A reaction has a standard free-energy change of − 13.50 KJ mol − 1...

Naomi Rowland

Naomi Rowland

Answered

2022-11-26

A reaction has a standard free-energy change of 13.50  KJ mol 1 ( 3.227  kcal mol 1 ). Calculate the equilibrium constant for the reaction at 25 degree Celsius

Answer & Explanation

Dakota Murillo

Dakota Murillo

Expert

2022-11-27Added 6 answers

General guidance
Concepts and reason
This problem is based on the concept of thermodynamics.
The thermodynamic potential which is used to calculate maximum reversible work done at constant pressure and temperature is called Gibbs free energy.
Fundamentals
In a chemical reaction, the value of reaction quotient when the reaction reach equilibrium is called equilibrium constant.
The relation between change in Gibbs free energy Δ G and equilibrium constant ( K ) is as follow, Δ G = R T ln K...… (1)
Here, T is temperature and R is gas constant.
Convert change in Gibbs free energy in joules per mole as follows:
Δ G = ( 13.50 k J m o l ) ( 1000 J 1 k J ) = 13500 J   m o l 1
Convert temperature in kelvin as follows:
T k = T c + 273.15
Substitute 25 C for T in above equation as follows:
T k = ( 25 + 273.15 ) K = 298.15 K
The gibbs free energy is in k J / m o l It is converted into J / m o l by the use of conversion factor. Temperature is converted into Kelvin by adding 273.15 factor to it.
Rearrange equation (1) for K as follows:
ln K = Δ G R T K = exp ( Δ G R T )
Substitute 8.314 J K 1 m o l 1 for R, 13500 J   m o l 1 for Δ G and 298.15 K for T in above equation as follows:
K = exp ( ( 13500 J   m o l 1 ) ( 8.314 J   K 1 m o l 1 ) ( 298.15 K ) ) K = 231.86
The equilibrium constant is 231.86.

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