Chapter 12, Problem 12.76PAE

(a)

Interpretation Introduction

To determine:

Write chemical equations and equilibrium, expressions for the reactions of ammonia with water.

Explanation of Solution

$N{H}_3\left(g\right)+H_{2}O\left(l\right)\to N{H}_4^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$

Apply the concept

$aA+bB\stackrel{}{\rightleftharpoons }cC+dD$

Rate of equilibrium reaction $\left(K\right)=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

So, here, rate of equilibrium reaction $\left(K\right)=\frac{\left[N{H}_4^{+}\right]\left[O{H}^{-}\right]}{\left[N{H}_3\right]\left[H_{2}O\right]}$.

In this equilibrium, water is pure liquid and its concentration is constant $\left[H_{2}O\right]=1$

Dissociation constant $\left(K_a\right)=\frac{\left[N{H}_4^{+}\right]\left[O{H}^{-}\right]}{\left[N{H}_3\right]}$

(b)

Interpretation Introduction

To determine:

Write chemical equations of equilibrium expressions for the reactions of methylamine. With water.

Explanation of Solution

$C{H}_{3}N{H}_2\left(aq\right)+H_{2}O\left(l\right)\to C{H}_{3}N{H}_3^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$

Apply the concept

$aA+bB\stackrel{}{\rightleftharpoons }cC+dD$

Rate of equilibrium reaction $\left(K\right)=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Rate of equilibrium reaction $\left(K\right)=\frac{\left[C{H}_{3}N{H}_3^{+}\right]\left(O{H}^{-}\right)}{\left[C{H}_{3}N{H}_2\right]\left[H_{2}O\right]}$.

In this equilibrium, $\left[H_{2}O\right]=1$

Dissociation constant $\left(K_a\right)=\frac{\left[C{H}_{3}N{H}_3^{+}\right]\left(O{H}^{-}\right)}{\left[C{H}_{3}N{H}_2\right]}$

(c)

Interpretation Introduction

To determine: Write chemical equations and equilibrium expressions for weak bases acetate ion $C^{3}CO{O}^{-}$ with water.

Explanation of Solution

$CHO{O}^{-}\left(aq\right)+H_{2}O\left(l\right)\to C{H}_{3}COOH\left(aq\right)+O{H}^{-}\left(aq\right)$

Apply the concept

$aA+bB\stackrel{}{\rightleftharpoons }cC+dD$

Rate of equilibrium reaction $\left(K\right)=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Rate of equilibrium constant is as $\left(K\right)=\frac{\left[C{H}_{3}COOH\right]\left[O{H}^{-}\right]}{\left[CHO{O}^{-}\right]\left[H_{2}O\right]}$.

In this equilibrium, $\left[H_{2}O\right]=1$

Dissociation constant $\left(K_a\right)=\frac{\left[C{H}_{3}COOH\right]\left[O{H}^{-}\right]}{\left[CHO{O}^{-}\right]}$

(d)

Interpretation Introduction

To determine: Write chemical equations and equilibrium expressions for hydrogen carbonate ion $HC{o}_3^{-}$ with water.

Explanation of Solution

$HC{o}_3^{-}\left(aq\right)+H_{2}O\left(l\right)\to H{2}_{}C{o}_3\left(aq\right)+O{H}^{-}\left(aq\right)$

Rate of equilibrium constant for reaction

$aA+bB\stackrel{}{\rightleftharpoons }cC+dD$

Rate of equilibrium reaction $\left(K\right)=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Rate of equilibrium constant is as $\left(K\right)=\frac{\left[H{2}_{}C{o}_3\right]\left[O{H}^{-}\right]}{\left[HC{o}_3^{-}\right]\left[H_{2}O\right]}$

In this equilibrium, $\left[H_{2}O\right]=1$

Dissociation constant $\left(K_a\right)=\frac{\left[H{2}_{}C{o}_3\right]\left[O{H}^{-}\right]}{\left[HC{o}_3^{-}\right]}$

$\left[H{2}_{}C{o}_3\right]\left[O{H}^{-}\right]=K_a\left[HC{o}_3^{-}\right]$

(e)

Interpretation Introduction

To determine: Write chemical equations and equilibrium expressions for aniline ion $C_6{H}_{5}N{H}_2$ with water.

Explanation of Solution

$C_6{H}_{5}N{H}_2\left(aq\right)+H_{2}O\left(l\right)\to C_6{H}_{5}N{H}_3^{+}\left(aq\right)+O{H}^{-}\left(aq\right)$

Apply the concept

Rate of equilibrium constant for reaction

$aA+bB\stackrel{}{\rightleftharpoons }cC+dD$

Rate of equilibrium reaction $\left(K\right)=\frac{{\left[C\right]}^c{\left[D\right]}^d}{{\left[A\right]}^a{\left[B\right]}^b}$

Rate of equilibrium constant is as $\left(K\right)=\frac{\left[C_6{H}_{5}N{H}_3^{+}\right]\left[O{H}^{-}\right]}{\left[C_6{H}_{5}N{H}_2\right]\left[H_{2}O\right]}$

In this equilibrium, $\left[H_{2}O\right]=1$

Dissociation constant $\left(K_a\right)=\frac{\left[C_6{H}_{5}N{H}_3^{+}\right]\left[O{H}^{-}\right]}{\left[C_6{H}_{5}N{H}_2\right]}$

$\left[C_6{H}_{5}N{H}_3^{+}\right]\left[O{H}^{-}\right]=K_a\left[C_6{H}_{5}N{H}_2\right]$

Conclusion

Hence, all the parts have been described.