Question

Consider a weak acid HA with a Ka value of 1.6 x 10-7. Calculate the pH of a solution that is 5.0 x 10-7 M HA and 5.0 x 10-7 M NaA.

Short answer

Answer

The pH of the buffer solution can be found as 6.8.

Step-by-step solution

Given Information

The weak acid HA’s concentration and its conjugate base is $\mathbf{5}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathit{M}$The constant for acid dissociation for a weak acid is $\mathbf{1}\mathbf{.}\mathbf{6}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{7}}\mathit{M}$

Calculation of Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation can be denoted as,

$$\begin{gathered} \mathit{p}\mathit{H}\mathbf{=}\mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\frac{\left[A^{-}\right]}{\left[HA\right]} \\ \mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{-}\mathit{l}\mathit{o}\mathit{g}{\mathit{K}}_{\mathbf{a}} \\ \mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{-}\mathit{l}\mathit{o}\mathit{g}\left(1.6\times {10}^{-7}\right) \\ \mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8} \end{gathered}$$

Substitution of values in equation to find pH

On putting all the values,

$$\begin{gathered} \mathit{p}\mathit{H}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\left(\frac{5\times {10}^{-7}}{5\times {10}^{-7}}\right) \\ \mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\left(1\right) \\ \mathit{p}\mathit{H}\mathbf{=}\mathbf{6}\mathbf{.}\mathbf{8} \end{gathered}$$