Exemplar Problems

Problem 7 : A weak base (BOH) with a dissociation constant K_b of $$(2.0 \times 10^{-5}) M$$ ionizes partially in water to give OH^- and B⁺ ions. Calculate the pH of a 0.02 M solution of (BOH).

Solution :

Given K_w at 25°C, we can use it to find the concentration of H⁺ ions [H⁺] in the solution.

$$(K_w = [H^+][OH^-] = 1.0 \times 10^{-14})$$

We are told that the solution is neutral, so [H⁺] = [OH^-]. Therefore,

$$([H^+][OH^-] = 1.0 \times 10^{-14})$$

$$([H^+] = 1.0 \times 10^{-7})$$

Take the square root of both sides:

$$[H^+] = \sqrt{1.0 \times 10^{-14}} = 1.0 \times 10^{-7} \text{ M}]$$

Now, we can calculate the pH:

$$[pH = -\log[H^+] = -\log(1.0 \times 10^{-7}) = 7]$$

So, the pH of the solution is 7.