Question

This single equilibrium equation applies to different phenomena described in this or the preceding chapter. \(\mathrm{CH}_{3} \mathrm{COOH}+\mathrm{H}_{2} \mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{CH}_{3} \mathrm{COO}^{-}\) Of these four phenomena, ionization of pure acid, common-ion effect, buffer solution, and hydrolysis, indicate which occurs if (a) \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) are high, but \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is very low. (b) \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is high, but \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) are very low. (c) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) is high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are low. (d) \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is low.

Short answer

The phenomena occurring in each case are as follows: (a) ionization of pure acid (b) hydrolysis (c) common-ion effect (d) buffer solution.

Step-by-step solution

Identify the Concept

These phenomena are characterized by different behaviors of concentrations of components in the equilibrium equation. If the concentrations of the different chemicals given the equation are high or low, different phenomena will occur. Let's look at each case separately.

Analyze Case (a)

For case (a), \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) are high, but \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is very low. This is the behavior we can expect in ionization of pure acid. When acid ionizes, it produces a high concentration of \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{CH}_{3} \mathrm{COOH}\), while the concentration of \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) which is the conjugate base of the acid remains low.

Analyze Case (b)

For case (b), \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) is high, but \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) are very low. This is characteristic of hydrolysis. In hydrolysis, the concentration of the base \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) is high, while other constituents' concentrations remain low.

Analyze Case (c)

For case (c), \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) is high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are low. This is a situation of common-ion effect. In this effect, including a common ion in a solution would suppress the ionization of a weak acid or a weak base. Here, the concentration of \(\mathrm{CH}_{3} \mathrm{COOH}\) is high, suppressing the ionization of the acid, leading to the low concentrations of \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\).

Analyze Case (d)

Finally, for case (d), \(\left[\mathrm{CH}_{3} \mathrm{COOH}\right]\) and \(\left[\mathrm{CH}_{3} \mathrm{COO}^{-}\right]\) are high, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is low. This scenario is of buffer solution. A buffer solution resists changes in pH when small amounts of an acid or an alkali are added to it. Here, \(\mathrm{CH}_{3} \mathrm{COOH}\) and its conjugate base \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) exist in high concentrations, but \(\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\) is low.

Key concepts

Ionization of Acids

When acids dissolve in water, they undergo a process known as ionization. This occurs when the acid molecules are donated to water, resulting in the formation of hydronium ions \(\mathrm{H}_3\mathrm{O}^+\) and the conjugate base of the acid. For example, acetic acid \(\mathrm{CH}_3\mathrm{COOH}\) ionizing in water forms \(\mathrm{H}_3\mathrm{O}^+\) and acetate ions \(\mathrm{CH}_3\mathrm{COO}^-\). In a scenario where the concentration of \(\mathrm{H}_3\mathrm{O}^+\) is high and the original acid remains high but the conjugate base is low, it suggests a high degree of ionization, common in strong acids or when a weak acid is not present in equilibrium with its conjugate base.

Understanding this process is crucial for comprehending how acids affect chemical equilibrium and the pH of solutions. It is also the fundamental principle behind acid-base titrations and the pH scale.

Common-Ion Effect

The common-ion effect occurs when a solution containing a weak acid or base is mixed with a second compound that has an ion in common with the weak acid or base. This added common ion suppresses the ionization of the weak acid or base. In the exercise, the high concentration of acetic acid accompanies low concentrations of both \(\mathrm{H}_3\mathrm{O}^+\) and acetate ions \(\mathrm{CH}_3\mathrm{COO}^-\), demonstrating the common-ion effect in action.

It's important to note that this effect can lead to a decrease in the solubility of compounds and is also leveraged in buffer solutions to maintain a relatively constant pH in a system.

Buffer Solutions

Buffer solutions are a mixture of a weak acid and its conjugate base (or a weak base and its conjugate acid) that resists changes in pH when small quantities of an acid or base are added. In our exercise, the simultaneous high concentration of both \(\mathrm{CH}_3\mathrm{COOH}\) and \(\mathrm{CH}_3\mathrm{COO}^-\) with a low concentration of \(\mathrm{H}_3\mathrm{O}^+\) indicates the presence of a buffer solution.

Buffers are vital in various biological systems and industrial processes, where maintaining a stable pH is essential for reactions to proceed correctly and for the stability of compounds.

Hydrolysis

Hydrolysis is a reaction involving the breaking of a bond in a molecule using water. When salts dissolve in water, they can react with the water molecules in a process called salt hydrolysis, which affects the pH of the solution. Speaking to our exercise, a high concentration of acetate ions \(\mathrm{CH}_3\mathrm{COO}^-\) with low concentrations of acetic acid and \(\mathrm{H}_3\mathrm{O}^+\) can result from the hydrolysis of the acetate ion in water.

This concept is integral in predicting the behavior of salt solutions and understanding the resultant pH of these solutions. Hydrolysis is also a key step in many biochemical reactions, including the digestion of food.