Question

A solution contains a mixture of acids: 0.50 M HA (K_a = 1.0 × 10^-3), 0.20 M HB (K_a = 1.0 × 10^-10), and 0.10 M HC (K_a = 1.0 × 10^-12). Calculate the [H⁺] in this solution.

Short answer

Total conc. of [H⁺] is 0.022.

Step-by-step solution

[H+] ion concentration of HA

For weak acids

$\begin{array}{l}{\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{K}}_{\text{a}}\text{×C}}\\ {\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{1×10}}^{\text{-3}}\text{×0.5}}{\text{=2.2×10}}^{\text{-2}}\end{array}$

[H+] ion concentration of HB

For weak acids

$\begin{array}{l}{\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{K}}_{\text{a}}\text{×C}}\\ {\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{1×10}}^{\text{-10}}\text{×0.2}}\\ {\text{[H}}^{\text{+}}{\text{]=4.5×10}}^{\text{-6}}\end{array}$

[H+] ion concentration of HC 

For weak acids

$\begin{array}{l}{\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{K}}_{\text{a}}\text{×C}}\\ {\text{[H}}^{\text{+}}\text{]=}\sqrt{{\text{1×10}}^{\text{-12}}\text{×0.1}}\\ {\text{[H}}^{\text{+}}{\text{]=3.2×10}}^{\text{-7}}\end{array}$

As the concentration due to HB and HC is very low so total conc. Of [H⁺] is 0.022.