Equilibrium Constant and Gibbs Free Energy Calculation

How can we calculate ΔG for a reaction if the equilibrium constant K is given?

The equilibrium constant K for a reaction is determined to be 4.28 at 24.02°C. What is the ΔG for the reaction (in J/mol, rounding to the nearest one)?

Calculation of ΔG for the reaction:

ΔG for the reaction is approximately -3,890 J/mol.

The relationship between the equilibrium constant K and the Gibbs free energy change (∆G) for a reaction at a particular temperature can be described by the following equation:

∆G = -RT ln K

Where:

R is the gas constant (8.314 J/K/mol),

T is the temperature in Kelvin,

ln denotes the natural logarithm.

To solve for ∆G, we need to know the value of K and the temperature.

Plugging in the values:

ΔG = - (8.314 J/mol × K) × 297.17 K × ln(4.28)

ΔG = - (8.314 J/mol × K) × 297.17 K × 1.449

ΔG = - 3,892 J/mol

Rounding to the nearest one, we get:

ΔG = -3,890 J/mol

By using the equation above, we can calculate the Gibbs free energy change (∆G) for a reaction based on the equilibrium constant K and the temperature. Understanding this calculation is important in determining the spontaneity of chemical reactions.