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Thermodynamics, Gibbs, and Spontaneity cheat sheet - grade 11-12

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Chemistry Grade 11-12

Thermodynamics, Gibbs, and Spontaneity Cheat Sheet

A printable reference covering enthalpy, entropy, Gibbs free energy, equilibrium, and spontaneity for grades 11-12.

TopicsThermodynamicsChemical ReactionsEnergyHeatChemistryStudy Guide
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Thermodynamics explains how energy changes determine whether chemical and physical processes are likely to occur. This cheat sheet helps students connect heat flow, disorder, temperature, and spontaneity in one organized reference. It is especially useful for predicting reactions using enthalpy, entropy, and Gibbs free energy.

These ideas are central in chemistry, biology, environmental science, and engineering.

Key Facts

  • Gibbs free energy is calculated by ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S, where TT must be in kelvins.
  • A process is spontaneous at constant temperature and pressure when ΔG<0\Delta G < 0.
  • A process is nonspontaneous at constant temperature and pressure when ΔG>0\Delta G > 0.
  • A system is at equilibrium when ΔG=0\Delta G = 0 and there is no net change in reaction progress.
  • Entropy change can be estimated by ΔS=Sproducts−Sreactants\Delta S = S_{\text{products}} - S_{\text{reactants}} using standard molar entropy values.
  • Standard Gibbs free energy and equilibrium are related by ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K.
  • For nonstandard conditions, Gibbs free energy is calculated by ΔG=ΔG∘+RTln⁡Q\Delta G = \Delta G^\circ + RT\ln Q.
  • A temperature threshold for spontaneity occurs when ΔG=0\Delta G = 0, so T=ΔHΔST = \frac{\Delta H}{\Delta S} if ΔH\Delta H and ΔS\Delta S use compatible units.

Vocabulary

Enthalpy
Enthalpy is the heat content of a system at constant pressure, represented by HH.
Entropy
Entropy is a measure of energy dispersal or disorder in a system, represented by SS.
Gibbs Free Energy
Gibbs free energy is the energy available to do useful work, represented by GG.
Spontaneous Process
A spontaneous process is one that can occur without continuous outside energy input when ΔG<0\Delta G < 0.
Equilibrium Constant
The equilibrium constant KK compares product and reactant amounts at equilibrium for a reversible reaction.
Reaction Quotient
The reaction quotient QQ compares product and reactant amounts at any moment before equilibrium is reached.

Common Mistakes to Avoid

  • Using Celsius instead of kelvins in ΔG=ΔH−TΔS\Delta G = \Delta H - T\Delta S is wrong because thermodynamic temperature must be absolute.
  • Forgetting to convert ΔS\Delta S from J mol−1 K−1\text{J}\,\text{mol}^{-1}\,\text{K}^{-1} to kJ mol−1 K−1\text{kJ}\,\text{mol}^{-1}\,\text{K}^{-1} is wrong when ΔH\Delta H is in kJ mol−1\text{kJ}\,\text{mol}^{-1}.
  • Assuming every exothermic reaction is spontaneous is wrong because entropy and temperature also affect ΔG\Delta G.
  • Confusing ΔG\Delta G with ΔG∘\Delta G^\circ is wrong because ΔG∘\Delta G^\circ applies only to standard-state conditions.
  • Treating a positive ΔS\Delta S as always spontaneous is wrong because ΔH\Delta H may still make ΔG\Delta G positive at a given temperature.

Practice Questions

  1. 1 Calculate ΔG\Delta G for a reaction with ΔH=−45.0 kJ mol−1\Delta H = -45.0\ \text{kJ}\,\text{mol}^{-1}, ΔS=−120 J mol−1 K−1\Delta S = -120\ \text{J}\,\text{mol}^{-1}\,\text{K}^{-1}, and T=298 KT = 298\ \text{K}.
  2. 2 Find the temperature at which a reaction changes spontaneity if ΔH=80.0 kJ mol−1\Delta H = 80.0\ \text{kJ}\,\text{mol}^{-1} and ΔS=200 J mol−1 K−1\Delta S = 200\ \text{J}\,\text{mol}^{-1}\,\text{K}^{-1}.
  3. 3 Use ΔG∘=−RTln⁡K\Delta G^\circ = -RT\ln K to determine whether KK is greater than 11 or less than 11 when ΔG∘=−12.5 kJ mol−1\Delta G^\circ = -12.5\ \text{kJ}\,\text{mol}^{-1} at 298 K298\ \text{K}.
  4. 4 Explain why a reaction with ΔH>0\Delta H > 0 and ΔS>0\Delta S > 0 may be nonspontaneous at low temperature but spontaneous at high temperature.

Understanding Thermodynamics, Gibbs, and Spontaneity

Entropy is best understood as the number of possible arrangements available to particles and energy. A crystal has particles held in a regular pattern, so it has relatively few arrangements. A liquid has more freedom of motion.

A gas has far more possible positions and speeds. Mixing, dissolving, melting, and gas formation often increase entropy for this reason. Entropy is not simply a measure of messiness.

A neat container of gas can have high entropy because its particles can occupy many microscopic states. Chemists consider the entropy change of the system and the entropy change of the surroundings. Heat released into the surroundings spreads energy among nearby particles, which tends to raise the surroundings' entropy.

Enthalpy describes heat transferred at constant pressure, which is the usual condition for reactions in open containers. A reaction with negative enthalpy releases heat. A reaction with positive enthalpy absorbs heat.

Gibbs free energy weighs this heat effect against the entropy effect at a particular temperature. The four possible sign combinations are useful for quick predictions. Negative enthalpy with positive entropy favors a process at every temperature.

Positive enthalpy with negative entropy opposes it at every temperature. When both changes have the same sign, temperature decides the outcome.

Temperature must be converted to kelvins because the Gibbs calculation uses an absolute temperature scale. Celsius values can produce meaningless results in this context.

Equilibrium does not mean that a reaction has stopped. At equilibrium, forward and reverse reactions continue at equal rates. The amounts of reactants and products stay constant overall.

The equilibrium constant describes the favored balance of products and reactants at a given temperature. Large equilibrium constants mean the product side is favored. Small values mean the reactant side is favored.

A mixture not at equilibrium has a reaction quotient based on its current concentrations or gas pressures. Comparing this value with the equilibrium constant predicts which direction will lower Gibbs free energy. This matters in calculations involving acids, solubility, electrochemical cells, and industrial reactions.

Spontaneous does not mean fast. Rusting is thermodynamically favored under many conditions, yet it can take a long time. Diamond changing into graphite is another famous example of a favorable change that is extremely slow.

Reaction rate depends on activation energy and the path of the reaction, not only on Gibbs free energy. Catalysts speed reactions by providing a lower activation energy pathway. They do not change the equilibrium position.

When solving problems, track signs carefully, keep energy units compatible, and check whether the question gives standard conditions or actual concentrations. Pay close attention to whether entropy values are given per mole and whether temperature changes the sign of the predicted free energy.