2.5
Gibbs Free Energy and Thermodynamic Favorability
The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction o…
The change in Gibbs free energy, or delta G, is the energy absorbed or released when energy-storing bonds are formed or broken, respectively.
The sign of delta G depends on the signs and the relative values of enthalpy, entropy, and temperature.
If delta H is negative and delta S is positive, delta G is negative at all temperatures. Thus, exothermic reactions where the entropy of the system increases are always spontaneous.
If both delta H and delta S are negative, delta G depends on the temperature. Reactions with negative enthalpy and entropy changes are spontaneous only at low temperatures.
Delta G is also dependent on temperature if both delta H and delta S are positive. Reactions with positive enthalpy and entropy changes are spontaneous only at higher temperatures.
When delta H is positive and delta S is negative, delta G is always positive, and the reaction is nonspontaneous at all temperatures.
For any reaction mixture composition, the delta G for the reaction is the sum of the standard free energy and RT times the natural log of the reaction quotient.
When the reactants and products are at equilibrium, the free energy change is zero, and the reaction quotient equals the equilibrium constant. So, the standard free energy change equals negative RT ln(K).
If delta G naught is less than zero, ln(K) is positive, meaning K is greater than 1. In this case, product formation is favored at equilibrium. The larger the equilibrium constant, the greater the decrease in Gibbs free energy.
Reactions with negative delta G values involve the release of free energy to the surroundings and are called ‘exergonic’ reactions.
Conversely, if delta G naught is greater than zero, ln(K) is negative, meaning K is less than 1, and the reverse direction of the reaction is favored.
Reactions with a positive delta G absorb free energy from the surroundings and are called ‘endergonic’ reactions.
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Q1: What does delta G tell you about whether a reaction will occur spontaneously?
Delta G, or Gibbs free energy change, indicates a reaction's spontaneity. A negative delta G means the reaction is spontaneous and releases free energy to surroundings, called an exergonic reaction. A positive delta G means the reaction is nonspontaneous and absorbs free energy, called an endergonic reaction. When delta G equals zero, the system is at equilibrium with forward and reverse driving forces balanced.
Q2: How do enthalpy and entropy changes determine delta G at different temperatures?
Delta G depends on both enthalpy and entropy changes and temperature. When delta H is negative and delta S is positive, delta G is always negative, making the reaction spontaneous at all temperatures. When both are negative, the reaction is spontaneous only at low temperatures. When both are positive, spontaneity occurs only at higher temperatures. When delta H is positive and delta S is negative, delta G is always positive, making the reaction nonspontaneous at all temperatures.
Q3: What is the relationship between the equilibrium constant and standard free energy change?
The standard free energy change equals negative RT times the natural logarithm of the equilibrium constant. If delta G naught is less than zero, the equilibrium constant is greater than 1, favoring product formation. If delta G naught is greater than zero, the equilibrium constant is less than 1, favoring the reverse reaction. This relationship links these two essential thermodynamic properties and allows deriving one from the other.
Q4: How does the reaction quotient Q relate to delta G and reaction direction?
For any reaction mixture composition, delta G equals the standard free energy plus RT times the natural log of the reaction quotient. When Q is less than the equilibrium constant K, the reaction proceeds forward until equilibrium is reached. When Q exceeds K, the reaction proceeds in reverse. At equilibrium, Q equals K and delta G equals zero, indicating no net driving force in either direction.
Q5: What is the difference between exergonic and endergonic reactions?
Exergonic reactions have negative delta G values and release free energy to surroundings, proceeding spontaneously. Endergonic reactions have positive delta G values and absorb free energy from surroundings, occurring nonspontaneously. The magnitude of delta G reflects the driving force strength. Larger negative delta G values indicate stronger spontaneity, while larger positive values indicate greater resistance to the forward reaction.
Q6: How does temperature affect the spontaneity of reactions with positive enthalpy and entropy changes?
When both delta H and delta S are positive, the reaction is temperature-dependent. At low temperatures, the negative TΔS term is small, making delta G positive and the reaction nonspontaneous. At higher temperatures, the TΔS term becomes large enough to overcome the positive delta H, making delta G negative and the reaction spontaneous. This explains why some endothermic reactions become favorable only at elevated temperatures.
Q7: How do nonstandard conditions affect the free energy change of a reaction?
Under nonstandard conditions with pressures other than 100 kPa or concentrations other than 1 M, delta G is calculated using the standard free energy change plus RT times the natural log of the reaction quotient. This equation shows how actual reaction conditions deviate from standard states. The reaction quotient Q allows predicting whether a reaction will proceed forward or reverse to reach equilibrium under any given set of conditions.