When cadmium metal is reduced Cu^2+ in solution Cd^2+ forms in addition to copper metal. If ∆G° =-143kJ, Calculate K at 25°C
To find the equilibrium constant (K) for the reaction, we can use the relationship between Gibbs free energy change (ΔG°) and the equilibrium constant, which is given by the formula:
ΔG° = -RT * ln(K)
Where:
- ΔG° is the standard Gibbs free energy change (-143 kJ/mol)
- R is the universal gas constant (8.314 J/mol*K)
- T is the temperature (25°C = 298.15 K)
- K is the equilibrium constant we want to determine
First, we need to change the value of ΔG° to J/mol (since R is given in J/mol*K). We can do this by multiplying it by 1000:
ΔG° = -143 kJ/mol * 1000 J/kJ = -143,000 J/mol
Now, we can solve for K:
-143,000 J/mol = -1 * (8.314 J/mol*K) * (298.15 K) * ln(K)
To isolate ln(K), we can divide both sides by -1 * R * T:
ln(K) = -143,000 J/mol / [(-1) * (8.314 J/mol*K) * (298.15 K)] = 6.4047
Now, we can take the inverse of the natural logarithm (e^x) to solve for K:
K = e^(6.4047) ≈ 603.57
So, the equilibrium constant K for the reaction at 25°C is approximately 603.57.