A reaction has a standard free-energy change of –12.40 kJ mol–1 (–2.964 kcal mol–1). Calculate the equilibrium constant for the reaction at 25 °C.
dG = -RT*lnK
To calculate the equilibrium constant (K) for a reaction using the standard free-energy change (ΔG°), you can use the equation:
ΔG° = -RT ln(K)
Where:
- ΔG° is the standard free-energy change (in joules).
- R is the gas constant (8.314 J/(mol·K)).
- T is the temperature in Kelvin.
- K is the equilibrium constant.
Given ΔG° = -12.40 kJ/mol, we need to convert it to J/mol:
ΔG° = -12.40 kJ/mol × 1000 J/kJ = -12400 J/mol
Next, we convert the temperature to Kelvin. We are given the temperature as 25 °C. To convert it to Kelvin, we use the equation:
T(K) = T(°C) + 273.15
T(K) = 25 °C + 273.15 = 298.15 K
Now, we can substitute the variables and solve for K:
-12400 J/mol = -8.314 J/(mol·K) × 298.15 K × ln(K)
To isolate ln(K), divide both sides of the equation by -8.314 J/(mol·K) × 298.15 K:
ln(K) = -12400 J/mol / (8.314 J/(mol·K) × 298.15 K)
ln(K) ≈ -4.768
K ≈ e^-4.768
Using a calculator, we find that K ≈ 0.00869.
So, the equilibrium constant for the reaction at 25 °C is approximately 0.00869.