Question

The \(\mathrm{pH}\) of a solution of \(0.10 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) increases when which of the following substances is added? (a) \(\mathrm{NaHSO}_{4}\) (b) \(\mathrm{HClO}_{4}\) (c) \(\mathrm{KNO}_{3}\) (d) \(\mathrm{K}_{2} \mathrm{CO}_{3}\)

Short answer

(d) K2CO3

Step-by-step solution

Understanding pH and Acid-Base Reactions

The pH of a solution is a measure of its acidity or basicity. When an acid is dissolved in water, it donates protons (H+) to the solution, which lowers the pH. When a base is dissolved, it accepts protons or donates hydroxide ions (OH-), which increases the pH. The given solution is of acetic acid (CH3COOH), a weak acid, so its pH is less than 7. To increase the pH, we should add a base to it.

Analyzing the Effect of Each Substance

Each of the given substances will either act as an acid, base, or neutral substance in water. (a) NaHSO4 will act as an acid because HSO4- is the conjugate base of the strong acid H2SO4, which makes NaHSO4 a weak acid. (b) HClO4 is a strong acid and will decrease the pH. (c) KNO3 is a salt that comes from a strong acid and a strong base, so it will not affect the pH substantially. (d) K2CO3 is a salt that comes from a weak acid (H2CO3) and a strong base (KOH), and will therefore produce basic solutions when dissolved in water.

Selecting the Substance That Increases pH

The only substance that will increase the pH of the acetic acid solution is the one that acts as a base. Substance (d) K2CO3, when it dissolves, forms K+ and CO3(2-) ions. The carbonate ion (CO3(2-)) will react with the H+ ions from the acetic acid to form HCO3(-), thus removing H+ ions from the solution and causing the pH to increase.

Key concepts

Understanding Acid-Base Reactions

The cornerstone of understanding how pH changes involve grasping acid-base reactions. These reactions are simply the transfer of protons (H+) from one substance to another. Acids are proton donors, which means they increase the concentration of H+ in a solution, resulting in a lower pH. Bases, on the other hand, either accept these protons or donate hydroxide ions (OH-), leading to a reduction in H+ concentration and a higher pH.

When we look at acetic acid (CH_{3}COOH), this weak acid ionizes in water to a small extent, providing H+ ions which bestow the solution with an acidic pH (less than 7). To alter the pH towards alkalinity, one would add a substance that either absorbs these H+ ions or donates OH- ions.

Conjugate Acids and Bases

The concept of conjugate acids and bases is critical to predicting the behavior of substances in solution. When an acid donates a proton, it forms its conjugate base; conversely, when a base accepts a proton, it forms its conjugate acid. These pairs are intimately connected — the strength of an acid is directly related to the weakness of its conjugate base and vice versa.

For example, when NaHSO_{4} disassociates, it releases HSO4- ions, which are the conjugate base of the strong acid H2SO4. However, because HSO4- can still donate a H+ ion, it behaves as an acid in the water, albeit a weaker one compared to its 'parent' H2SO4. Understanding this relationship helps us anticipate the impact a substance may have on pH when it is introduced to a solution.

Salt Hydrolysis

Salt hydrolysis plays a pivotal role in pH changes. Salts are formed from the neutralization reaction between an acid and a base. When salts dissolve in water, their ions may react with water in a process known as hydrolysis, influencing the pH. Salts from a strong acid and a strong base, like KNO_{3}, are neutral in water as neither the cations nor the anions react significantly with water. However, salts from a strong base and a weak acid, or vice versa, can undergo hydrolysis, creating an acidic or basic solution.

Take K_{2}CO_{3} as an example. It dissociates into K+ and CO3(2-) ions. The carbonate ion is the conjugate base of a weak acid, so it undergoes hydrolysis, grabbing a H+ from water to form HCO3(-) and OH- ions. This increase in OH- (hydroxide ion) concentration causes the pH to rise, making the solution more basic.

Acetic Acid Behavior in Solutions

Acetic acid (CH_{3}COOH) is a prime example of a weak acid. Unlike strong acids, it does not completely ionize in solution. Instead, it establishes an equilibrium between the undissociated acetic acid and the acetate ions (CH_{3}COO^{-}) formed along with H+. This delicate balance can be shifted by adding other substances.

For instance, if we add a salt like K_{2}CO_{3}, which contains the conjugate base of a weak acid, it will promote a decrease in the H+ concentration. Why is that? The CO3(2-) ions generated from the salt will attract H+ to form bicarbonate (HCO3(-)), thereby removing H+ available from the acetic acid equilibrium and increasing the solution's pH. This is an interplay of acid-base chemistry that elegantly demonstrates the principle of Le Chatelier’s principle, which states that a system at equilibrium will shift to counteract any imposed change.