Question

Calculate the pH of a solution formed by mixing 100.0 mL of 0.100 M NaF and 100.0 mL of 0.025 M HCl.

Short answer

Answer

The value of pH=3.62.

Step-by-step solution

Henderson-Hasselbalch equation

The Henderson-Hasselbalch equation can be denoted as,

$\mathit{p}\mathit{H}\mathbf{=}\mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\frac{\left[conjugatebase\right]}{\left[acid\right]}$

Given Information

The information can be given as $\mathbf{100}\mathit{m}\mathit{L}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{1}\mathit{M}\mathit{N}\mathit{a}\mathit{F}\mathbf{}\mathit{a}\mathit{n}\mathit{d}\mathbf{}\mathbf{100}\mathit{m}\mathit{L}\mathbf{}\mathit{o}\mathit{f}\mathbf{}\mathbf{0}\mathbf{.}\mathbf{025}\mathit{M}\mathit{H}\mathit{C}\mathit{l}\mathbf{.}$

The number of moles of NaF and HCl can be denoted as,

$$\begin{gathered} \mathit{N}\mathit{a}\mathit{F}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{1}\mathbf{m}\mathbf{o}\mathbf{l}}{\mathbf{100}\mathbf{m}\mathbf{L}}\mathbf{\times }\mathbf{100}\mathit{m}\mathit{L} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{01}\mathit{m}\mathit{o}\mathit{l} \\ \mathit{H}\mathit{C}\mathit{l}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{025}\mathbf{m}\mathbf{o}\mathbf{l}}{\mathbf{1000}\mathbf{m}\mathbf{L}}\mathbf{\times }\mathbf{100}\mathit{m}\mathit{L} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{0025}\mathit{m}\mathit{o}\mathit{l} \end{gathered}$$

Finding the value of pH

The formation of reaction can be denoted as,

${\mathit{H}}^{\mathbf{+}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{F}}^{\mathbf{-}}\mathbf{\to }\mathit{H}\mathit{F}$

Then,

$$\begin{gathered} \mathit{p}\mathit{H}\mathbf{=}\mathit{p}{\mathit{K}}_{\mathbf{a}}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\frac{\left[F^{-}\right]}{\left[HF\right]} \\ \mathbf{=}\mathbf{3}\mathbf{.}\mathbf{14}\mathbf{+}\mathit{l}\mathit{o}\mathit{g}\left(\frac{0.0075mol/200mL}{0.0025mol/200mL}\right) \\ \mathit{p}\mathit{H}\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{62} \end{gathered}$$