What is the relationship between the standard free-energy change, ∆G°, for a reaction and the equilibrium constant, K? What is the sign of ∆G° when: (a) K > 1? (b) K = 1? (c) K < 1?

Name: Chemistry
Author: McMurry
ISBN: 9781292336145

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Understand the relationship between the standard free-energy change (\( \Delta G^\circ \)) and the equilibrium constant (\( K \)) using the equation: \( \Delta G^\circ = -RT \ln K \), where \( R \) is the universal gas constant and \( T \) is the temperature in Kelvin.

Analyze the equation \( \Delta G^\circ = -RT \ln K \) to determine the sign of \( \Delta G^\circ \) based on the value of \( K \).

For case (a), when \( K > 1 \), \( \ln K \) is positive, making \( \Delta G^\circ \) negative, indicating that the reaction is spontaneous under standard conditions.

For case (b), when \( K = 1 \), \( \ln K \) is zero, resulting in \( \Delta G^\circ = 0 \), meaning the system is at equilibrium under standard conditions.

For case (c), when \( K < 1 \), \( \ln K \) is negative, making \( \Delta G^\circ \) positive, indicating that the reaction is non-spontaneous under standard conditions.

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Standard Free Energy Change (∆G°)

The standard free energy change (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction under standard conditions (1 M concentration, 1 atm pressure, and a specified temperature). A negative ∆G° suggests that a reaction is spontaneous, while a positive ∆G° indicates non-spontaneity. It is a crucial factor in predicting whether a reaction will proceed in the forward direction.

Equilibrium Constant (K)

The equilibrium constant (K) is a dimensionless value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. A K value greater than 1 indicates that products are favored at equilibrium, while a K value less than 1 suggests that reactants are favored. The value of K provides insight into the extent of a reaction's progress towards completion.

Relationship between ∆G° and K

The relationship between standard free energy change (∆G°) and the equilibrium constant (K) is described by the equation ∆G° = -RT ln(K), where R is the gas constant and T is the temperature in Kelvin. This equation shows that when K > 1, ∆G° is negative, indicating a spontaneous reaction; when K = 1, ∆G° is zero, indicating equilibrium; and when K < 1, ∆G° is positive, indicating non-spontaneity.