Chapter 17, Problem 5CR

Interpretation Introduction

Interpretation:

The amphoteric nature of water is to be explained. The chemical equation for the autoionization of water and the expression for the equilibrium constant, ${\text{K}}_{\text{w}}$ for the given reaction are to be stated. At ${\text{25 }}^{\text{ο}}\text{C}$, the values of ${\text{K}}_{\text{w}},\left[{\text{H}}^{+}\right]$ and $\left[{\text{OH}}^{-}\right]$ are to be determined. The comparison of $\left[{\text{H}}^{+}\right]$ with $\left[{\text{OH}}^{-}\right]$ in an acidic solution and in basic solution is to be stated.

Concept Introduction:

The substances which have ability to accept a proton as well as to donate a proton are known as amphoteric substances. The partially dissociation of a liquid into its ions is known as autoionization reaction.

Answer to Problem 5CR

In the reaction of ammonia and water, ammonia will accept a proton from water and acts as a base and water donates a proton and acts as an acid. The corresponding chemical reaction is shown below.

${\text{NH}}_{\text{3}}(aq)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{NH}}_4{}^{+}(aq)+{\text{OH}}^{-}(aq)$

In the reaction of water and hydrochloric acid, water will accept a proton from hydrochloric acid and acts as a base. The corresponding chemical reaction is shown below.

$\text{HCl}(aq)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\to {\text{H}}_3{\text{O}}^{+}(aq)+{\text{Cl}}^{-}(aq)$

Both the above reactions show that water is an amphoteric substance.

The chemical equation for the autoionization of water is shown below.

${\text{H}}_{\text{2}}\text{O}(l)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{H}}_3{\text{O}}^{+}(aq)+{\text{OH}}^{-}(aq)$

The value of ${\text{K}}_{\text{W}}$ is $1\times {10}^{-14}$ at ${25}^{\circ }\text{C}$, where, $\left[{\text{H}}^{+}\right]=\left[{\text{OH}}^{-}\right]$. The equilibrium constant for the above reaction is,

$\text{K}=\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]$

The concentration of ${\text{H}}^{+}$ and ${\text{OH}}^{-}$ is $1\times {10}^{-7}\text{M}$.

The hydrolysis of an acid results in the formation of hydrogen ions while the hydrolysis of a base results in the formation of the hydroxyl ions. In the acidic solution, the concentration of hydrogen ions is greater than the concentration of hydroxide ion. While in basic solution, the concentration of hydroxyl ion is greater than the concentration of the hydrogen ion.

Explanation of Solution

According to Bronsted-Lowry concept, the stronger base (than water) has tendency to accept the proton from the water. In the reaction of ammonia and water, here, water donates a proton to ammonia and acts as an acid. The corresponding chemical reaction is shown below.

${\text{NH}}_{\text{3}}(aq)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{NH}}_4{}^{+}(aq)+{\text{OH}}^{-}(aq)$

Similarly, the stronger acid (than water) has tendency to donate a proton to water. In the reaction of water and hydrochloric acid, the water accepts a proton from hydrochloric acid and acts as a base. The corresponding chemical reaction is shown below.

$\text{HCl}(aq)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\to {\text{H}}_3{\text{O}}^{+}(aq)+{\text{Cl}}^{-}(aq)$

Hence, water is an amphoteric substance.

The chemical equation for the autoionization of water is shown below.

${\text{H}}_{\text{2}}\text{O}(l)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{H}}_3{\text{O}}^{+}(aq)+{\text{OH}}^{-}(aq)$

The equilibrium constant for the above reaction is as follows:

$\begin{array}{c}\text{K}=\frac{\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]}{{\left[{\text{H}}_{\text{2}}\text{O}\right]}^2}\\ \text{K}{\left[{\text{H}}_{\text{2}}\text{O}\right]}^2=\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]\\ {\text{K}}_{\text{W}}=\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]\end{array}$ $\left({\text{K}}_{\text{W}}=\text{K}{\left[{\text{H}}_{\text{2}}\text{O}\right]}^2\right)$

The value of ${\text{K}}_{\text{W}}$ is $1\times {10}^{-14}$ at ${25}^{\circ }\text{C}$, where, $\left[{\text{H}}^{+}\right]=\left[{\text{OH}}^{-}\right]$. The concentration of $\left[{\text{H}}^{+}\right]$ and $\left[{\text{OH}}^{-}\right]$ is calculated as follows:

$\begin{array}{c}{\text{K}}_{\text{W}}=\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]\\ 1\times {10}^{-14}={\left[{\text{H}}_3{\text{O}}^{+}\right]}^2\left(\because \left[{\text{H}}_3{\text{O}}^{+}\right]=\left[{\text{OH}}^{-}\right]\text{at}{25}^{\circ }\text{C}\right)\\ \left[{\text{H}}_3{\text{O}}^{+}\right]=\left[{\text{OH}}^{-}\right]=1\times {10}^{-7}\text{M}\end{array}$

Therefore, the concentration of ${\text{H}}^{+}$ and ${\text{OH}}^{-}$ is $1\times {10}^{-7}\text{M}$.

The hydrolysis of an acid results in the formation of hydrogen ions while the hydrolysis of a base results in the formation of the hydroxyl ions. In the acidic solution, the concentration of hydrogen ions is greater than the number of hydroxide ion. While in basic solution, the concentration of hydroxyl ion is greater than the concentration of the hydrogen ions.

Conclusion

According to Bronsted-Lowry concept, the base (stronger than water) has tendency to accept the proton from the water. Similarly, an acid (stronger than water) has tendency to donate a proton to water.

In the reaction of ammonia and water, ammonia will accept a proton from water and acts as a base and water donates a proton and acts as an acid. The corresponding chemical reaction is shown below.

${\text{NH}}_{\text{3}}(aq)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{NH}}_4{}^{+}(aq)+{\text{OH}}^{-}(aq)$

In the reaction of water and hydrochloric acid, water will accept a proton from hydrochloric acid and acts as a base. The corresponding chemical reaction is shown below.

$\text{HCl}(aq)+{\text{H}}_{\text{2}}\text{O}\left(\text{l}\right)\to {\text{H}}_3{\text{O}}^{+}(aq)+{\text{Cl}}^{-}(aq)$

Both the above reactions show that water is an amphoteric substance.

The chemical equation for the autoionization of water is shown below.

${\text{H}}_{\text{2}}\text{O}(l)+{\text{H}}_{\text{2}}\text{O}(l)\rightleftharpoons {\text{H}}_3{\text{O}}^{+}(aq)+{\text{OH}}^{-}(aq)$

The equilibrium constant for the above reaction is,

$\text{K}=\frac{\left[{\text{H}}_3{\text{O}}^{+}\right]\left[{\text{OH}}^{-}\right]}{{\left[{\text{H}}_{\text{2}}\text{O}\right]}^2}$

The concentration of ${\text{H}}^{+}$ and ${\text{OH}}^{-}$ is $1\times {10}^{-7}\text{M}$.

The hydrolysis of an acid results in the formation of hydrogen ions while the hydrolysis of a base results in the formation of the hydroxyl ions. In the acidic solution, the concentration of hydrogen ions is greater than the number of hydroxide ion. While in basic solution, the concentration of hydroxyl ion is greater than the concentration of the hydrogen ion.