What is the value of K for this aqueous reaction at 298 K? Delta G= 13.75 K/mol?

gibbs-free-energy

#1

What is the value of K for this aqueous reaction at 298 K? Delta G= 13.75 K/mol?
A+B<–> C+D

Concepts and reason
The value of reaction quotient of a chemical reaction that reaches the equilibrium is called as equilibrium constant.
Equilibrium constant K is related to temperature and standard Gibbs free energy change as shown in the following formula.
image
Here, image is free energy change, T is temperature, R is gas constant, and K is equilibrium constant.
Because the system is thermodynamic system, we can use the above formula to calculate the equilibrium constant.
Calculate the equilibrium constant by substituting the given values.

Fundamentals
For a reaction, equilibrium constant can be calculated by using concentrations of the reactants and products.
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Gibbs free energy is the available energy in a system. The free energy change depends on several thermodynamic parameters like enthalpy change, entropy change, and temperature.

Answer:

The relationship between the equilibrium constant and Gibbs free energy change is as follows:
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Gibbs free energy change is image
image

Convert the free energy change from kilo joules into joules by using the following conversion factor.
1 KJ = 1000 J
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Calculate the equilibrium constant by substituting the Gibbs free energy change in the formula.

Substitute the values of Gibbs energy change, temperature in the above formula.
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Equilibrium constant (K) of the reaction is 0.0039.

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By substituting all the parameters in the formula, the equilibrium constant obtained with correct significant figures as 0.0039.