Chapter 19, Problem 63A

a.

Interpretation Introduction

Interpretation : The pH of the solution is to be found.

Concept Introduction : The negative logarithm of the concentration of hydrogen ions is the pH of a solution. The formula to calculate pH is given as:

  $\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}$

Answer to Problem 63A

The pH of the solution is $12$ and it is basic in nature.

Explanation of Solution

The concentration of hydroxide ion is $1\times {10}^{-2}\text{M}$ .

The formula to calculate pH is given as:

  $\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}$

The concentration of hydrogen ions is given by rearranging the formula of the ion product constant for water $\left({\text{K}}_{\text{w}}\right)$ .

  $[{\text{H}}^{\text{+}}]=\frac{{\text{K}}_w}{[{\text{OH}}^{-}\text{]}}$

To calculate the concentration of hydrogen ions, substitute the values in the above formula:

  $\begin{array}{c}[{\text{H}}^{\text{+}}]=\frac{{\text{K}}_w}{[{\text{OH}}^{-}\text{]}}\\ =\frac{1\times {10}^{-14}{\text{M}}^2}{1\times {10}^{-2}\text{M}}\\ =1\times {10}^{-12}\text{M}\end{array}$

To calculate the pH of the solution, substitute the values in the pH formula:

  $\begin{array}{c}\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}\\ \text{=}-\log \left(1\times {10}^{-12}\right)\\ \text{pH}=12\end{array}$

Since the pH is $12$ , the solution is basic in nature.

b.

Interpretation Introduction

Interpretation : The pH of the solution is to be found.

Concept Introduction : The negative logarithm of the concentration of hydrogen ions is the pH of a solution. The formula to calculate pH is given as

  $\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}$

Answer to Problem 63A

The pH of the solution is $2$ and it is acidic in nature.

Explanation of Solution

The concentration of hydrogen ions is $1\times {10}^{-2}\text{M}$ .

The formula to calculate pH is given as

  $\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}$

To calculate the pH of the solution, substitute the values in the above formula:

  $\begin{array}{c}\text{pH=}-{\text{log[H}}^{\text{+}}\text{]}\\ \text{=}-\log \left(1\times {10}^{-2}\right)\\ \text{pH}=2.00\end{array}$

Since the pH is $2.00$ , the solution is acidic in nature.