At 200 C, the standard Gibbs free energy of the reaction: 3A + B <---> 2C + D is -15000 kJ/kmol. What is the reaction equilibrium constant?

To calculate the reaction equilibrium constant (K), we can use the relationship between the standard Gibbs free energy change (ΔG°) and the equilibrium constant, which is given by the equation:

ΔG° = -RT ln(K)

Where:

• ΔG° is the standard Gibbs free energy change,
• R is the universal gas constant,
• T is the temperature in Kelvin,
• K is the equilibrium constant.

We can rearrange this equation to solve for K:

K = e^(-ΔG°/RT)

Given:

• ΔG° = -15000 kJ/kmol = -15000 * 10^3 J/kmol (since 1 kJ = 10^3 J),
• R = 8.314 J/(mol*K) (universal gas constant),
• T = 200°C = 200 + 273.15 = 473.15 K (converted from Celsius to Kelvin).

Substituting these values into the equation gives:

K = e^(-(-15000 * 10^3)/(8.314 * 473.15))

Calculate the value inside the exponent first, then use the exponential function to find K.