Determine the pH of a solution that is 0.125 M in CO3^2−. For carbonic acid (H2CO3), Ka1=4.3×10^−7 and Ka2=5.6×10^−11. What is the pH of the solution?

• A. pH = 13.00
• B. pH = 9.25
• C. pH = 7.00
• D. pH = 11.37

Answer: (D)

Verified step by step guidance

1. Identify the relevant chemical species and equilibria: In this problem, we are dealing with carbonate ion (CO3^2−) in solution, which can undergo hydrolysis to form bicarbonate (HCO3^−) and hydroxide ions (OH^−). The relevant equilibria are CO3^2− + H2O ⇌ HCO3^− + OH^−.
2. Use the equilibrium constant for the hydrolysis reaction: The equilibrium constant for the hydrolysis of CO3^2− can be derived from the second dissociation constant of carbonic acid (Ka2) and the ion product of water (Kw). The expression is Kb = Kw / Ka2, where Kw = 1.0 × 10^−14.
3. Set up the equilibrium expression: For the hydrolysis reaction, the equilibrium expression is Kb = [HCO3^−][OH^−] / [CO3^2−]. Assume that the initial concentration of CO3^2− is 0.125 M and that the change in concentration due to hydrolysis is x, so [HCO3^−] = x and [OH^−] = x.
4. Solve for x using the equilibrium expression: Substitute the known values into the equilibrium expression to solve for x, which represents the concentration of OH^− ions in the solution. This involves solving the equation Kb = x^2 / (0.125 - x).
5. Calculate the pH: Once you have the concentration of OH^− ions, calculate the pOH using the formula pOH = -log[OH^−]. Then, convert pOH to pH using the relationship pH + pOH = 14. This will give you the pH of the solution.