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?
Question
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?
Solution
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.
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