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.