ΔG° = -RT ln K

Definition

ΔG° is the standard Gibbs free energy change, which represents the maximum amount of useful work that can be obtained from a spontaneous chemical reaction at constant temperature and pressure. This term is directly related to the equilibrium constant (K) of the reaction, as described by the equation ΔG° = -RT ln K, where R is the universal gas constant, and T is the absolute temperature.

5 Must Know Facts For Your Next Test

1. The standard Gibbs free energy change, ΔG°, is a measure of the maximum amount of useful work that can be obtained from a spontaneous chemical reaction at standard conditions (25°C and 1 atm).
2. The negative sign in the equation ΔG° = -RT ln K indicates that a spontaneous reaction has a decrease in Gibbs free energy, meaning the reaction is thermodynamically favorable.
3. The value of ΔG° determines the direction and extent of a chemical reaction, with negative values indicating a spontaneous reaction and positive values indicating a non-spontaneous reaction.
4. The equilibrium constant (K) is a measure of the relative concentrations of products and reactants at equilibrium, and it is related to the Gibbs free energy change through the equation ΔG° = -RT ln K.
5. The magnitude of the equilibrium constant (K) is directly related to the value of ΔG°, with larger values of K corresponding to more negative values of ΔG°, indicating a more favorable and spontaneous reaction.

Review Questions

• Explain how the equation ΔG° = -RT ln K can be used to determine the spontaneity of a chemical reaction.
  • The equation ΔG° = -RT ln K provides a direct relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant (K) of a chemical reaction. If the value of ΔG° is negative, the equation indicates that the natural logarithm of the equilibrium constant (ln K) will be positive, meaning that the equilibrium constant (K) will be greater than 1. This signifies that the reaction is spontaneous and will proceed naturally towards the products. Conversely, if ΔG° is positive, the equation shows that ln K will be negative, and K will be less than 1, indicating a non-spontaneous reaction that requires the input of energy to proceed.
• Describe how the values of ΔG° and K can be used to predict the extent of a chemical reaction at equilibrium.
  • The relationship between ΔG° and K can be used to predict the extent of a chemical reaction at equilibrium. A more negative value of ΔG° corresponds to a larger value of the equilibrium constant (K), indicating that the reaction will proceed further towards the products at equilibrium. Conversely, a less negative or positive value of ΔG° corresponds to a smaller value of K, meaning that the reaction will not proceed as far towards the products and will have a lower extent of conversion at equilibrium. This relationship allows chemists to use the ΔG° or K values to estimate the position of the equilibrium and the relative concentrations of reactants and products at the end of the reaction.
• Analyze how changes in temperature can affect the values of ΔG° and K, and the implications for the spontaneity and extent of a chemical reaction.
  • According to the equation ΔG° = -RT ln K, changes in temperature (T) will affect the values of both ΔG° and K. As temperature increases, the value of -RT ln K will become more negative, resulting in a more negative value of ΔG°. This indicates that the reaction will become more spontaneous at higher temperatures. Additionally, the equilibrium constant (K) will increase with rising temperature, meaning the reaction will proceed further towards the products at equilibrium. Conversely, decreasing the temperature will make the reaction less spontaneous, with a less negative ΔG° and a smaller K value, resulting in a lower extent of conversion at equilibrium. Understanding these relationships between temperature, ΔG°, and K is crucial for predicting and controlling the behavior of chemical reactions in various applications.

Related terms

Gibbs Free Energy:

A thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature and pressure.

Equilibrium Constant (K): The ratio of the concentrations of the products to the reactants of a chemical reaction at equilibrium, raised to the power of their stoichiometric coefficients.

Spontaneous Reaction: A chemical reaction that occurs naturally without the input of external energy, resulting in a decrease in Gibbs free energy.