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
The balanced chemical equation for the reaction is:
Cd(s) + Cu^2+(aq) -> Cd^2+(aq) + Cu(s)
The standard Gibbs free energy change, ∆G° for the reaction is given as 143 kJ.
The relationship between ∆G° and the equilibrium constant (K) for a reaction is given by:
∆G° = -RTlnK
where R is the gas constant (8.314 J/mol.K) and T is the temperature in Kelvin (25°C = 298 K).
Substituting the given values, we get:
143,000 J = -8.314 J/mol.K x 298 K x ln K
ln K = -143,000 J / (8.314 J/mol.K x 298 K) = -57.36
K = e^(-57.36) = 1.06 x 10^-25
Therefore, the equilibrium constant (K) at 25°C is 1.06 x 10^-25.
To calculate the equilibrium constant (K), we can use the relationship between ΔG° and K, which is given by the equation:
ΔG° = -RT ln(K)
Where:
ΔG° = standard Gibbs free energy change (143 kJ)
R = gas constant (8.314 J/(mol·K))
T = temperature (25°C = 298 K)
Let's substitute the values into the equation and solve for K:
143 kJ = -8.314 J/(mol·K) * 298 K * ln(K)
First, let's convert the ΔG° value to J:
143 kJ = 143 x 10^3 J
Next, we rearrange the equation to solve for ln(K):
ln(K) = -143 x 10^3 J / (-8.314 J/(mol·K) * 298 K)
ln(K) = 173.01
Now we can solve for K by taking the exponent of both sides:
K = e^(ln(K))
K = e^(173.01)
Using a calculator, we find:
K ≈ 2.19 x 10^75