Chapter 22, Problem 14STP

To determine

To calculate: The concentration of hydronium ion at pH value 1.0 if pH is 3.0 at hydronium ion concentration 0.0010 M and it drops to 1.0 when hydronium ion concentration increases by factor of 100.

Explanation of Solution

Introduction:

The relationship between pH and hydronium ion concentration is as follows:

  $\text{pH}=-\log \left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]$

Here, $\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]$ is concentration of hydronium ion.

It is given that if pH is 3.0, the hydronium ion concentration of solution is 0.0010 M. It proves the following relation:

  $\begin{array}{c}\text{pH}=-\log \left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\\ 3=-\log \left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\\ \left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]={10}^{-3}\\ =0.0010\text{ M}\end{array}$

Now, when pH drops to 1, hydronium ion concentration increases by a factor of 100. Thus, hydronium ion concentration becomes:

  $\begin{array}{c}\left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]=100\times 0.0010\text{ M}\\ =0.1\text{ M}\end{array}$

This can be further confirmed by using the following relation:

  $\begin{array}{c}\text{pH}=-\log \left[{\text{H}}_{\text{3}}{\text{O}}^{+}\right]\\ =-\log \left(0.1\right)\\ =-\left(-1\right)\\ =1\end{array}$

Conclusion:

Thus, the hydronium ion concentration at pH 1 is 0.1 M.