Chapter 18, Problem 80A

Interpretation Introduction

Interpretation:

The concentration of hydroxyl ion is to be calculated for given hydrogen ion concentration.

Concept introduction:

In an aqueous solution,

$\begin{array}{l}{k}_w=\left[H^{+}\right]\times \left[O{H}^{-}\right]\\ where\\ k_{w}isionicproductofwater\end{array}$

Answer to Problem 80A

$\left[O{H}^{-}\right]=1.85\times {10}^{-12}M$

Explanation of Solution

$\begin{array}{l}{k}_w=\left[H^{+}\right]\times \left[O{H}^{-}\right]\\ \therefore \left[O{H}^{-}\right]=\frac{k_w}{\left[H^{+}\right]}\\ k_w={10}^{-14}at298K\end{array}$

Given:

$\left[H^{+}\right]=5.40\times {10}^{-3}M$

On substituting the values in the formula:

$\begin{array}{c}\left[O{H}^{-}\right]=\frac{{10}^{-14}}{5.4\times {10}^{-3}}\\ =1.85\times {10}^{-12}M\end{array}$

Conclusion

Thus,

$\left[O{H}^{-}\right]=1.85\times {10}^{-12}M$