Difficulty: Intermediate to Advanced | Prerequisites: Parts 1 and 2 (Systems/Processes, Heat/Calorimetry).
Big Picture
This is where thermochemistry becomes predictive. Enthalpy tells you how much heat a reaction absorbs or releases. Entropy tells you how energy disperses. Gibbs free energy combines both into a single number that answers the question every chemist cares about: will this reaction happen on its own? This section also connects thermodynamics to equilibrium through the relationship between ΔG and the equilibrium constant, closing the loop between energy and chemical behaviour.
Enthalpy (ΔH) measures the heat a reaction exchanges at constant pressure; entropy (ΔS) measures how energy disperses. Gibbs free energy (ΔG = ΔH − TΔS) combines both into one number: if ΔG is negative, the reaction is spontaneous. The relationship ΔG° = −RT ln(K_eq) ties thermodynamics directly to the equilibrium constant, letting you predict both whether and how far a reaction will proceed.
Enthalpy (H)
A measure of the potential energy stored in intermolecular attractions and chemical bonds. It is a state function, equal to the heat transferred at constant pressure. Think of it as the "heat content" of a substance under normal lab conditions.
Standard heat of formation (ΔH_f°)
The enthalpy required to produce one mole of a compound from its elements in their standard states (298 K, 1 atm). For any element already in its standard state, this value is zero.
Standard heat of reaction (ΔH_rxn°)
The enthalpy change of a reaction under standard conditions. Calculated as the sum of heats of formation of products minus the sum of heats of formation of reactants.
Hess's law
Enthalpy changes are additive: the total ΔH for a reaction is the same regardless of whether it occurs in one step or several. In simple terms, the path does not matter because enthalpy is a state function.
Bond dissociation energy (bond enthalpy)
The average energy required to break one mole of a specific type of bond in the gas phase. Breaking bonds is endothermic; forming bonds is exothermic with the same magnitude but opposite sign.
Standard heat of combustion (ΔH_comb)
The enthalpy change when a substance burns completely in the presence of O₂ (or sometimes F₂ or Cl₂). Larger alkanes produce more combustion products and release more energy.
Entropy (S)
A measure of the degree to which energy has dispersed throughout a system. Higher entropy means more disorder and more ways energy can be spread. It is a state function, measured in J/mol·K.
Second law of thermodynamics
Energy spontaneously disperses from localised to spread out, unless something prevents it. In simple terms, entropy in a closed system tends to increase.
Gibbs free energy (G)
Derived from enthalpy and entropy: ΔG = ΔH − TΔS. It indicates whether a reaction is spontaneous (ΔG < 0), at equilibrium (ΔG = 0), or nonspontaneous (ΔG > 0).
Exergonic
A reaction that releases free energy (ΔG < 0). It is spontaneous. This term describes Gibbs free energy specifically, not enthalpy.
Endergonic
A reaction that absorbs free energy (ΔG > 0). It is nonspontaneous.
Equilibrium constant (K_eq)
The ratio of product concentrations to reactant concentrations at equilibrium. Linked to Gibbs free energy by ΔG° = −RT ln(K_eq).
Reaction quotient (Q)
The same ratio as K_eq but measured at any point during the reaction, not just at equilibrium. Comparing Q to K_eq tells you which direction the reaction will shift.
Enthalpy is a state function equal to the heat transferred into or out of a system at constant pressure.
ΔH_rxn = H_products − H_reactants
Positive ΔH = endothermic (heat absorbed).
Negative ΔH = exothermic (heat released).
Phase change direction matters:
Solid → Liquid → Gas: endothermic (gases have more energy than liquids, which have more than solids).
Gas → Liquid → Solid: exothermic.
The enthalpy needed to form one mole of a compound from its elements in their standard states.
Any element in its standard state has ΔH_f° = 0. This is a reference point, not a measured value.
Calculated from heats of formation:
ΔH_rxn° = Σ ΔH_f°(products) − Σ ΔH_f°(reactants)
Because enthalpy is a state function, enthalpy changes are additive regardless of path.
If you can break a reaction into steps whose ΔH values you know, you can sum them to find the overall ΔH.
This law also applies to Gibbs free energy and entropy.
Breaking a bond requires energy (endothermic). Forming a bond releases the same amount of energy (exothermic).
ΔH_rxn = Σ ΔH_bonds broken − Σ ΔH_bonds formed
This equals total energy absorbed minus total energy released.
Note the direction: when using bond energies, the formula is reversed compared to heats of formation (reactants minus products for bond energies).
The enthalpy change when a substance burns completely in O₂ (or F₂, Cl₂).
Larger alkanes produce more combustion products and release more energy.
Entropy measures how energy is dispersed across a system at a given temperature.
ΔS = Q_rev / T, where Q_rev is the heat at reversible conditions and T is in Kelvin. Units: J/mol·K.
Entropy changes with phase:
Freezing decreases entropy (more ordered).
Boiling increases entropy (less ordered).
Sublimation gives the largest entropy increase (solid straight to gas).
Second law of thermodynamics: energy spontaneously disperses unless hindered. Entropy in a closed system tends to increase.
Entropy is maximised at equilibrium.
To predict entropy change in a reaction, compare the number of moles of gas on each side. More moles of gas on the product side typically means an increase in entropy.
Standard entropy of reaction: ΔS_rxn° = Σ ΔS_f°(products) − Σ ΔS_f°(reactants)
ΔG = ΔH − TΔS (T in Kelvin).
ΔG < 0: spontaneous (exergonic).
ΔG = 0: system is at equilibrium (ΔH = TΔS).
ΔG > 0: nonspontaneous (endergonic).
Terminology distinction: exergonic/endergonic describe Gibbs free energy. Exothermic/endothermic describe enthalpy.
−ΔH and +ΔS: spontaneous at all temperatures.
−ΔH and −ΔS: spontaneous at low temperatures only.
+ΔH and +ΔS: spontaneous at high temperatures only.
+ΔH and −ΔS: nonspontaneous at all temperatures.
When ΔH and ΔS have the same sign, spontaneity is temperature-dependent.
ΔG° = −RT ln(K_eq), where R is the ideal gas constant.
A larger K_eq means a more negative ΔG° and a more spontaneous reaction.
Standard free energy of formation for any element at standard conditions is 0.
Once a reaction begins, concentrations are no longer 1 M, so standard conditions no longer apply. Use:
ΔG_rxn = RT ln(Q / K_eq)
If Q < K_eq: ln is negative, ΔG is negative, reaction proceeds forward.
If Q > K_eq: ln is positive, ΔG is positive, reaction proceeds in reverse.
If Q = K_eq: ln is 0, ΔG = 0, system is at equilibrium.
Catalysts lower the activation energy but have no effect on ΔG.
The rate of reaction depends on activation energy, not on ΔG. A spontaneous reaction can still be slow.
\Delta H_{rxn} = H_{products} - H_{reactants}Enthalpy change of reaction. Positive = endothermic, negative = exothermic.
\Delta H_{rxn}^\circ = \sum \Delta H_f^\circ (products) - \sum \Delta H_f^\circ (reactants)Standard heat of reaction from heats of formation.
\Delta H_{rxn} = \sum \Delta H_{broken} - \sum \Delta H_{formed}Enthalpy from bond dissociation energies. Note: bonds broken (reactants) minus bonds formed (products).
\Delta S = \frac{Q_{rev}}{T}Entropy change. Q_rev is heat at reversible conditions, T in Kelvin.
\Delta S_{rxn}^\circ = \sum \Delta S_f^\circ (products) - \sum \Delta S_f^\circ (reactants)Standard entropy of reaction.
\Delta G = \Delta H - T\Delta SGibbs free energy. The master equation for spontaneity.
\Delta G^\circ = -RT \ln(K_{eq})Relates standard free energy to the equilibrium constant. R = 8.314 J/mol·K.
\Delta G_{rxn} = RT \ln\left(\frac{Q}{K_{eq}}\right)Free energy under non-standard conditions. Compares the reaction quotient Q to K_eq.
Hess's law is how chemists calculate the enthalpy of reactions they cannot measure directly, such as the formation of carbon monoxide (difficult to isolate as the sole product). Gibbs free energy is the reason batteries eventually die: the reaction inside them proceeds until ΔG reaches zero (equilibrium), at which point no more useful work can be extracted. The relationship between ΔG° and K_eq is central to drug design and biochemistry, where researchers tune molecular interactions to shift equilibrium toward a desired product.
Students often confuse exothermic/endothermic (which describe enthalpy) with exergonic/endergonic (which describe Gibbs free energy). A reaction can be endothermic yet still spontaneous if the entropy increase is large enough.
Assuming that a negative ΔG means a reaction is fast is a common error. ΔG tells you about thermodynamic favourability; the rate depends on the activation energy, which is a separate quantity entirely.
Students sometimes think catalysts change ΔG. They do not. Catalysts lower the activation energy and speed up the reaction, but the equilibrium position and free energy change remain the same.
When using bond dissociation energies, the formula is bonds broken minus bonds formed. Students frequently reverse this, or confuse it with the heats-of-formation formula (products minus reactants). The two formulas go in opposite directions.
⚠️ The spontaneity table (signs of ΔH and ΔS vs outcome) is a near-guaranteed exam question. Memorise all four combinations.
⚠️ Know the difference between the two ΔH_rxn formulas: heats of formation (products minus reactants) vs bond energies (broken minus formed). Getting these backwards is one of the most common calculation errors.
⚠️ Be able to apply Hess's law: given two or three sub-reactions with known ΔH values, find the overall ΔH by adding, reversing, or scaling them.
⚠️ Understand ΔG° = −RT ln(K_eq) and what it means: a large K_eq corresponds to a very negative ΔG°.
⚠️ Know how to use Q vs K_eq to predict the direction of a reaction under non-standard conditions.
⚠️ Remember that ΔH_f° = 0 for any element in its standard state. This trips students up when they forget to zero out elements in a calculation.
True or False: A reaction with ΔH > 0 and ΔS > 0 is spontaneous at all temperatures.
Answer: False. It is spontaneous only at high temperatures (where TΔS exceeds ΔH).
Fill in the blank: ΔG = 0 means the system is at ___.
Answer: Equilibrium.
True or False: Catalysts change the value of ΔG for a reaction.
Answer: False. Catalysts affect activation energy, not ΔG.
Fill in the blank: The standard heat of formation for any element in its standard state is ___.
Answer: Zero.
True or False: If Q < K_eq, the reaction will proceed in the forward direction.
Answer: True. ΔG is negative when Q < K_eq.
Q: A reaction has ΔH = −120 kJ and ΔS = −200 J/K. At what temperature (approximately) does it switch from spontaneous to nonspontaneous?
A: At equilibrium, ΔG = 0, so ΔH = TΔS. T = ΔH / ΔS = (−120,000 J) / (−200 J/K) = 600 K. Below 600 K, the reaction is spontaneous; above 600 K, it is nonspontaneous.
Q: Using Hess's law, calculate ΔH for: C(s) + O₂(g) → CO₂(g), given: (1) C(s) + ½O₂(g) → CO(g), ΔH₁ = −110.5 kJ and (2) CO(g) + ½O₂(g) → CO₂(g), ΔH₂ = −283.0 kJ.
A: Add the two reactions: C(s) + ½O₂ → CO + CO + ½O₂ → CO₂. The CO cancels. ΔH = ΔH₁ + ΔH₂ = −110.5 + (−283.0) = −393.5 kJ.
Q: For the reaction 2H₂(g) + O₂(g) → 2H₂O(l), ΔH_f°(H₂O(l)) = −285.8 kJ/mol. What is ΔH_rxn°?
A: ΔH_rxn° = Σ ΔH_f°(products) − Σ ΔH_f°(reactants) = [2 × (−285.8)] − [0 + 0] = −571.6 kJ. Elements in their standard states have ΔH_f° = 0.
Q: K_eq for a reaction at 298 K is 1.0 × 10⁵. Is ΔG° positive or negative, and roughly how large?
A: ΔG° = −RT ln(K_eq) = −(8.314)(298) ln(10⁵) = −(2477.6)(11.51) ≈ −28,500 J ≈ −28.5 kJ. It is negative, confirming the reaction strongly favours products.
Q: A reaction has Q = 10 and K_eq = 100. In which direction will it proceed?
A: Q < K_eq, so ΔG is negative and the reaction proceeds forward (toward more products) until Q rises to equal K_eq.
Gibbs free energy connects directly to chemical equilibrium (the K_eq chapter), because ΔG° = −RT ln(K_eq) bridges the two topics. Entropy links forward to the third law of thermodynamics (not covered here) and to statistical mechanics in more advanced courses. Bond dissociation energies connect to molecular structure and bonding theory from earlier chapters. The enthalpy and entropy concepts reappear in electrochemistry (ΔG = −nFE) and in biochemistry (ATP hydrolysis as a spontaneous, exergonic reaction that drives nonspontaneous processes).
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