form $\ce{NH3}$, **but not enough to return to its original value**.
+    
+    <img src="/resources/images/equilibrium-concentration.png" width=500>(Source: Kognity)</img>
+    
+    The same applies if instead $\ce{NH3}$ is reduced.
+    
+    <img src="/resources/images/equilibrium-concentration-2.png" width=500>(Source: Kognity)</img>
+
+Increasing the **pressure** of a gas will cause the position to shift in whatever direction would **decrease** the total moles of gas.
+
+!!! warning
+    Inert (uninvolved in a reaction) gases such as catalysts will not affect the position of equilibrium as it does not affect the **partial pressure** of the gas. In a similar vein, adding water to an aqueous solution will not cause any changes in equilibrium position.
+
+!!! warning
+    If given a system not at equilibrium, if a change is made that would change the prior equilibrium, it should be assumed that the system reaches equilibrium before the change is made, regardless if it is specified.
+
+### Gibbs free energy 2
+
+The value of Gibbs free energy changes as the reaction progresses, similar to enthalpy. At equilibrium, $\Delta G=0$, so a reaction is a result of a system attempting to minimise Gibbs free energy.
+
+**Standard Gibbs free energy** represents the Gibbs free energy of a chemical at standard state (1 mol/L for solutions, 100 kPa partial pressure for gases).
+$$\Delta G^\circ = \sum n\Delta G^\circ_\text{f products} - \sum n\Delta G^\circ_\text{f reactants}$$
+
+A negative $\Delta G^\circ$ indicates that the reaction will shift right to reach equilibrium as $\Delta G^\circ$ always decreases in **magnitude** as the reaction proceeds. It also means that the forward reaction is **spontaneous** while the backwards is not.
+
+### Reaction quotient
+
+The reaction quotient ($Q$) is a tool to compare the current state of a system to its equilibrium state.
+$$Q=\frac{\Pi[\text{products currently}]^p}{\Pi[\text{reactants currently}]^r}$$
+
+At equilibrium, $Q=K_c$ as they are the same equation, so the equilibrium will shift in whatever direction that would bring $Q$ closer to $K_c$
+
+!!! example
+    If $Q > K_c$, there are more products than reactants than at equilibrium, so the reaction will shift to make more **reactants**.
+
+### Dynamic equilibrium
+
+When $\Delta G$ is at a minimum, both sides of the reaction are equally spontaneous. Realistically, $\Delta G$ never reaches zero because entropy. TODO: wtf
+
+<img src="/resources/images/product-favoured-gibbs.png" width=700>(Source: Kognity)</img>
+
+Where $\Delta G$ is the Gibbs free energy at a given point of the reaction, $R$ is the gas constant, $T$ is the current temperature, and $Q$ is the reactant quotient:
+$$\Delta G = \Delta G^\circ + RT\ln Q$$
+
+Therefore, at equilibrium:
+$\Delta G = -RT\ln K_c$
+
+## Acids and bases
+
+!!! definition
+    - An **amphoteric** chemical may act as an acid or base depending on the situation.
+    - An **amphiprotic** chemical can **either accept or donate** $\ce{H+}$ depending on the situation.
+    - A **monoprotic** acid/base is one that can only accept/ionise one $\ce{H+}$ ion.
+    - An **alkali/alkaline** solution is an aqueous solution of a base, which may **not** necessarily be a **basic solution**.
+
+An **acid** and **base** are any two corrosive chemicals that react to form water and a salt. They also dissociate/ionise (depending on theory) in water to form electrolytes that conduct electricity.
+
+Acids:
+
+ - taste sour
+ - have a pH less than 7 in aqueous solutions at 25°C
+ - stain litmus paper **red**
+ - react with active metals to produce $\ce{H2_{(g)}}$ based on the activity series
+ - react with carbonates to form $\ce{CO2 + H2O}$
+
+Bases:
+
+ - taste bitter
+ - have a pH greater than 7 in aqueous solutions at 25°C
+ - feel slippery as they react with fats/oils to form soap
+ - stain litmus paper **blue**
+ - react with ammonium salts to product $\ce{NH3 + H2O}$
+
+### Arrhenius theory
+
+An acid **dissociates** in water to produce $\ce{H+}$ ions (protons).
+
+A base **dissociates** in water to produce $\ce{OH-}$ ions.
+
+### Bronsted-Lowry theory
+
+The Bronsted-Lowry theory focuses on reactions with water and less the acid and base ions themselves, so they **ionise** instead of **dissociate**.
+
+An acid is any compound that can **donate/ionise a proton ($\ce{H+}$) to water** to form a hydronium ion.
+$$\ce{acid + H2O -> acid- + H3O+}$$
+
+!!! info
+    In practice, the acid must contain a hydrogen atom attached by an easy-to-break bond (usually $\ce{H-O}$), but any high electronegativity difference polar bond would work as well.
+
+A base is any compound capable of **accepting/removing a proton ($\ce{H+}$) from an acid**.
+$$\ce{acid + base -> acid- + base+}$$
+
+!!! info
+    The proton usually comes from water. The base must be able to accept an $\ce{H+}$ ion to form a **dative covalent bond**, so they must contain **lone pairs**.
+
+Polyprotic acids ionise their $\ce{H+}$s one by one **sequentially**.
+
+!!! example
+    $\ce{
+    H3PO4 + H2O <=> H2PO4- + H3O+ \\
+    H2PO4- + H2O <=> HPO4^2- + H3O+ \\
+    HPO4^2- + H2O <=> PO4^3- + H3O+
+    }$
+    
+#### Conjugate acids/bases
+
+The result of a base obtaining a proton is a **conjugate acid**.
+
+The result of an acid losing a proton is a **conjugate base**.
+
+!!! example
+    In the reaction
+    $$\ce{NH3 + H2O -> NH4+ + OH-}$$
+    
+    $\ce{NH3}$ is a base that becomes a conjugate acid while $\ce{H2O}$ is an acid that becomes a conjugate base.
+
+### Louis theory
+
+A Lewis **acid** is any species that **accepts** an electron pair to form a dative covalent bond.
+
+A Lewis **base** is any species that **donates** an electron pair to form a dative covalent bond.
+
+### Strong/weak acids/bases
+
+**Strong** acids/bases will **completely** dissociate/ionise in an aqueous solution. This means that the initial concentration of acid will be equal to the end concentration of $\ce{H+ or H3O+}$.
+
+All strong polyprotic acids initially have a one-way reaction then follow with equilibrium reactions.
+
+!!! warning
+    Strength is a property of an acid and has nothing to do with its concentration.
+
+**Weak** acids/bases will only **partially** dissociate/ionise in an aqueous solution, leaving behind most of the initial acid ($\ce{[acid] > [H+]}$ at equilibrium).
+
+!!! warning
+    Measuring pH only returns $\ce{[H+] or [H3O+]}$, so it cannot be used to determine the concentration, identity, or strength of an acid.
+
+All weak polyprotic acid reactions are equilibrium reactions.
+
+!!! example
+    The following is a list of strong and weak acids:
+    
+    | Strong acid | Weak acid | Strong base | Weak base |
+    | --- | --- | --- | --- |
+    | $\ce{HClO4}$ | any $\ce{COOH}$ | $\ce{LiOH}$ | $\ce{NH3}$ |
+    | $\ce{HCl}$ | $\ce{CO2}$ | any $\ce{group\ 1 + OH}$ | $\ce{Al(OH)3}$ |
+    | $\ce{HBr}$ | $\ce{SO2}$ | any $\ce{group\ 2 + (OH)2}$ | |
+    | $\ce{HI}$ | $\ce{HF}$ | | |
+    | $\ce{H2SO4}$ | $\ce{HCN}$ | | |
+    | $\ce{HNO3}$ | $\ce{H3PO4}$ | | |
+
+To experimentally distinguish between a strong or weak acid/base, if their concentrations are equal, total **ion** concentration or $\ce{H3O+}$ concentration can be compared since the stronger acid ionises more.
+
+Practically, this means comparing the rate of reaction with a metal or water or measuring conductivity as they reflect total ion count.
+
+### pH and pOH
+
+This section will assume Bronsted-Lowry theory.
+
+pH represents $\ce{[H3O+]}$ logarithmically on a scale from 0 to 14.
+
+$$
+\ce{pH = -\log\big[H3O+_{(aq)}\big]} \\
+\ce{pOH = -\log\big[OH-_{(aq)}\big]}
+$$
+
+!!! warning
+    The number of sigfigs in pH is equal to the number of digits **after the decimal place**.
+
+A solution is **neutral** (neither acidic nor basic) when $\ce{[H3O+] = [OH-]}$. This happens to be $\ce{pH = 7}$ at SATP. In pure water, this is true as a small number of water molecules react with each other.
+
+In an equilibrium reaction between an acid and a base, $\ce{K_c = \frac{[H3O+][OH-]}{[H2O]}}$, but water has a constant concentration, so the equilibrium of the two ions is represented with the **water ionisation constant** $K_w$ is used.
+$$K_w = \ce{[H3O+][OH-] = 1.00\times10^{-14} @ SATP}$$
+
+As temperature **increases**, $K_w$ increases, therefore changing the pH of neutrality, but this may not necessarily change the acidity of the solution as the ion concentration is still the same.
+
+As pH increases, $\ce{[H3O+]}$ decreases, so $\ce{[OH-]}$ must increase to keep $K_w$ constant and maintain equilibrium.
+$$\ce{pK_w = pH + pOH}$$
+
+At 25°C, $\ce{pK_w = 14.0000}$, so:
+$$\ce{14 = pH + pOH}$$
+
+### Acid/base dissociation
+
+An equilibrium will be reached when a weak acid or base dissociates/ionises in water. The extent that the acid or base has dissociated/ionised can be quantified with **percent dissociation/ionisation**.
+$$\text{% ionisation} = \frac{\text{[acid ionised]}}{\text{[original acid]}}\times 100\%$$
+
+!!! note
+    When performing an approximation assumption in an ICE table, the assumption is also valid if the % ionisation is less than 5%.
+
+The $K_c$ of acid ionisation/dissociation is known as $K_a$, the **acid dissociation constant**.
+$$
+\ce{H2O_{(l)} + HX_{(aq)} <=> H3O+_{(aq)} + X-_{(aq)}}$$
+$$K_a = \ce{\frac{[X-][H3O+]}{[HX]}}$$
+
+The $K_c$ of base ionisation/dissociation is known as $K_b$, the **base dissociation constant**.
+$$\ce{H2O_{(l)} + X_{(aq)} <=> OH-_{(aq)} + HX+_{(aq)}}$$
+$$K_b = \ce{\frac{[HX+][OH-]}{[X]}}$$
+
+!!! example
+    $$\ce{NH3_{(aq)} + H2O_{(l)} <=> NH4+_{(aq)} + OH-_{(aq)}}$$
+    $$K_b = \ce{\frac{[NH4+] [OH-]}{[NH3]}}$$
+
+!!! warning
+    $K_a$ and $K_b$ only apply to acids and bases, respectively. Morphine, a base, does not have a $K_a$, but its conjugate acid does.
+
+At all temperatures:
+$$K_a \times K_b = K_w$$
+$$pK_a + pK_b = pK_w$$
+
+### Acid strength
+
+A **higher** $K_a$ or $K_b$ indicates that the acid or base is **stronger**, increasing percent ionisation. 
+
+**Strong acids/bases** have an effectively infinite $K_a$/$K_b$ in water, so they are all practically equally strong in water (this may not be true in other solvents).
+
+As $K_a$ and $K_b$ are inversely correlated, an **increase** in $K_a$ leads to a **decrease** in $K_b$.
+
+The conjugate acid/base of a **strong** acid/base is effectively infinitely weak such that it does not affect pH at all.
+
+Contrarily, the conjugate of a **weak** acid/base is measurably weak, strong enough to have $K_a$/$K_b$ that affect the pH and act as an acid or base.
+
+As $p$ indicates negative log, $\ce{pK_{\{a, b\}}}$ is **inversely** correlated with $\ce{K_{\{a, b\}}}$ so that none of the variables can be directly compared without conversion.
+
+### Acidity of salt solutions
+
+!!! definition
+    - A **salt** is an ionic compound that dissociates in water.
+
+The pH of a salt solution depends on the combination of the acidity of each of its dissociated ions. Whichever is **stronger** pushes the acidity of a solution in its direction.
+
+An ion originating from a **strong** acid/base is immeasurably weak and **has no effect**.
+
+An ion originating from a **weak** acid/base is measurably weak and **has an effect**.
+
+!!! example
+    For the salt NaCl: $\ce{HCl_{(aq)} + NaOH_{(aq)} -> H2O_{(l)} + NaCl_{(aq)}}$  
+    As both $\ce{HCl}$ and $\ce{NaOH}$ are strong, their conjugate acids/bases are both immeasurably weak, having no effect on the pH of the solution. Therefore, NaCl is a **neutral** salt.
+
+If both dissociated ions have a measurable effect, the acidity depends on whichever is stronger via $K_a$/$K_b$.
+
+### Titration curves
+
+!!! definition
+    - A **titrant** or **standard** is a solution with known properties that goes in the burette.
+    - A **sample** or **analyte** is a solution with potentially unknown properties that goes in the sample flask.
+    - The **equivalence point** of a titration is the point at which the solution is neutral $\ce{[H+] = [OH-]}$.
+
+A **titration curve** is generated in a titration where the pH of the solution is graphed against the volume of titrant added. Depending on the type or strength of the sample and titrant, different graphs can be generated.
+
+Unlike the diagrams below, in a sketch, the following information is needed:
+
+ - the initial pH of the solution (the pH of the sample)
+ - the pH after a lot of titrant is added (assumed to be the pH of the titrant)
+ - the volume of titrant required to neutralise the sample ($c_\ce{H}v_\ce{H}=c_\ce{OH}v_\ce{OH}$)
+ - the relative pH at the equivalence point (the relative pH of the salt solution)
+
+The graph can be split into two halves: the acid half and the base half. In the following diagram, both the acid and base are **strong**, so their lines are identically shaped:
+
+ - the line starts at the initial pH, hugging the line, until,
+ - it sharply curves to the vertical, crossing the equivalence point, and
+ - continues vertically.
+
+The same applies to the base but it instead ends at the final pH.
+
+<img src="/resources/images/s-s-titration.png" width=700>(Source: Kognity)</img>
+
+In scenarios where the **sample** is a **weak** acid/base, instead:
+
+ - the line immediately briefly rapidly rises from the initial pH, then
+ - gradually increases, until
+ - a sudden curve to the vertical (but less sudden than a strong acid/base), and
+ - continues vertically.
+
+<img src="/resources/images/w-s-titration.png" width=700>(Source: Kognity)</img>
+
+In scenarios where the **titrant** is a **weak** acid/base, it will take much more titrant to bring the pH of the sample to the level of the titrant. As such, the "brief rapid rise" is ignored and the line only gradually approaches but **clearly does not reach** the final pH.
+
+<img src="/resources/images/s-w-titration.png" width=700>(Source: Kognity)</img>
+
+In scenarios where the sample is a **polyprotic** acid/base, as its ions dissociate sequentially, it can be treated as multiple consecutive titrations where the first sample is **strong** but any subsequent titrations are **weak**.
+
+Each equivalent point volume after the first is a direct multiple of that first equivalent point volume.
+
+<img src="/resources/images/polyprotic-titration.png" width=700>(Source: Kognity)</img>
+
+### Titration curve analysis
+
+The **aha!** equation, also known as the Henderson-Hasselbach equation, is derived from the equilibrium equation.
+
+$$\ce{pH = pK_a + \log\frac{[A-]}{[HA]}}$$
+
+To graphically determine the $pK_a$ of a sample given a titration curve, the pH at the volume at **half** of the equivalence point can be identified. At that point, $pH = pK_a$.
+
+!!! warning
+    - If a weak **base** is the sample, this will return the $pK_a$ of the conjugate acid. The pH of the base can be determined by $14-pK_a$.
+    - If numbers are not given, drawing a line through the straight bits can give pH and equivalence volume values. However, **none** of these lines should be **parallel** to the axes.
+    - In titrations involving **polyprotic** compounds, as they are effectively multiple titrations, half of the equivalence point is actually half the distance between two equivalence points.
+    - This equation can **also be used to determine the pH of a buffer between a salt/acid and acid/base** as it can be assumed that there is no change to concentrations, but **cannot be used to determine the initial pH between an acid/base and water**.
+
+### pH indicators
+
+A pH indicator is a **weak acid/base** that is at one colour in a certain pH range and another in another pH range. Where $X$ is the indicator, it will form an equilibrium with the hydrogen ions in the solution:
+$$\ce{HX <=> H+ + X-}$$
+
+The indicator is **protonated** on the left and **deprotonated** on the right. The titrant can be viewed as an external stress on this equilibrium: if a base is added to an acid, the equilibrium will shift to the right to free up hydrogen ions, and vice versa.
+
+If the difference in concentration of $\ce{X-}$ and $\ce{HX}$ is **greater than** approximately 10:1, the solution will appear to be the colour of the higher concentration, meaning that pH indicators will change colour at a pH in the range of their $\ce{pK_a}\pm 1$.
+
+In choosing a good pH indicator, it must change colour in the **vertical** section of the titration curve to see the greatest effect, and it must be easily observable.
+
+As the weak curve has less of a vertical section than a strong curve, it is best to pick an indicator that changes **after** the equivalence point, which will require the **relative pH** at the equivalence point.
+
+The observability of an indicator depends on the colour it is changing to (or the **direction** the pH is changing). In general, humans are much better at noticing the **appearance** of **red** and **blue**.
+
+A **universal indicator** is a mixture of different pH indicators to change colours multiple times over the pH range. In this case, the colour wheel can used to determine the colour that will be formed (e.g., blue + blue + yellow = green). The shade of the colour does not matter.
+
+### Buffers
+
+!!! definition
+    - A **buffer solution** is one that can resist pH change when small quantities of a strong acid or base are added.
+    - An **acidic buffer** is one where an acid and extra of its conjugate base as a salt are present in the solution.
+    - A **basic buffer** is one where a base and extra of its conjugate acid as a salt are present in the solution.
+    - A **protonated** compound contains its proton.
+    - A **deprotonated** compound has lost its proton.
+    - The **buffering capacity** of a buffer is the quantity of strong titrant that can be added to the buffer without a significant change in pH.
+
+The **buffer region** is the pH range of a **weak** acid/base before the equivalence point that requires a large volume of titrant for a gradual pH change. In this region, there is sufficient undissociated acid/base to replenish those neutralised via Le Chatelier's principle.
+
+In the equilibrium between a weak acid and its component ions:
+$$\ce{HA <=> H+ + A-}$$
+
+A buffer solution is created when **excess** $\ce{A-}$ is added (the salt of the conjugate base) such that the position of equilibrium is shifted to the left to the point that **none of the original acid has dissociated** such that $\ce{[equilibrium HA] = [added HA]}$ and $\ce{[equilibrium A-] = [added A-]}$. It is used to **maintain** a certain pH in a solution.
+
+When the titrant is added to an **acidic buffer**:
+
+ - if an acid is added, $\ce{[H+]}$ increases, shifting the position to the left. This can be done repeatedly because of the excess $\ce{A-}$ present to react with the protons.
+ - if a base is added, $\ce{[H+]}$ decreases as they react, shifting the position to the right. This can be done repeatedly because of the excess $\ce{HA}$ from the original shift to the left from the salt addition.
+
+!!! example
+    To form the **acetic acid/acetate buffer** $\ce{CH3COOH <=> H+ + CH3COO-}$, if 1 mol/L $\ce{CH3COONa}$ is added to 0.1 mol/L $\ce{CH3COOH}$:
+    
+    The addition of $\ce{CH3COO-}$ will shift the position to the left, protonating it such that there will be 0.1 mol/L $\ce{CH3COOH}$ and 1 mol/L $\ce{CH3COO-}$.
+    
+    - If an acid is added, it will **shift left** and further react to form more $\ce{CH3COOH}$, reducing the change in pH.
+    - If a base is added, it will **shift right** by reacting with hydrogen ions to reduce their concentration, releasing more $\ce{H+ + CH3COO-}$ to replenish the lost hydrogen ions, reducing the change in pH.
+    
+This naturally occurs without a buffer, but a buffer significantly increases the quantity of titrant that can be added before the pH changes rapidly.
+
+The same applies to a **basic buffer** but in opposite directions. The salt of the conjugate acid is used instead.
+$$\ce{B + H2O <=> HB + OH-}$$
+
+!!! example
+    To form the **ammonia/ammonium buffer** $\ce{NH3 + H2O <=> NH4+ + OH-}$, if 1 mol/L $\ce{NH4+}$ is added to 0.1 mol/L $\ce{NH3}$:
+    
+    The addition of $\ce{NH4+}$ will shift the position to the left, deprotonating it such that there will be 0.1 mol/L $\ce{NH3}$ and 1 mol/L $\ce{NH4+}$.
+    
+    - If an acid is added, it will **shift right** by reacting with hydroxide ions to reduce their concentration, releasing more $\ce{NH4+ + OH-}$ to replenish the lost hydroxide ions, reducing the change in pH.
+    - If a base is added, it will **shift left** and further react to form more $\ce{NH3 + H2O}$, reducing the change in pH.
+
+To make an effective buffer, salt of the conjugate base/the conjugate acid is required to initially shift the position left. Adding more salt/acid increases the titrant that can be buffered.
+
+A buffer only acts over a certain pH. In order for it to be effective, the ratio of $\ce{[A-]}$ to $\ce{[HA]}$ must be within 10x or 0.1x, although usually buffers are made with 90% excess salt/acid + 10% acid/base or vice versa. Using the **aha!** equation, this means that the **range of a buffer** is equal to $pK_a\pm 1$, where $pK_a$ is that of the **acid/conjugate acid of the base**.
+

docs/g12/snc4mz.md

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+# HL Chemistry 3
+
+The course code for this page is **SNC4MZ**.
+
+## Organic chemistry
+
+!!! definition
+    - An **organic molecule** is one with at least one carbon atom covalently bonded to another carbon or hydrogen atom (i.e., at least one C-H or C to C bond)
+
+Carbon is unique in organic chemistry as it is the only element with the following properties:
+
+ - It is in the second row of the periodic table, meaning it has less electron shells, thus forming stronger bonds
+ - It can covalently bond to up to 4 other atoms
+ - Because each of its valence electrons is involved in bonding, it can form single through triple bonds
+ - The molecular geometry can be anything from tetrahedral to linear depending on its bonding
+ 
+Carbon is also able to bond to itself in the following ways:
+
+ - long straight chains
+ - long straight chains with branches
+ - rings
+
+<img src="/resources/images/cool-carbon.png" width=700>(Source: Kognity)</img>
+
+### Simple hydrocarbons
+
+!!! definition
+    - A **branched hydrocarbon** is one with at least one "side group" extending from the main hydrocarbon chain.
+    - A **functional group** is a group of atoms responsible for the characteristic properties of a molecule (e.g. C=C)
+    - A **homologous series** is a family of organic compounds with the same functional group but the hydrocarbon chain length changes by 1 $\ce{CH2}$ group.
+
+These only contain carbon and hydrogen.
+
+**Alkanes** are a homologous series that only contain single bonds between carbons, and are named with the number of carbons with the suffix "-ane".
+
+<img src="/resources/images/alkanes.png" width=700>(Source: Kognity)</img>
+
+| Carbon atoms | Prefix |
+| --- | --- |
+| 1 | Meth |
+| 2 | Eth |
+| 3 | Prop |
+| 4 | But |
+| 5 | Pent |
+| 6 | Hex |
+| 7 | Hept |
+| 8 | Oct |
+| 9 | Non |
+| 10 | Dec |
+
+!!! example
+    A molecule with only hydrogen and three carbon atoms all held together with single covalent bonds is called "propane".
+
+**Alkenes** contain **at least** one carbon-carbon double bond and are named with a prefix with the total number of carbon atoms and "-ene".
+
+**Alkynes** contain **at least** one carbon-carbon triple bond and are named with a prefix with the total number of carbon atoms and "-ene".
+
+!!! warning
+    The lack of standardisation prior to IUPAC means that some IUPAC names have common names that are still widely used today.
+    
+    - acetylene: **ethyne**
+    - vinyl: **propene**
+    - ethylene: **ethene**
+
+The general formula for an **acyclic** hydrocarbon with no rings is as follows, where $n$ is the number of carbon atoms, $x$ is the number of double bonds, and $y$ is the number of triple bonds.
+$$\ce{C_nH_{2n+2-2x-4y}}$$
+
+### Representing organic compounds
+
+A simple **molecular formula** is the least useful as it provides no information on structure and bonding.
+$$\ce{C6H14}$$
+
+A **complete structural diagram** shows all atoms by their chemical symbols and uses lines like a Lewis Dot diagram to represent bonds. VSEPR shapes do not need to be taken into account because these are 2D representations of the molecule.
+
+A **condensed structural diagram** is a complete structural diagram but C-H bonds are aggregated into a formula.
+$$\ce{CH3 - CH2 - CH2 - CH2 - CH2 - CH3}$$
+
+A **structural formula** or **expanded molecular formula** is a condensed structural diagram but there are no bond lines. The bond organisation is inferred based on the number of hydrogens on each carbon. Carbon chain side groups (branches) are shown with parentheses.
+$$\ce{CH3CH2CH2CH2CH2CH3}$$
+
+A **condensed structural formula** is a structural formula but any consecutive repeated $\ce{CH2}$ groups are factored with parentheses.
+$$\ce{CH3(CH2)_4CH3}$$
+
+A **line diagram** or **skeletal structural formula** removes carbons and hydrogens and replaces all carbon-carbon bonds with lines, where the number of lines represents the type of bond. Each line is bent where a carbon atom would be, except for triple bonds as those are linear. Non-carbon groups such as $\ce{OH}$ can be shown in collapsed form.
+
+!!! example
+    These are the ways to represent pentane, $\ce{C5H12}$. The structural formula is mislabeled as a condensed structural diagram.
+    <img src="/resources/images/pentane.png" width=700>(Source: Kognity)</img>
+
+### General nomenclature
+
+To name an organic compound:
+
+1. Find the **longest acyclic chain** of carbon atoms as the parent chain.
+2. Assign numbers from 1 to $n$ for each carbon atom in the parent chain.
+    - The numbers should be arranged in a way that the highest priority functional group in the chain is assigned the lowest number possible.
+    - Apply the **first branch rule** only if there is a tie: If there are side chains, the parent chain should be numbered such that the location of any side chains have the lowest number possible.
+        - If there is a tie, the location with the most branches wins.
+        - If there is a tie, the rest of the chain is compared in sequence applying the first branch rule.
+        - If there is a tie, the first location with the side chain group name that is alphabetically greater wins.
+        - If there is a tie, it doesn't matter which side is picked as the whole thing is symmetrical.
+3. Name the main chain based on the name of the functional group and location number for the functional group in the format "number-name".
+4. Name the side groups.
+    - If the group is not carbon, name it by its identity.
+    - Otherwise, name the hydrocarbon based on the number of carbons in the side group with the ending "yl".
+    - If there is more than one identical side group in the **whole chain**, combine their numbers and names with a Greek prefix.
+    - Assign a number representing the carbon atom of the parent chain that the side group is attached to in the form "numbers-name".
+5. Arrange the name with each side group with their numbers in alphabetical order, discounting any prefixes due to duplicates, followed by the parent chain.
+6. Join everything together:
+    - Drop the ending vowel from the prefix if there is a double vowel unless it is "i".
+    - Separate numbers from words with dashes.
+    - Separate numbers from numbers with commas.
+    - Do not separate words from words.
+
+!!! tip
+    In hydrocarbons:
+    
+    - Atoms with double or triple bonds share equal priority as the highest functional group.
+    - The main chain will be named as an alkane if there are only single bonds.
+    - If there is exactly one double or triple bond, it will be named as an alkene or alkyne with its position inserted between the prefix and ending.
+        - e.g., "pentane", "pent-2-ene"
+    - If there are multiple double or triple bonds, their numbers are also included, but an "a" is appended to the prefix and a Greek prefix added to the suffix.
+        - e.g., "penta-1,3-diene", "hexa-1,3,5-triyne"
+    - If there are both double and triple bonds, the "-ene" becomes "-en" and is always before "-yne".
+        - e.g., "pent-4-en-2-yne"
+
+!!! example
+    tf
+
+Other **side chains** with equal priority as double or triple bonds *in side chains* include:
+
+ - halogens, which have their "-ine" suffix replaced with "o" (e.g., "chloro")
+ - $\ce{NO2}$: "nitro-"
+ - benzene (as a side chain): "phenyl"
+
+If there is no other option and there is a **branched side chain**, name it based on the total number of carbon atoms in the side chain.
+
+!!! example
+    tf
+
+### Cyclic aliphatic hydrocarbons
+
+These contain rings that **are not** benzene rings.
+
+$$\ce{C_nH_{2n-2x}}$$
+
+!!! warning
+    Cyclic hydrocarbons **do not** contain any triple bonds as it would force the carbon ring to widen too much.
+
+Cyclic aliphatic hydrocarbons are named the same way as acyclic hydrocarbons except they have a "**cyclo-**" at the start of the name of their parent chain.
+
+!!! example
+    cyclohexa-1,3-diene
+
+The initial double bond should be numbered such that the lowest number is assigned to both sides of the bond (numbers 1 and 2 should be to either side of the double bond). If there is more than one double bond, the ring should be numbered such that the lowest number is assigned to both.
+
+The **first branch rule** still applies. (See [HL Chemistry 3#General nomenclature](/snc4mz/#general-nomenclature).)
+
+!!! example
+    tf
+
+!!! warning
+    Rings can be side chains, and are named accordingly (e.g., "cyclopropyl"). The "cyclo-" prefix is counted when sorting names alphabetically as it describes the group.
+
+### Cyclic aromatic hydrocarbons
+
+These contain benzene rings, which do not actually have single/double bonds as they actually have delocalised pi bonds.
+
+<img src="/resources/images/benzene.png" width=700>(Source: Kognity)</img>
+
+As benzene rings do not have double bonds, they are named according to the **first branch rule**.
+
+### Isomers
+
+**Structural isomers** are two chemicals that have the same chemical formulas but have different structural formulas, resulting in different chemical properties.
+
+**Hydrocarbon chain isomers** are two chemicals with the same chemical formulas but have different carbon/hydrogen arrangements.
+
+!!! example
+    The following are two hydrocarbon chain isomers (and, by extension, structural isomers) of $\ce{C5H12}$.
+    <img src="/resources/images/structural-isomer-g5h12.png" width=700>(Source: Kognity)</img>
+
+**Positional isomers** are two chemicals with the same chemical formulas **and functional groups** but have different structural formulas.
+
+!!! example
+    The following are positional isomers (and, by extension, structural isomers) of $\ce{C4H8}$.
+    <img src="/resources/images/positional-isomers.png" width=700>(Source: Kognity)</img>
+
+**Functional group isomers** are chemicals with the same chemical formulas but **different functional groups**.
+
+!!! example
+    The following are functional group isomers (and, by extension, structural isomers) of $\ce{C3H6O2}$.
+    <img src="/resources/images/functional-group-isomers.png" width=700>(Source: Kognity)</img>
+
+**Geometric** or **cis/trans isomers** are two chemicals have the same chemical formulas and atom arrangements but are positioned differently, thus having ambiguous names.
+
+In order for this to occur, there must be two different atoms or groups of atoms bonded to each carbon atom in the double bond.
+
+ - A **cis** hydrocarbon isomer will have its main chain enter and exit the double bond on the **same side**.
+ - A **trans** hydrocarbon isomer will have its main chain enter and exit the double bond on **opposite sides**.
+
+Unlike the examples below, these should be named with "cis" or "trans" at the beginning as a **separate word without a hyphen**.
+
+!!! example
+    The following are two geometric isomers of but-2-ene:
+    <img src="/resources/images/cis-trans-but-2-ene.png" width=700>(Source: Kognity)</img>
+
+ - In acyclic compounds, this is because the double bond prevents simply rotating one side but not the other as it would force breaking the pi bond.
+ - In cyclic compounds, this is because the ring's other side is similar to a double bond, preventing rotation around the axis.
+ 
+!!! example
+    The following are cis-trans isomers of dichlorocyclobutane (notice the chlorine):
+    <img src="/resources/images/cis-trans-ring.png" width=700>(Source: Kognity)</img>
+
+Isomers may have different physical properties in:
+
+ - **polarity**: a cis isomer may cause a molecule to be polar as opposed to its trans variant
+ - **packing efficiency**: a non-branching hydrocarbon chain will pack better than a branching one, and a continuously trans chain will pack better than a cis one
+
+These change the strength and type of intermolecular forces involved so affect their melting/boiling points.
+
+Isomers may also have different chemical properties as cis isomers are more likely to bump into themselves to make some reactions more viable
+
+### Benzene reactions
+
+!!! definition
+    - An **electrophile** is any species that is or would be electron deficient (+) in the presence of a pi bond.
+    
+In reactions involving a benzene ring, the ring itself is **stable** and will not break apart because of the strength of delocalised pi bonds.
+
+Therefore, only the hydrogens can be swapped out via **electrophilic substitution**, where an hydrogen atom is substituted with an electrophile. The concentration of electrons in the delocalised pi area attracts electrophiles to initiate the bond.
+
+In the mechanism diagram below, $\ce{E+}$ represents the electrophile. Curly arrows are used to show the movement of electrons from the **delocalised area to the electrophile** and **hydrogen atom to the delocalised area**.
+
+<img src="/resources/images/benzene-substitution-mechanism.png" width=900>(Source: Kognity)</img>
+
+The **first step** (the change from the first to the second diagram) is the **slow step** due to the highest activation energy due to the requirement to break a bond.
+
+<img src="/resources/images/benzene-substitution-mechanism-graph.png" width=900>(Source: Kognity)</img>
+
+#### Benzene nitration
+
+!!! definition
+    - A **nitrating mixture** is a mixture of concentrated sulfuric and nitric acids.
+
+In a **nitrating mixture**, benzene will react with positive nitronium ions at **~50°C** to form nitrobenzene, outlined in the reaction mechanism diagrams below.
+
+$$\ce{C6H6 + HNO3_{(aq)} ->[conc H2SO4][50^\circ C] C6H5NO2 + H2O_{(l)}}$$
+
+<img src="/resources/images/benzene-nitration-mechanism.png" width=900>(Source: Random Quora Person)</img>
+
+The first step is to **form the nitronium ion** through a Bronsted-Lowry acid-base reaction between the acids.
+
+$$\ce{HNO3_{(aq)} + H2SO4_{(aq)} <=> H2NO3+_{(aq)} + HSO4-_{(aq)}}$$
+
+The lone pair on the oxygen of the nitric acid attracts a hydrogen atom, which becomes an $\ce{H+}$ ion as sulfuric acid's oxygen takes its electrons. The hydrogen ion bonds to the nitric acid.
+
+$$\ce{H2NO3+_{(aq)} <=> H2O_{(l)} + NO2+_{(aq)}}$$
+
+The oxygen-hydrogen group is conveniently able to form water by taking both electrons it was sharing with the nitrogen. The other single-bonded oxygen compensates with a dative covalent bond with the nitrogen to form the nitronium ion.
+
+The second step is to **react with benzene** through electrophilic substitution, with electrons moving back from the dative oxygen-nitrogen bond back to the oxygen.
+
+### Alkane reactions
+
+!!! definition
+    - **Halogenation** is the introduction of a halogen into a compound.
+
+#### Substitution halogenation
+
+Because a sigma bond must be broken, alkanes are not very reactive. In the presence of light, alkanes will react with halogens in their standard state through halogenation, replacing one of their hydrogens. **Fluorine** is an exception that does not require light because it is highly reactive.
+
+If the halogen is in excess and the reaction continues, more of the halogen (**not the hydrogen-halogen product**) will react with the alkane until all hydrogens have been substituted.
+
+!!! example
+    $$\ce{CH3CH3 + Cl2_{(g)} ->[light] CH3CH2Cl + HCl_{(g)}}$$
+    
+    If $\ce{Cl2}$ is in excess:
+    $$
+    \ce{
+    CH3CH2Cl + Cl2_{(g)} ->[light] CH3CHCl2 + HCl_{(g)} \\
+    ... \\
+    CCl3CHCl + Cl2_{(g)} ->[light] CCl3CCl3 + HCl_{(g)}
+    }
+    $$
+
+The order that hydrogens are substituted in is **random**. If there is more than one possibility, all of them are written as products, ignoring balancing.
+
+!!! example
+    Propane reacts with chlorine gas to form either 1-chloropropane or 2-chloropropane.
+    $$\ce{CH3CH2CH3 + Cl2 ->[hf] CH3CH2CH2Cl + CH3CHClCH3 + HCl}$$
+
+!!! example
+    1-bromoethane reacts with chlorine gas to form either 1,1-dibromoethane (40% chance) or 1,2-dibromoethane (60% chance) because each hydrogen is equally likely to be substituted, and there are 2 and 3 that would form them, respectively.
+    $$\ce{CH2ClCH3 + Cl2 ->[hf] CHCl2CH3 + CH2ClCH2Cl + HCl}$$
+
+#### Free radical substitution
+
+!!! definition
+    - A **free radical** is a species with a lone unpaired electron.
+    - **Homolytic fission** is the dissociation of a chemical bond in a neutral molecule where each product takes one electron, generating two free radicals.
+    - **Heterolytic fission** is the dissociation of a chemical bond in a neutral molecule where one product takes both electrons.
+
+The free radicals are first produced with the help of light energy.
+
+$$\ce{Br2 ->[hf] Br. + Br.}$$
+
+They are then spread to organic compounds and reformed.
+
+$$
+\ce{
+Br. + CH4 -> .CH3 + HBr \\
+Br2 + .CH3 -> CH3Br + Br.
+}
+$$
+
+This cycle only ends when all radicals are used up, through reactions that end up with a net loss in radicals, such as:
+
+ - $\ce{Br. + Br. -> Br2}$ (unlikely, contributes a little)
+ - $\ce{.CH3 + Br. -> CH3Br}$ (likely)
+ - $\ce{.CH3 + .CH3 -> CH3CH3}$ (likely)
+
+!!! warning
+    The free radical is on the carbon atom, not the hydrogen atoms, so the marker goes at the beginning.
+
+### Alkene/yne addition reactions
+
+!!! definition
+    - A **carbocation** is a compound with a $\ce{C+}$ atom.
+    - The **primary** (1°), **secondary** (2°), and **tertiary** (3°) carbocations are carbocations bonded to one, two, and three other carbon atoms, respectively.
+
+The presence of double/triple bonds make alkenes and alkynes more reactive and also allow the **addition** of species as pi bonds are easier to break. Addition always takes precedence over substitution when possible.
+
+These **spontaneous** reactions break the double/triple bond down a level and slot themselves in (i.e., alkynes form alkenes, alkenes form alkanes).
+
+$$
+\ce{alkene + Br2 -> alkaneBr2} \\
+\ce{alkyne + Br2 -> alkeneBr2}
+$$
+
+<img src="/resources/images/alkene-addition.png" width=900>(Source: Kognity)</img>
+
+1. If the non-alkene/yne reactant does not have a dipole moment, the electrons concentrated in the double/triple bond of the alkene/yne induce a dipole by repelling the electrons closest to it.
+2. The positive dipole (such as H in HBr) is attracted to the double bond, and **two electrons** in the bond are used to form a **dative** bond with the positive dipole.
+3. No longer needing its old bond, the previously positive dipole loses **both electrons** in its old bond to the negative dipole.
+4. The now positive carbon atom attracts the now negative ion.
+5. The negative ion forms a **dative** bond with the positive carbon atom.
+
+!!! warning
+    - If an **alkene is formed**, the same randomness of where the atoms attach applies, so it is possible that a cis/trans isomer is formed.
+    - If an **asymmetrical alkane** is formed, the same randomness of where the atoms attach applies after applying Markovnikov's rule, so it is possible that positional isomers are formed.
+
+**Markovnikov's rule** states that in Soviet Russia, the rich get richer. Hydrogens preferentially bond to the carbon with the **most hydrogens** if there is one — otherwise it randomly chooses one available.
+
+This is because carbocations with that are *more highly substituted* (are bonded to more carbon atoms) are more stable, so they last longer and are more likely to form a bond with the negative dipole.
+
+The preferred product is the **major product** while the other is the **minor product**. Some minor product will still be produced if the negative dipole is speedy enough, although it will be vastly outnumbered by the major product.
+
+#### Halogenation
+
+Unlike alkane substitution, addition halogenation is spontaneous.
+
+$$\ce{alkene + Br2 -> alkaneBr2}$$
+
+!!! example
+    This process is used to test for alkenes/alkynes in a solution. As bromine water is red-brown, if alkenes/alkynes are present, the water will be **decolourised** from red-brown to become more colourless.
+
+!!! example
+    <img src="/resources/images/halogenation.jpeg" width=700>(Source: Kognity)</img>
+
+#### Hydrogenation
+
+The addition of hydrogen follows the same principle as that of halogenation.
+
+$$\ce{alkene + H2 ->[\text{heat, high pressure, Ni/Pt/Pd}] alkane}$$
+
+!!! example
+     <img src="/resources/images/hydrogenation.png" width=700>(Source: Kognity)</img>
+
+#### Hydrohalogenation
+
+The addition of both a hydrogen and halogen follows similar principles.
+
+$$\ce{alkene + HBr -> alkaneBr}$$
+
+#### Hydration
+
+Hydration is the addition of an $\ce{H-OH}$ group (colloquially known as water) onto an alkene/yne within 6 mol/L $\ce{H+}$ to produce an alcohol.
+
+$$\ce{alkene + H2O ->[6 mol/L H+] alkaneOH}$$
+
+!!! example
+    <img src="/resources/images/hydration.jpeg" width=700>(Source: Kognity)</img>
+
+### Nucleophilic substitution
+
+!!! definition
+    - A **nucleophile** is a species with a lone pair or a negative charge.
+
+Nucleophilic substitution replaces a group of atoms attached to a C with a nucleophile. Both processes involve the **leaving group** taking both electrons, becoming negative in the process, and forming a carbocation as the other product, which attracts and bonds with the nucleophile.
+
+Effectively all reactions here involve the formation or stealing of dative covalent bonds.
+
+Where $\ce{X}$ is a halogen:
+$$\ce{R-X_{(l)} + OH-_{(aq)} -> R-OH_{(aq)} + X-_{(aq)}}$$
+
+If substituting with hydroxide, it must be **warm** and **aqueous** (dilute).
+
+Generally:
+
+| Carbocation type | Substitution type |
+| --- | --- |
+| Primary | S<sub>N</sub>2 |
+| Secondary | Both/either |
+| Tertiary | S<sub>N</sub>1 |
+
+#### S<sub>N</sub>1
+
+This **two-step** reaction involves the heterolytic fission of the C-X bond to form a carbocation + halide ion (slow), followed by the nucleophile's lone pairs/negative charge attracting it to the carbocation.
+
+The "1" refers to the order of the rate-limiting step being a **unimolecular** collision.
+
+<img src="/resources/images/sn1-1.png" width=700 />
+<img src="/resources/images/sn1-2.png" width=700>(Source: Kognity)</img>
+
+!!! warning
+    Be sure to draw VSEPR, unlike in the diagrams above.
+
+#### S<sub>N</sub>2
+
+This **single-step** reaction has the nucleophile forming a bond with the central atom **opposite the leaving group** in a "back-side attack". The oncoming nucleophile repels the other groups, causing them to move away, effectively **reflecting** ("inverting") the remaining groups across the vertical axis.
+
+The "2" refers to the order of the rate-limiting step being a **bimolecular** collision.
+
+<img src="/resources/images/sn2-substitution.png" width=900>(Source: Kognity)</img>
+
+!!! warning
+    Dashes must be drawn for the transition state for bonds breaking/forming. In this case, drawing the front/back lines for the bottom two atoms may be ignored in favour of regular lines instead to avoid the ambiguity of forming bonds.
+
+#### Factors affecting substitution type
+
+**Steric hindrance** is the effect of other parts of a molecule getting in the way to the central atom, preventing a reaction. If there is not enough space for a backside attack, S<sub>N</sub>2 cannot happen. Therefore, this makes 3° S<sub>N</sub>2 substitution not viable.
+
+**Steric stress reduction** is the resistance of groups against being forced together. In a 3° carbocation, pushing the groups together for a backside attack increases steric stress. This encourages S<sub>N</sub>1 substitution **only for 3°** to maintain a tetrahedral geometry.
+
+The **positive inductive effect** is the effect that causes more highly substituted carbons to be more stable. Electrons on neighbouring carbon atoms can move closer to the carbon ion, creating an electron-donating effect that slightly balances its charge, increasing its stability and thus window of opportunity for a **S<sub>N</sub>1** substitution.
+
+### Alcohols
+
+An **alcohol** is an organic compound with a $\ce{-OH}$ (hydroxyl) functional group.
+
+It has a **higher priority** than double and triple bonds, and alcohol names are suffixed with **-ol**.
+
+!!! warning
+    The -ol suffix is a standard suffix following the same numbering rules as -en and -yne. As functional groups are ordered from lowest to highest priority in their name, similar to how a -yne can have an -en, an -ol can also have an -en and **-yn** before it.
+    
+    - Therefore, $\ce{CH3OH}$ is methanol, *not* methol.
+
+!!! example
+    Some alcohols and their common names:
+    
+    - **Glycerol**: propan-1,2,3-triol
+    - **Ethyl alcohol** or drinking alcohol: ethanol
+    - **Isopropanol** or rubbing alcohol: propan-2-ol
+
+The **type** of an alcohol (primary/secondary/tertiary) is that of the would-be carbocation it is attached to.
+
+#### Alcohol combustion
+
+Alcohols are combustible, and can undergo complete and incomplete combustion.
+
+$$
+\ce{alcohol + O2 -> CO2 + H2O (complete) \\
+alcohol + O2 -> CO2 + H2O + CO + C (incomplete)}
+$$
+
+#### Alcohol elimination
+
+Under significantly more acidic conditions than hydration, the opposite process can be used to revert an alcohol into its base components.
+
+$$\ce{alcohol ->[12 mol/L H2SO4] H2O + alkene}$$
+
+!!! warning
+    When choosing a new double bond to form in the alkene, it must bond to the carbon the OH group was attached to. In elimination, **Markovnikov's rule does not apply**.
+
+### Aldehydes
+
+!!! definition
+    - A **carbonyl** is $\ce{C=O}$.
+    - A **hydroxyl** is $\ce{-OH}$. In a side group, it is named **hydroxy**.
+
+In the presence of an oxidising agent that is **limited** and acid, **primary** alcohols will oxidise to form aldehydes, where a hydroxyl group becomes a carbonyl group and the hydrogen migrates to the carbon.
+
+ - $\ce{K2Cr2O7}$
+ - $\ce{Cr2O7^2-}$
+ - $\ce{KMnO4}$
+ - $\ce{MnO4-}$
+
+An aldehyde is named like an alcohol but has a higher naming priority, with a suffix of **-al**. As aldehydes must be at the end of a chain, numbering their position is not required.
+
+!!! example
+    - butanal ($\ce{CH3CH2CH2COH}$)
+    - The common name of **methanal** is **formaldehyde**.
+
+<img src="/resources/images/alcohol-aldehyde.png" width=900>(Source: Kognity)</img>
+
+Aldehydes will continue to react to ketones if the oxidising agent is not limited. To prevent this, the aldehyde is separated and removed from the mixture through distillation.
+
+<img src="/resources/images/aldehyde-distillation.png" width=900>(Source: Kognity)</img>
+
+The mixture is heated to a temperature greater than the aldehyde's boiling point but less than the alcohol's, such that the gaseous aldehyde enters the condenser and is cooled by the water jacket.
+
+An aldehyde can also be reduced in a process similar to **hydrogenation** to reverse the reaction.
+
+$$\ce{aldehyde + H2 ->[\text{high temp, high pressure, Pt/Pd/Ni}] alcohol}$$
+
+### Ketones
+
+In the presence of an oxidising agent and acid, **secondary** alcohols will oxidise to form ketones, where the hydrogen plops off completely.
+
+<img src="/resources/images/alcohol-ketone.png" width=900>(Source: Kognity)</img>
+
+Because there is no possible reaction afterward (no more hydrogens), distillation is not required.
+
+Ketones have equal priority to aldehydes and are named the same but with a suffix of **-one**. A position number *is* required because ketones can be located anywhere on the chain.
+
+!!! example
+    - 3-ethyl-4,4-difluoro-5-hydroxylhexan-2-one
+    - 1,1-dibromo-4-cyclopropylhex-5-en-2-one
+
+### Carboxylic acids
+
+Aldehydes will react again if there is excess oxidising agent to form a carboxylic acid.
+
+<img src="/resources/images/alcohol-acid.png" width=900>(Source: Kognity)</img>
+
+Instead of distillation, **reflux** is used to keep the aldehyde in the mixture. The vaporised aldehyde condenses and returns to the mixture.
+
+<img src="/resources/images/alcohol-reflux.png" width=900>(Source: Kognity)</img>
+
+Carboxylic acids have higher priority than aldehydes/ketones and are named the same but with a suffix of **-oic acid**. Similar to aldehydes, because the $\ce{COOH}$ can only exist on the end of a chain, position numbers are omitted.
+
+!!! example
+    - **Benzoic acid**: $\ce{benzene-COOH}$
+    - 3,3-difluoropent-4-enoic acid
+    - 3-ethylhexanedioic acid
+    - The common name of **ethanoic acid** is **acetic acid**.
+    - The common name of **ethanedioic acid** is **oxalic acid**.
+    - The common name of **methanoic acid** is **formic acid**.
+    - Look up citric acid because I'm not writing that down.
+
+#### Carboxylic acid salts
+
+If the ionising hydrogen is removed ($\ce{COOH -> COO-}$), a carboxylic acid can form a salt by reacting with a metal to form an **ionic compound**. Salts are named as an ionic compound would be, with the acid component resuffixed to **-oate**.
+
+$$\ce{R-COOH + NaOH -> R-COONa + H2O}$$
+
+!!! example
+    - sodium ethanoate
+    - lithium benzoate
+
+#### Identifying alcohols
+
+The **Lucas test** is used to in part determine the type of alcohol (primary/secondary/tertiary) through the **nucleophilic substitution** of OH with Cl. To perform this substitution, **anhydrous** zinc chloride and **concentrated** HCl must be present.
+
+$$\ce{R-OH + HCl ->[ZnCl2] R-Cl + H2O}$$
+
+This test is only valid on **small** alcohols because (<6 carbons) as longer ones are insoluble.
+
+The insoluble halogenoalkane becomes visible, making the solution **cloudy**. Because the reaction is an S<sub>N</sub>1 reaction:
+
+ - Primary alcohols will **not** react
+ - Secondary alcohols react slowly
+ - Tertiary alcohols react rapidly
+
+Alternatively, **oxidising** alcohols to aldehydes/ketones through S<sub>N</sub>2 by reducing $\ce{Cr2O7^2-}$ (orange) to $\ce{Cr^3+}$ (green) will identify the alcohol.
+
+ - Primary alcohols will react quickly
+ - Secondary alcohols will react slowly
+ - Tertiary alcohols will **not** react
+
+### Ethers
+
+!!! definition
+    - A **condensation reaction** or **dehydration synthesis** involves two small molecules reacting to form water and another molecule.
+
+Ethers are formed by reacting two alcohols through dehydration synthesis in sulfuric acid.
+
+$$\ce{R-OH + HO-R ->[H2SO4] R-O-R + H2O}$$
+
+To name ethers, the shorter alkyl group is named as a side chain while the longer is as the main chain, separated by "oxy".
+$$\ce{short + oxy + long}$$
+
+Usually, if the "side chain" is at position 1, the position number is omitted.
+
+!!! example
+    - pentoxypentane (pentan-1-ol + pentan-1-ol)
+    - 2-ethoxybutane (ethan-2-ol + butan-1-ol)
+    - 2-chloro-3-methoxypentane (chloro is at position 2, methoxy is at position 3 on the pentane)
+    - The common name of **ethoxyethane** is **diethyl ether**.
+
+### Esters
+
+When an alcohol and carboxylic acid react in sulfuric acid **and heat**, the only the $\ce{O}$ from the alcohol remains in the ester while that in the acid forms a water. The formed $\ce{COO}$ is known as the **ester linkage**.
+
+<img src="/resources/images/ester-formation.png" width=900>(Source: Kognity)</img>
+
+Esters are named with the alcohol as the side group and the acid as its salt variant with a space in between. If the side chain looks like an alkane, its position number and -ane suffix can be dropped.
+$$\text{alcohol-yl acid-oate}$$
+
+!!! warning
+    The carbon in the ester linkage is included as a carbon of the main chain of the ester.
+
+!!! example
+    - Propyl pentanoate or propan-1-yl pentanoate is formed from propan-1-ol and pentanoic acid.
+    - Propyl 2-chloroethanoate
+    - Hexan-3-yl propanoate
+
+Esters hydrolyse to their original components if catalysed by an acid or base.
+$$\ce{ester + H2O ->[H2SO4] alcohol + carboxylic acid}$$
+$$\ce{ester + H2O ->[NaOH] alcohol + RCOONa ->[react with acid] alcohol + carboxylic acid}$$
+
+### Amines
+
+Amines are $\ce{NR3}$ derived from ammonia ($\ce{NH3}$), where R is either H or a carbon group. Similar to alcohols, they can be primary/secondary/tertiary depending on the number of carbon groups attached. The **main chain** is the longest carbon chain.
+
+Amines have a priority between double/triple bonds and alcohols, and are named like alcohols but with a suffix of **-amine**.
+
+If there are any side groups attached to the nitrogen, they are named as if they were side groups on the main chain with a **number of $N$**.
+
+!!! example
+    <img src="/resources/images/amine-name-simple.png" width=700 />
+    <img src="/resources/images/amine-name-mid.png" width=700 />
+    <img src="/resources/images/amine-name-hard.png" width=700>(Source: Kognity)</img>
+
+#### Amine synthesis
+
+Amines can be formed through **halogenoalkane substitution**, where ammonia or another amine is alkylated in an S<sub>N</sub>2 reaction.
+$$\ce{NH3 + CH3Cl -> CH3NH4Cl ->[OH-] CH3NH2}$$
+
+!!! example
+    $\ce{CH3NH2 + CH3Cl -> CH3NH2CH3Cl ->[OH-] CH3NH2CH3}$
+
+### Amides
+
+Amides are formed from a reaction between an amine and a carboxylic acid through dehydration synthesis, similar to the formation of an ester. The $\ce{N-C=O}$ link is known as the **amide link**.
+
+$$\ce{R-COOH + N-R -> R-CON-R}$$
+
+Amides carry the suffix **-amide** and are otherwise named equivalently to esters, but *without* spaces.
+
+!!! example
+    <img src="/resources/images/amide-names.png" width=700>(Source: Kognity)</img>
+
+### Nitriles
+
+Nitriles consist of a cyanide(s) attached at the end of a carbon chain.
+
+$$\ce{R-C#N}$$
+
+As they can only be placed at the end of a carbon chain, a positional number is not used. These have the highest priority of all organic compounds and use the suffix **-nitrile** and the prefix **cyano-**.
+
+!!! example
+    - methanenitrile
+    - methanedinitrile
+
+Nitriles are synthesised through the nucleophilic substitution of halogenoalkanes, **extending their carbon chain**.
+$$\ce{R-X + C#N- -> R-C#N + X-}$$
+
+### Reduction reactions
+
+**Hydride reagents** include $\ce{LiAlH4}$ and $\ce{NaBH4}$, the former of which requires ether because it reacts violently with water. Always use $\ce{LiAlH4}$ unless specified otherwise.
+
+**Aldehydes** can be reduced to **primary alcohols**.
+
+$$\ce{aldehyde ->[LiAlH4, ether, then acid] 1^\circ alcohol}$$
+
+**Amides** can be reduced to their **amines**, reacting twice such that the O pops off. The name is a simple `amide.replace("amide", "amine")`.
+
+$$\ce{amide ->[LiAlH4, ether, then acid] amine}$$
+
+!!! warning
+    $\ce{LiAlH4}$ is required for this reaction.
+
+**Carboxylic acids** can be reduced to **primary alcohols** with the $\ce{C=O}$ plopping off.
+
+$$\ce{carboxylic acid ->[LiAlH4, ether, then acid] 1^\circ alcohol}$$
+
+**Esters** can be reduced to **two primary alcohols** with each alcohol keeping an O and gaining an H to make OH.
+
+$$\ce{ester ->[LiAlH4, ether, then acid] 1^\circ alcohol + 1^\circ alcohol}$$
+
+**Nitriles** can be double reduced to **amines**.
+
+$$\ce{nitrile ->[LiAlH4, ether, then acid] amine}$$
+
+### Retro-synthesis
+
+Retro-synthesis is basically a language of math but for chem, with products on the left and reactants on the right. The bottom right contains initial reactant(s) and the top left contains the product(s).
+
+"A is made from B which is made from C":
+
+$$\ce{
+A => B react with alcohol using H2SO4 in reflux \\
+B => C
+}$$
+
+
+!!! example
+    $$\ce{
+    ethanoic acid => ethanol (react w/K2Cr2O7 in H+) \\
+    ethanol => chloroethane (react w/warm dilute hydroxide)
+    }$$
+
+### Simple polymers
+
+!!! definition
+    - **Polymers** are large molecules made from many monomers in long chains.
+    - **Plastics** are polymers formed through addition.
+    - A **homopolymer** has identical monomers.
+    - A **heteropolymer** has multiple distinct monomers.
+    - A **monomer** is the repeating segment in a polymer.
+
+Polymer properties change based on the type of linkages, the presence of side chains, and the extent of crosslinking between other chains.
+
+The **addition formation** of an **addition polymer** opens up pi bonds which are used to bond to other monomers. Monomers are continuously added until the process ends with hydrogen atoms capping the ends.
+
+<img src="/resources/images/addition-polymer.png" width=700>(Source: Kognity)</img>
+
+Only the two carbons directly involved in the double bond go in the main chain of the polymer, with all others expressed as side groups.
+
+<img src="/resources/images/addition-polymer-notation.png" width=900>(Source: Kognity)</img>
+
+**Polymer notation** is the formula/condensed formula/structural diagram of the **repeating unit only** with crossed out brackets and the number of repetitions at the bottom right (or $n$ if unknown). Side groups should be clearly expressed as side groups. Polymers are named with the prefix **poly-** on the repeating unit.
+
+!!! example
+    $$\ce{-(-CH2-CH2-) -_3}$$
+
+#### Crosslinking
+
+!!! definition
+    - **Crosslinking** is the bond between side chains of separate polymers, connecting them.
+
+The crosslinking between polymers depends on the side chains. If there are multiple double bonds in monomers, those can be used in different chains which can attach them together.
+
+!!! example
+    divinylbenzene
+
+!!! example
+    If an OH side group meets another OH side group, they may react to form $\ce{O=O}$ and connect the two polymers.
+
+### Polyesters and polyamides
+
+!!! definition
+    - **Condensation polymers** are polymers formed via dehydration synthesis and produce water.
+
+A **polyester** has monomers connected via an ester linkage on both ends. **Unlike addition polymers**, any carbons between the functional groups are included in the parent polymer chain.
+
+<img src="/resources/images/polyester-formation.png" width=700>(Source: Kognity)</img>
+
+The repeating unit should be **copy-pastable** — it should not end with oxygen on both ends. The link is broken where it would normally break — between the C-O of the ester linkage, such that the O goes to the side of the alcohol.
+
+<img src="/resources/images/polyester-notation.png" width=700>(Source: Kognity)</img>
+
+A **polyamide** has monomers connected via an amide linkage on both ends.
+
+<img src="/resources/images/polyamide-formation.png" width=700>(Source: Kognity)</img>
+
+!!! warning
+    There should be a hydrogen attached to the nitrogen at the end of the amine.
+
+### E/Z isomers
+
+E/Z isomers are a generalised form of cis-trans isomers, where priority is determined by atomic number. If both sides with the higher atomic number are on the **same** side, the isomer is a Z-isomer (German: *ze zame zide*). E/Z isomers are placed at the beginning surrounded by parentheses.
+
+!!! example
+    (Z)-2-bromo-1-chloro-1-fluoroethene:
+    <img src="/resources/images/ez-example.png" width=700>(Source: Kognity)</img>
+
+If the atoms are of equal priority, the sum of atomic numbers that they are directly connected to are compared (double bonds count twice), repeating as necessary.
+
+!!! example
+    (Z)-1-chloro-1-fluoro-2-methyl-1-butene (left) and (E)-1-chloro-1-fluoro-2-methyl-1-butene (right).
+    <img src="/resources/images/special-ez-isomer.png" width=700>(Source: Kognity)</img>
+
+If there are multiple E/Z isomers, they are separated by commas and numbered according to their earliest position on the main chain.
+
+!!! example
+    (2Z, 3E)-R
+
+### Optical isomers
+
+!!! definition
+    - An **enantiomer** is an optical isomer.
+    - A **chiral centre** is a carbon atom with four different groups attached to it.
+    - The **chirality** of a carbon atom represents its ability to form an enantiomer.
+    - A **racemic mixture** is a mixture of exactly one half of each enantiomer of a species such that it is not optically active.
+    - A **dextrorotary** enantiomer rotates rightward (+).
+    - A **levrorotary** enantiomer rotates leftward (-).
+
+Optical isomers are mirrored across the y-axis with the same compounds put on the same bonds. **Four distinct groups** must be attached to the central carbon atom to have optical isomers.
+
+In the data booklet, all amino acids are chiral except for glyine and proline.
+
+!!! example
+    <img src="/resources/images/enantiomer.ex.png" width=700>(Source: Kognity)</img>
+
+An **optically active** species is one that can rotate the plane of polarised light. Please see [SL Physics 1#Polarisation](/sph3u7/#polarisation) for more information.
+
+A species that rotates the plane clockwise is positive, while counter-clockwise is negative. Both enantiomers have the same magnitude of polarisation except for the direction. If there is a mixture of both enantiomers, the angle changes depending on the proportion of each isomer.
+
+Enantiomers have the same physical properties except for the direction of polarised light. They also have mostly the same chemical properties except for chemical reactions with other enantiomers of different compounds.
+
+### Properties of organic compounds
+
+**Alcohols** are able to form hydrogen bonds, so are soluble in water. Increasing the length of the main chain decreases solubility as the rest of the molecule is non-polar, but this can be compensated by adding more hydroxyls too.
+
+In general:
+
+ - m/ethanols are miscible
+ - butanols are 10-15% v/v miscible
+ - alcohols longer than octanols are effectively insoluble
+
+Although the boiling point of an alcohol will always be higher than its corresponding alkane, the difference between the two will decrease as chain length increases as the proportion of force the alcohol provides decreases relative to the larger contributor in the LDF from the main chain.
+
+Low mass **esters** smell good, and large mass esters are oily/waxy.
+
+**Amines** smell bad and are all Bronsted-Lowry weak bases because they can accept protons and form dative bonds.
+
+The solubility of compounds is directly related to their melting/boiling point — compounds that cannot hydrogen bond with themselves but can with water have an advantage.
+
+From greatest to lowest melting point:
+
+**Hydrogen bonding**
+
+   - Water is able to hydrogen bond with two other molecules per molecule, efficiently using all its lone pairs and Hs.
+   - Carboxylic acids are less efficient than water but more than alcohols as an the OH can attract to an O on a different molecule.
+   - Alcohols
+   - Primary/secondary amines can hydrogen bond but the N-H bond is less polar than O-H, decreasing its strength.
+
+**Dipole-dipole interaction**
+
+   - Aldehydes and ketones
+   - Esters are less polar than aldehydes because the single bond O attracts electrons from the C=O.
+   - Ethers have horizontal components to their dipole vectors that cancel out, so they are least polar.
+
+**London dispersion forces**
+
+   - Alkynes' triple bonds means that packing is easier, increasing LDFs.
+   - Alkanes
+   - Alkenes' double bonds means that there are less electrons than their alkane counter parts, reducing LDFs.
+
+$$\ce{
+water >> \\
+carboxylic acids > alcohols > amines >> \\
+ethers > aldehydes/ketones >> \\
+alkynes > alkanes > alkenes
+}$$
+
+## Resources
+
+ - [IB Chemistry Data Booklet](/resources/g11/ib-chemistry-data-booklet.pdf)
+ - [IB HL Chemistry Syllabus](/resources/g11/ib-chemistry-syllabus.pdf)
+ - [Significant Figures/Digits](/resources/g11/chemistry-sig-figs.pdf)
+ - [Error Analysis and Significant Figures (long)](/resources/g11/error-analysis-sig-figs.pdf)
+ - [General Guidelines for Writing a Formal Laboratory Report](/resources/g11/lab-report-guidelines.pdf)
+ - [Designing an IB Investigation](/resources/g11/designing-investigation.pdf)
+ - [Textbook: Pearson Higher Level Chemistry](/resources/g12/textbook-hl-chem.pdf) ([Answers](/resources/g12/textbook-hl-chem-answers.pdf)) - [mini Eifueo](/resources/g12/textbook-hl-chem-eifueo.pdf)