- 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.
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.
$\Delta H$ 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:
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.
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).
$\Delta H_B$, 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:
$$\Delta H = \sum n\Delta H_B\text{reactants} - \sum n\Delta H_B\text{products}$$
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.
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 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.
$$\Delta H = \sum \Delta H \text{ of intermediate reactions}$$
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).
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.
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.
- 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.
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.
- 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.
**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.
Gibb's 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.
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.
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.
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.
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.
- 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.
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:
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.
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:
- **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.
- **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.
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:
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.
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: $e^\frac{-E_a}{RT}$.
