Question

Calculate the pH of a 1.0 × 10^-7 M solution of NaOH in water.

Short answer

Answer

pH of the 1.0 × 10^-7 M NaOH = 7.2

Step-by-step solution

Deriving Formula

As the solution is dilute so amount of OH^- ions which comes from water cannot be ignored.

Positive charge = Negative Charge

In the given case,

$$\begin{gathered} \left[{\mathrm{OH}}^{-}\right]=\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{Na}}^{+}\right] \\ \left[{\mathrm{Na}}^{+}\right]=1\times {10}^{-7} \\ {}^{\mathrm{K}}\mathrm{w}=\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{OH}}^{-}\right]\Rightarrow \left[{\mathrm{H}}^{+}\right]=\frac{{}^{\mathrm{K}}\mathrm{w}}{\left[{\mathrm{OH}}^{-}\right]} \\ \left[{\mathrm{OH}}^{-}\right]=\left[{\mathrm{Na}}^{+}\right]+\frac{{}^{\mathrm{K}}\mathrm{w}}{\left[{\mathrm{OH}}^{-}\right]} \end{gathered}$$