Question

Calculate the pH of 7.0 × 10^-7 M HCl solution.

Short answer

Answer

pH of the 7.0 × 10^-7 M HCl = 6.15

Step-by-step solution

Deriving Formula

As the solution is dilute so amount of H⁺ ions which comes from water cannot be ignored.

Positive charge = Negative Charge

In the given case,

$$\begin{gathered} \left[{\mathrm{H}}^{+}\right]=\left[{\mathrm{OH}}^{-}\right]+\left[C{I}^{-}\right] \\ \left[C{I}^{-}\right]=7\times {10}^{-7} \\ {K}_W=\left[H^{+}\right]\left[O{H}^{-}\right]\Rightarrow \left[O{H}^{-}\right]=\frac{K_w}{\left[H^{+}\right]} \\ \left[H^{+}\right]=\left[CI\right]+\frac{K_w}{\left[H^{+}\right]} \end{gathered}$$

Calculation of pH for Given Solution

$$\begin{gathered} \left[{\mathrm{H}}^{+}\right]=\left(7\times {10}^{-7}\right)+\frac{1\times {10}^{-14}}{\left[{\mathrm{H}}^{+}\right]} \\ \left[{\mathrm{H}}^{+}\right]=\frac{7\times {10}^{-7}\left[{\mathrm{H}}^{+}\right]+1\times {10}^{-14}}{\left[{\mathrm{H}}^{+}\right]} \\ {\left[{\mathrm{H}}^{+}\right]}^2-7\times {10}^{-7}\left[{\mathrm{H}}^{+}\right]-1\times {10}^{-14}=0 \end{gathered}$$