Question

Enter your answer in the provided box. Ksp for Co(OH)2 at 25°C is 3.3 × 10?16. Using this and data from your textbook, calculate the value of ?G o f for Co(OH)2(s). kJ/mol

Answer 1

The value of ?G°f for Co(OH)2(s) is -25.94 kJ/mol.

Step-by-step explanation:

To calculate the standard Gibbs free energy change (?G°f) for Co(OH)2(s), we can use the equilibrium constant, Ksp. The equation for Ksp for Co(OH)2 is:

Co(OH)2(s) → Co2+(aq) + 2OH-(aq)

We can use the stoichiometry of the reaction to relate the concentration of Co2+ ions to the concentration of Co(OH)2(s).

As the concentration of Co(OH)2(s) does not change (since it is a solid), we can assume it is constant and equal to 1. Therefore, the concentration of Co2+ ions is equal to the solubility of Co(OH)2(s), which we can calculate using the value of Ksp provided.

Ksp = [Co2+][OH-]2

[Co2+] = x (solubility of Co(OH)2)

[OH-] = 2x (due to stoichiometry)

Substituting these values into the Ksp expression:

Ksp = x(2x)2 = 4x3

Substituting the value of Ksp provided (3.3 × 10-16):

3.3 × 10-16 = 4x3

Solving for x using the cubic root:

x = (3.3 × 10-16/4)(1/3)

x = 1.27 × 10-6

Therefore, the solubility of Co(OH)2(s) is 1.27 × 10-6 M. Since ?G°f = -RT ln(Ksp), we can calculate the ?G°f using the ideal gas constant (R) and the temperature (25°C) in Kelvin:

?G°f = -(8.314 J/mol·K)(298.15 K) ln(3.3 × 10-16)

?G°f = -25.94 kJ/mol