Difficulty: Intermediate | Prerequisites: Molar mass, balanced equations, basic algebra and logarithms
This material covers the energetics of chemical reactions, the behaviour of gases and solutions, and the principles that govern whether and how far a reaction proceeds. These topics occupy roughly the final third of CHM 11500 and tie everything together: you need molar mass and balanced equations to do Hess's Law calculations, you need an understanding of bonding to reason about enthalpy, and you need equilibrium to understand acids and bases. If any one of these areas is shaky, it tends to ripple into the others, so building them in sequence pays off.
Enthalpy changes tell you whether a reaction releases or absorbs heat. Gas laws relate pressure, volume, and temperature. Equilibrium and Le Chatelier's Principle predict how systems respond to stress. Acids and bases are quantified by pH, pKa, and the Lewis/Bronsted-Lowry definitions.
Exothermic reaction
A reaction that releases heat to the surroundings. The enthalpy change (ΔH) is negative.
In simple terms, the reaction gives off heat, so the surroundings get warmer.
Endothermic reaction
A reaction that absorbs heat from the surroundings. ΔH is positive.
In simple terms, the reaction takes in heat, so the surroundings get cooler.
Enthalpy of formation (ΔH°f)
The enthalpy change when one mole of a compound is formed from its elements in their standard states.
In simple terms, it is the "energy cost" of building one mole of a compound from scratch.
Hess's Law
The total enthalpy change for a reaction is the sum of the enthalpy changes for each step of the reaction, regardless of the pathway taken. This allows you to calculate ΔH_rxn from standard enthalpies of formation.
Gibbs free energy (ΔG)
A thermodynamic quantity combining enthalpy and entropy: ΔG = ΔH - TΔS. A negative ΔG means the reaction is spontaneous under the given conditions.
In simple terms, ΔG tells you whether a reaction will happen on its own.
Activation energy (Ea)
The minimum energy that reacting molecules must possess for a collision to result in a chemical reaction. It is the height of the energy barrier between reactants and products on an energy diagram.
Catalyst
A substance that increases the rate of a reaction by providing an alternative pathway with a lower activation energy. The catalyst is not consumed in the reaction.
Boyle's Law
At constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂. If volume decreases, pressure increases.
Triple point
The specific temperature and pressure at which all three phases (solid, liquid, gas) of a substance coexist in equilibrium on a phase diagram.
Molarity (M)
The concentration of a solution expressed as moles of solute per litre of solution: M = mol / L.
Dissociation
The process by which an ionic compound separates into its individual ions when dissolved in water.
Le Chatelier's Principle
If an external stress (change in concentration, pressure, or temperature) is applied to a system at equilibrium, the system shifts to partially counteract that stress and re-establish equilibrium.
Equilibrium constant (Keq)
A ratio of product concentrations to reactant concentrations, each raised to their stoichiometric coefficients, at equilibrium. A large Keq favours products; a small Keq favours reactants.
pH
A logarithmic measure of the hydrogen ion concentration in a solution: pH = -log[H⁺]. Lower pH means more acidic.
pKa
The negative log of the acid dissociation constant (Ka): pKa = -log(Ka). A lower pKa means a stronger acid.
Lewis acid
An electron-pair acceptor. Lewis acids have an empty or incomplete valence shell.
In simple terms, a Lewis acid is hungry for electrons.
Lewis base
An electron-pair donor. Lewis bases have a lone pair available to donate.
In simple terms, a Lewis base has spare electrons to offer.
Buffer
A solution containing a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists changes in pH when small amounts of strong acid or base are added.
Exothermic: heat is released to the surroundings; ΔH is negative. The products are lower in energy than the reactants.
Endothermic: heat is absorbed from the surroundings; ΔH is positive. The products are higher in energy than the reactants.
A negative ΔG (Gibbs free energy) means a reaction is spontaneous. This is distinct from exothermic: a reaction can be endothermic but still spontaneous if the entropy increase is large enough (TΔS term dominates).
The standard enthalpy of reaction is calculated using:
ΔH_rxn = Σ [n x ΔH°f (products)] - Σ [n x ΔH°f (reactants)]
where n is the stoichiometric coefficient.
For the reaction: 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(g)
Given ΔH°f values (kJ/mol): NH₃(g) = -45.9, NO(g) = +90.3, H₂O(g) = -241.8, O₂(g) = 0.0
Products: [4(+90.3) + 6(-241.8)] = [361.2 + (-1450.8)] = -1089.6 kJ
Reactants: [4(-45.9) + 5(0.0)] = -183.6 kJ
ΔH_rxn = -1089.6 - (-183.6) = -1089.6 + 183.6 = -906.0 kJ
The reaction is exothermic (ΔH is negative).
Activation energy is the minimum energy required for reactants to form products. On an energy diagram, it is the difference between the energy of the reactants and the peak of the energy barrier (the transition state).
A catalyst lowers the activation energy by providing an alternative reaction pathway. This increases the reaction rate but does not change the overall enthalpy change or the equilibrium position.
At constant temperature: P₁V₁ = P₂V₂.
If the volume of a gas is decreased while temperature remains constant, the pressure increases. The molecules are squeezed into a smaller space, so they collide with the container walls more frequently.
A phase diagram plots pressure vs temperature and shows the regions where a substance exists as a solid, liquid, or gas.
The triple point is the unique temperature and pressure at which all three phases coexist in equilibrium.
The critical point is the temperature and pressure above which the liquid and gas phases become indistinguishable (a supercritical fluid).
When an ionic compound dissolves in water, it dissociates into its constituent ions.
CaCl₂ → Ca²⁺ + 2Cl⁻
One formula unit produces 3 ions (1 Ca²⁺ + 2 Cl⁻). So 2.0 moles of CaCl₂ produce 2.0 x 3 = 6.0 moles of solute particles.
Molarity = moles of solute / litres of solution.
Worked example: How many millilitres of 2.48 M HCl are required to obtain 0.80 moles of Cl⁻ ions?
HCl is a strong acid and dissociates completely: HCl → H⁺ + Cl⁻. The ratio of HCl to Cl⁻ is 1:1, so you need 0.80 moles of HCl.
Volume = moles / molarity = 0.80 mol / 2.48 mol/L = 0.3226 L = 322.6 mL, which rounds to 320 mL (2 sig figs).
When a system at equilibrium is disturbed, it shifts to partially offset the disturbance.
Worked example: CO(g) + 3H₂(g) ⇌ CH₄(g) + H₂O(g)
Reactant side: 1 + 3 = 4 moles of gas. Product side: 1 + 1 = 2 moles of gas.
If pressure is increased, the equilibrium shifts toward the side with fewer moles of gas to reduce pressure. That is the product side (right). The equilibrium shifts to the right.
Note: changing pressure does not change the value of Keq. Only temperature changes Keq.
A lower pKa means a stronger acid (it donates protons more readily).
Given: Acid A (pKa 2.43), Acid B (pKa 4.55), Acid C (pKa 8.23), Acid D (pKa 11.89).
Acid A is the strongest because it has the lowest pKa.
pH = -log[H⁺], which means [H⁺] = 10⁻ᵖᴴ.
Worked example: A 0.25 M butyric acid solution has a pH of 2.71.
[H⁺] = 10⁻²·⁷¹ = 1.95 x 10⁻³ M (approximately 0.00195 M).
A Lewis acid accepts an electron pair. A Lewis base donates an electron pair.
Al³⁺ has an empty valence shell and accepts electron pairs: Lewis acid.
H⁺ has no electrons at all and accepts an electron pair: Lewis acid.
NH₃ has a lone pair on nitrogen available to donate: Lewis base.
BCl₃ has an incomplete octet on boron and accepts an electron pair: Lewis acid.
NH₃ is the Lewis base in this set.
A buffer resists pH changes because it contains both a weak acid/base and its conjugate partner.
Worked example: A buffer of NH₃ (weak base) and NH₄Cl (provides the conjugate acid NH₄⁺).
When a small amount of strong acid (H⁺) is added:
The H⁺ reacts with the weak base NH₃: NH₃ + H⁺ → NH₄⁺
The concentration of NH₃ decreases and the concentration of NH₄⁺ increases.
The pH drops slightly but far less than it would in pure water, because the buffer absorbs the added acid.
ΔH_rxn = Σ [n x ΔH°f (products)] - Σ [n x ΔH°f (reactants)]
ΔG = ΔH - TΔS
Boyle's Law: P₁V₁ = P₂V₂ (at constant T)
Molarity: M = mol / L
pH = -log[H⁺]
[H⁺] = 10⁻ᵖᴴ
pKa = -log(Ka)
Hess's Law is how engineers calculate the energy output of fuels without having to burn every possible mixture in a calorimeter. Boyle's Law governs everything from how your lungs expand to how scuba divers manage compressed air at depth. Buffer systems maintain the pH of your blood at approximately 7.4, and the carbonic acid/bicarbonate buffer is the primary system responsible for this. Le Chatelier's Principle is the basis of industrial chemistry: the Haber process for making ammonia manipulates temperature and pressure to maximise yield.
Students often think that exothermic reactions are always spontaneous. Spontaneity depends on ΔG, not ΔH alone. An exothermic reaction with a large decrease in entropy can be non-spontaneous at high temperatures.
Students confuse the effect of pressure changes on Keq with shifts in equilibrium position. Pressure changes shift the equilibrium but do not change Keq; only temperature changes Keq.
Students sometimes think a catalyst changes the equilibrium position. It does not. A catalyst speeds up both the forward and reverse reactions equally, reaching the same equilibrium faster.
Students often assume that the "strongest acid" has the highest pKa. The opposite is true: the strongest acid has the lowest pKa.
⚠️ Hess's Law calculations are almost guaranteed on the exam. The most common error is forgetting to multiply ΔH°f by the stoichiometric coefficient, or getting the sign wrong (products minus reactants).
⚠️ Le Chatelier's Principle questions require you to count moles of gas on each side to predict the effect of a pressure change.
⚠️ The distinction between "spontaneous" (negative ΔG) and "exothermic" (negative ΔH) is a classic exam trap. A question asking "if ΔG is negative, the reaction is:" has the answer "spontaneous," not "exothermic."
⚠️ Calculating [H⁺] from pH (or vice versa) is a routine short-answer question. Make sure you can use the 10⁻ˣ function on your calculator.
⚠️ Lewis acid/base identification: look for lone pairs (Lewis base) or empty orbitals/incomplete octets (Lewis acid). NH₃ is the textbook Lewis base.
⚠️ Buffer questions: know that adding strong acid consumes the weak base component and produces more conjugate acid. The concentrations shift, but the pH changes only slightly.
True or false: An exothermic reaction has a positive ΔH. False (ΔH is negative for exothermic reactions).
Fill in the blank: According to Boyle's Law, pressure and volume are ___ proportional at constant temperature. Inversely.
True or false: A negative ΔG means the reaction is at equilibrium. False (it means the reaction is spontaneous; ΔG = 0 at equilibrium).
Fill in the blank: The acid with pKa 2.43 is ___ (stronger/weaker) than the acid with pKa 8.23. Stronger.
True or false: A catalyst changes the equilibrium constant Keq. False (it only changes the rate at which equilibrium is reached).
Q: Which of the following describes an exothermic reaction: (a) heat is absorbed, ΔH positive; or (b) heat is released, ΔH negative?
A: (b) Heat is released to the surroundings and ΔH is negative.
Q: Calculate ΔH_rxn for 4NH₃(g) + 5O₂(g) → 4NO(g) + 6H₂O(g) using the given ΔH°f values: NH₃ = -45.9, NO = +90.3, H₂O = -241.8, O₂ = 0.0 kJ/mol.
A: ΔH_rxn = [4(90.3) + 6(-241.8)] - [4(-45.9) + 5(0)] = -1089.6 - (-183.6) = -906.0 kJ.
Q: According to Boyle's Law, if the volume of a gas is halved at constant temperature, what happens to the pressure?
A: The pressure doubles.
Q: How many moles of ions are produced when 2.0 moles of CaCl₂ dissolve completely in water?
A: 6.0 moles (2.0 mol Ca²⁺ + 4.0 mol Cl⁻).
Q: The triple point on a phase diagram is the point where what happens?
A: All three phases (solid, liquid, gas) coexist in equilibrium at a specific temperature and pressure.
Q: Which substance can act as a Lewis base: Al³⁺, H⁺, NH₃, or BCl₃?
A: NH₃. It has a lone pair of electrons on nitrogen available to donate.
Q: In a buffer system of NH₃ and NH₄Cl, what happens to [NH₃] when a small amount of strong acid is added?
A: [NH₃] decreases because NH₃ reacts with the added H⁺ to form NH₄⁺.
Q: A solution has a pH of 2.71. What is the [H⁺] concentration?
A: [H⁺] = 10⁻²·⁷¹ = 1.95 x 10⁻³ M.
Q: How will an increase in pressure affect the equilibrium CO(g) + 3H₂(g) ⇌ CH₄(g) + H₂O(g)?
A: The equilibrium shifts to the right (toward products), because the product side has fewer moles of gas (2 vs 4).
Thermochemistry connects back to bonding (bond energies determine ΔH) and forward to kinetics and equilibrium. Le Chatelier's Principle is the qualitative counterpart to the equilibrium constant expression, which becomes quantitative in CHM 11600. Acid-base chemistry builds on the concepts of equilibrium (Ka is just a specialised Keq) and connects to buffer design in biochemistry. Gas laws connect to stoichiometry through molar volume at STP and to kinetics through the molecular interpretation of temperature and pressure.
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