a. For each of the acid-base reactions in section 2.3, compare the pKa values of the acids on either side of the equilibrium arrows to prove that the equilibrium lies in the direction indicated. (The pKa values you need are found in section 2.3 or in problem 13)

b. Do the same for the acid-base reaction in section 2.1

According to acid-base theory, the equilibrium will lie in a direction that favors the formation of a weaker acid.

Compare the pka values of the acid that loses a proton and the conjugate acid of the base, the equilibrium lies in the direction of the weaker acid.

$$\begin{gathered} \text{HCl}\text{+}{\text{H}}_{\text{2}}\text{O}\to {\text{Cl}}^{\text{-}}\text{+}{\text{H}}_{\text{3}}{\text{O}}^{\text{+}} \\ {\text{pK}}_{\text{a}}\text{= 15}{\text{pK}}_{\text{a}}\text{= 15} \end{gathered}$$

Both have the same pKa value.

$$\begin{gathered} {\text{CH}}_{\text{3}}\text{OH}\text{+}{\text{H}}_{\text{3}}{\text{O}}^{\text{+}}\rightleftharpoons {\text{CH}}_{\text{3}}{\text{OH}}_{\text{2}}^{\text{+}}\text{+}{\text{H}}_{\text{2}}\text{O} \\ \text{pKa}\text{= - 1.7}\text{pKa}\text{= - 2.5} \end{gathered}$$

Weaker acid stronger acid

Here, the equilibrium lies on the left side that is backward reaction is favored which is in agreement with the arrow indicated.

$$\begin{gathered} {\text{CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{+}{\text{OH}}^{\text{-}}\rightleftharpoons {\text{CH}}_{\text{3}}{\text{NH}}^{\text{-}}\text{+}{\text{H}}_{\text{2}}\text{O} \\ \text{pKa}\text{= 40}\text{pKa}\text{= 15} \end{gathered}$$

Weaker acid stronger acid

Here, the equilibrium lies on the left side that is backward reaction is favored which is in agreement with the arrow indicated.

$$\begin{gathered} {\text{CH}}_{\text{3}}{\text{NH}}_{\text{2}}\text{+}{\text{H}}_{\text{3}}{\text{O}}^{\text{+}\rightleftharpoons }{\text{CH}}_{\text{3}}{\text{NH}}_{\text{3}}^{\text{+}}\text{+}{\text{H}}_{\text{2}}\text{O} \\ \text{pKa}\text{= - 1.7}\text{pKa}\text{= 10} \end{gathered}$$

Stronger acid weaker acid

Here, the equilibrium lies on the right side that is forward reaction is favored which is in agreement with the arrow indicated.

$$\begin{gathered} \text{HCl}\text{+}{\text{H}}_{\text{2}}\text{O}\rightleftharpoons {\text{Cl}}^{\text{-}}\text{+}{\text{H}}_{\text{3}}{\text{O}}^{\text{+}} \\ \text{pKa}\text{= - 6.3}\text{pKa}\text{= - 1.7} \end{gathered}$$

Stronger acid weaker acid

Here, the equilibrium lies on the right side that is forward reaction is favoured which is in agreement with the arrow indicated.

$$\begin{gathered} {\text{NH}}_{\text{3}}\text{+}{\text{H}}_{\text{2}}\text{O}\rightleftharpoons {\text{NH}}_{\text{4}}^{\text{+}}\text{+}{\text{OH}}^{\text{-}} \\ \text{pKa}\text{= 15}\text{pKa}\text{= 10} \end{gathered}$$

Weaker acid stronger acid

Here, the equilibrium lies on the left side that is backward reaction is favored which is in agreement with the arrow indicated.