In simple terms
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The Decider: Will a Reaction Go?
Gibbs free energy, ΔG, combines a reaction's heat change (ΔH) and disorder change (ΔS) into a single value that tells us if it will happen spontaneously. A negative ΔG means the reaction is feasible and can proceed without continuous energy input.
Imagine deciding whether to tidy your room. The effort required is the enthalpy change (ΔH > 0, endothermic). The resulting order is a decrease in entropy (ΔS < 0). This is a non-spontaneous task (ΔG > 0). Conversely, a party starting spontaneously involves people gathering (exothermic, ΔH < 0) and creating more disorder (entropy increases, ΔS > 0), making it a very spontaneous event (ΔG < 0). Gibbs free energy is the overall 'willingness' of a process to occur.
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ΔG = ΔH − TΔS — spontaneous when ΔG < 0.
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ΔG° = −nFE° for electrochemical cells.
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Temperature can reverse feasibility if ΔH and ΔS oppose.
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ΔG and equilibrium: ΔG° = −RT ln K.
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The Gibbs Free Energy Equation
The Gibbs free energy change (ΔG) represents the portion of the total energy change of a system that is available to perform useful work. It is the ultimate criterion for the spontaneity of a process. The relationship between Gibbs free energy, enthalpy, and entropy is defined by a crucial equation.
ΔG = ΔH - TΔS
ΔG < 0: The reaction is spontaneous (feasible) in the forward direction.
ΔG > 0: The reaction is non-spontaneous. The reverse reaction is spontaneous.
ΔG = 0: The system is at equilibrium.
The Influence of Temperature on Feasibility
The temperature (T) in the Gibbs equation acts as a weighting factor for the entropy change. This means that the spontaneity of some reactions can depend on the temperature. We can analyse four possible scenarios based on the signs of ΔH and ΔS.
Case 1: ΔH < 0, ΔS > 0 (e.g., combustion). The reaction is exothermic and increases disorder. ΔG is always negative. Spontaneous at all temperatures.
Case 2: ΔH > 0, ΔS < 0 (e.g., 2H₂O₂(l) → 2H₂O(l) + O₂(g) in reverse). The reaction is endothermic and increases order. ΔG is always positive. Non-spontaneous at all temperatures.
Case 3: ΔH < 0, ΔS < 0 (e.g., freezing of water). The reaction is exothermic but decreases disorder. The -TΔS term is positive. The reaction is spontaneous only at low temperatures where the favourable ΔH term dominates.
Case 4: ΔH > 0, ΔS > 0 (e.g., melting of ice). The reaction is endothermic but increases disorder. The -TΔS term is negative. The reaction is spontaneous only at high temperatures where the favourable -TΔS term overcomes the unfavourable ΔH term.
The most common error in ΔG calculations is forgetting to convert the units of ΔS from J K⁻¹ mol⁻¹ to kJ K⁻¹ mol⁻¹ (by dividing by 1000) to match the units of ΔH, which are typically in kJ mol⁻¹.
Gibbs Free Energy, Equilibrium and Electrochemistry
The standard Gibbs free energy change, ΔG°, is also directly related to two other important chemical quantities: the equilibrium constant, K, and the standard cell potential, E°cell. These relationships allow us to link thermodynamics with equilibrium and electrochemistry.
ΔG° = -RT ln K
ΔG° = -nFE°
This equation links the spontaneity of a reaction under standard conditions (ΔG°) to the position of its equilibrium.
If ΔG° is negative, ln K must be positive, so K > 1. The equilibrium lies to the right, favouring products.
If ΔG° is positive, ln K must be negative, so K < 1. The equilibrium lies to the left, favouring reactants.
R is the gas constant, 8.31 J K⁻¹ mol⁻¹. Note the units are Joules, so ΔG° must also be in Joules for this calculation.
This equation connects the maximum work available from a reaction (ΔG°) to the electrical potential it can generate in an electrochemical cell (E°).
A spontaneous reaction (ΔG° < 0) will have a positive E°cell.
n is the number of moles of electrons transferred in the balanced redox equation.
F is the Faraday constant, 96500 C mol⁻¹.
Worked examples
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The decomposition of calcium carbonate, CaCO₃(s) → CaO(s) + CO₂(g), has a standard enthalpy change of reaction, ΔH°, of +178 kJ mol⁻¹ and a standard entropy change, ΔS°, of +161 J K⁻¹ mol⁻¹. Calculate the minimum temperature at which this reaction becomes spontaneous under standard pressure.
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Identify the condition for spontaneity: The reaction becomes spontaneous when ΔG° ≤ 0. The minimum temperature for spontaneity is when ΔG° = 0.
The standard electrode potential, E°cell, for the reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) is +1.10 V. Calculate the standard Gibbs free energy change, ΔG°, for this reaction at 298 K. (Faraday constant, F = 96500 C mol⁻¹).
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Identify the relevant equation: ΔG° = -nFE°
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What is Gibbs free energy change, ΔG?
The overall change in energy during a chemical reaction that is available to do useful work. It determines the spontaneity of a reaction.
Key takeaways
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ΔG < 0: The reaction is spontaneous (feasible) in the forward direction.
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ΔG > 0: The reaction is non-spontaneous. The reverse reaction is spontaneous.
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ΔG = 0: The system is at equilibrium.
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