Chapter 17, Problem 10PE

Interpretation Introduction

Interpretation:

The solutions A, B, C and D are to be arranged in the basis of increase in their acidity.

Concept introduction:

The $\text{pH}$ scale tells about the strength of an acid and a base. It measures the concentration of the hydrogen ions. There is an inverse relation between the $\text{pH}$ value and the concentration of the hydrogen ion. Higher the concentration of hydrogen ions, lesser the value of $\text{pH}$. There is an inverse relation between the $\text{pOH}$ value and the concentration of the hydroxide ion. Higher the concentration of hydroxide ions, lesser the value of $\text{pOH}$.

Answer to Problem 10PE

The increasing order of acidity is shown below.

$\begin{array}{c}\text{C}<\text{D}<\text{B}<\text{A}\\ {10}^{-7}\text{M}<{10}^{-5}\text{M}<{10}^{-4}\text{M}<{10}^{-2}\text{M}\end{array}$

Explanation of Solution

Solution A has the value of $\left[{\text{H}}^{\text{+}}\right]={10}^{-2}\text{M}$.

Solution B has the value of $\left[{\text{OH}}^{-}\right]={10}^{-10}\text{M}$.

The relationship between $\left[{\text{OH}}^{-}\right]$ and $\left[{\text{H}}^{\text{+}}\right]$ is shown below.

${\text{K}}_{\text{W}}=\left[{\text{H}}^{+}\right]\left[{\text{OH}}^{-}\right]$…(1)

The value of ${\text{K}}_{\text{W}}$ is ${10}^{-14}\text{M}$.

Substitute the values of $\left[{\text{OH}}^{-}\right]$ and ${\text{K}}_{\text{W}}$ in equation (1).

$\begin{array}{rll}{\text{10}}^{-14}& =& \left[{\text{H}}^{+}\right]\times {10}^{-10}\\ \left[{\text{H}}^{+}\right]& =& \frac{{\text{10}}^{-14}}{{10}^{-10}}\\ & =& {10}^{-4}\text{M}\end{array}$

So, for solution B, the value of $\left[{\text{H}}^{\text{+}}\right]$ is ${10}^{-4}\text{M}$.

Solution C has the value of $\text{pH}=7$.

The relationship between $\text{pH}$ and $\left[{\text{H}}^{\text{+}}\right]$ is shown below.

$\left[{\text{H}}^{+}\right]={10}^{-\text{pH}}\text{M}$…(2)

Substitute the value of $\text{pH}$ in equation (2).

$\left[{\text{H}}^{+}\right]={10}^{-\text{7}}\text{M}$

So, for solution C, the value of $\left[{\text{H}}^{\text{+}}\right]$ is ${10}^{-\text{7}}\text{M}$.

Solution D has the value of $\text{pOH}=9$.

The relationship between $\text{pH}$ and $\text{pOH}$ is shown below.

$\text{pH}+\text{pOH}=14$…(3)

Substitute the value of $\text{pOH}$ in equation (3).

$\text{pH}+\text{9}=14$

So, the value of $\text{pH}$ is calculated as shown below.

$\begin{array}{rll}\text{pH}& =& 14-9\\ & =& 5\end{array}$

Substitute the value of $\text{pH}$ in equation (2).

$\left[{\text{H}}^{+}\right]={10}^{-\text{5}}\text{M}$

So, for solution D, the value of $\left[{\text{H}}^{\text{+}}\right]$ is ${10}^{-\text{5}}\text{M}$.

The hydrogen ion concentration for solution A, B, C and D are ${10}^{-2}\text{M}$, ${10}^{-4}\text{M}$, ${10}^{-\text{7}}\text{M}$, ${10}^{-\text{5}}\text{M}$ respectively.

Therefore, the increasing order of acidity is shown below.

$\begin{array}{c}\text{C}<\text{D}<\text{B}<\text{A}\\ {10}^{-7}\text{M}<{10}^{-5}\text{M}<{10}^{-4}\text{M}<{10}^{-2}\text{M}\end{array}$

Conclusion

The acidity is arranged in increasing order as $\text{C}<\text{D}<\text{B}<\text{A}$.