26 KiB
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 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.
(Source:
Kognity)
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.
(Source:
Kognity)
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.
(Source:
Kognity)
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.
(Source:
Kognity)
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.
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. \[\Delta G^\theta = \Delta H^\theta - T\Delta S^\theta\]
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.
(Source:
Kognity)
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.
(Source:
Kognity)
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.
(Source:
Kognity)
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.
(Source:
Kognity)
Visualised with a Maxwell-Boltzmann distribution:
(Source:
Kognity)
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:
(Source:
Kognity)
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.
(Source:
Kognity)
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.
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. \[\ce{A + B <=> C}\]
(Source:
Kognity)
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
(Source:
Kognity)
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.