Chapter 21, Problem 3TS

To determine

The pH of the solution when the concentration of hydronium ion in the solution of volume $\text{500 mL}$ is ${10}^{-1}\text{ M}=0.1\text{ M}$ after adding water to the solution.

Answer to Problem 3TS

The pH of the solution will be $1.3$ after adding the water.

Explanation of Solution

The pH is used for indicating the acidity of the solution. The concentration of hydronium ions is used for calculating the pH. The pH is calculated by taking the negative log of the concentration of the hydronium ions.

The concentration of the hydronium ions is given as $0.1\text{ M}$ .

The volume of the solution is doubled by adding the water. So, the concentration of the solution and the hydronium ions will be halved.

So, the concentration of the hydronium ions after adding water will be $0.05\text{ M}$ .

The pH can be calculated as,

$\begin{array}{c}\text{pH}=-\log {\text{[H}}^{+}]\\ =-\log (0.05\text{ M})\\ =-(-1.3)\\ =1.3\end{array}$

So, the pH is $1.3$ after adding the water.

Conclusion:

Therefore, the pH of the solution will be $1.3$ after adding the water.