Question

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on \(\left[\mathrm{H}^{+}\right]\) are given in LIST-II. (Note: Degree of dissociation \((\alpha)\) of weak acid and weak base is \(<<1\); degree of hydrolysis of salt \(\left\langle<1 ;\left[\mathrm{H}^{+}\right]\right.\) represents the concentration of \(\mathrm{H}^{+}\) ions \()\) LIST-I P. \((10 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid) diluted to \(60 \mathrm{~mL}\) Q. \((20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{NaOH}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid) diluted to \(80 \mathrm{~mL}\) R. \((20 \mathrm{~mL}\) of \(0.1 \mathrm{M} \mathrm{HCl}+20 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) ammonia solution) diluted to \(80 \mathrm{~mL}\) S. \(10 \mathrm{~mL}\) saturated solution of \(\mathrm{Ni}(\mathrm{OH})_{2}\) in equilibrium with excess solid \(\mathrm{Ni}(\mathrm{OH})_{2}\) is diluted to \(20 \mathrm{~mL}\) (solid \(\mathrm{Ni}(\mathrm{OH})_{2}\) is still present after dilution). LIST-II 1\. the value of \(\left[\mathrm{H}^{+}\right]\) does not change on dilution 2\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to half of its initial value on dilution 3\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to two times of its initial value on dilution 4\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to \(\frac{1}{\sqrt{2}}\) times of its initial value on dilution 5\. the value of \(\left[\mathrm{H}^{+}\right]\) changes to \(\sqrt{2}\) times of its initial value on dilution

Short answer

The effects of dilution on [H+] are P: 1, Q: 1, R: 5, S: 1.

Step-by-step solution

Understanding the System and Dilution Effect: P

For mixture P, we have a weak acid (acetic acid) and a strong base (NaOH). When diluted, the concentration of the strong base and the weak acid decreases, but since NaOH is a strong base and completely dissociates, the amount of OH- produced from NaOH will react completely with an equivalent amount of acetic acid, forming water and a salt. The reaction goes to completion, meaning all NaOH reacts until it runs out. Since there's more acetic acid than NaOH, the remaining acetic acid will have a reduced concentration due to dilution, reducing its ionization, and hence the concentration of H+ does not change significantly because NaOH was limiting. Answer: 1.

Understanding the System and Dilution Effect: Q

For mixture Q, the ratio of NaOH and acetic acid is 1:1. Upon dilution, the concentrations of both NaOH and acetic acid reduce equally. However, since they are in the same ratio and will react completely, the final concentration of H+ (which is associated with the weak acid) will remain virtually unchanged. There is no excess reactant, and the change in concentration due to dilution affects both reactants equally, keeping the pH largely unchanged. Answer: 1.

Understanding the System and Dilution Effect: R

For mixture R, an acid-base reaction occurs between HCl (a strong acid) and ammonia (a weak base). HCl dissociates completely, whereas the dissociation of ammonia is very low \(\alpha << 1\). When this mixture is diluted, the concentration of NH4+ will decrease while the OH- from ammonia will increase (due to increased dissociation, though still small), causing a slight increase in pH and decrease in [H+]. The strong acid's change in dissociation is negligible due to its complete ionization. Answer: 5.

Understanding the System and Dilution Effect: S

For solution S, Ni(OH)2 is a weak base and is in a saturated solution with its solid. According to Le Chatelier's principle, the dilution will shift the equilibrium to the right to form more ions, OH- and Ni2+. However, since there is an excess solid present, it will keep dissolving to a certain degree to maintain the saturation. Therefore, the OH- concentration increases and the H+ concentration decreases, but the presence of solid maintains the solubility product, so H+ concentration doesn't change significantly. Answer: 1.

Key concepts

Dilution Effect on pH

The dilution effect on pH is an essential concept to understand when studying solutions of acids and bases. Dilution refers to the process of reducing the concentration of a solute in a solution, typically by adding more solvent. In the context of acids and bases, diluting an acid or a base with water affects its pH, which is a measure of the acidity or basicity of the solution.

For a strong acid or base, dilution will generally decrease the concentration of hydrogen ions ([H^+]) or hydroxide ions ([OH^-]), leading to a change in pH. However, for weak acids or bases, the effect of dilution on pH is not as straightforward. In dilute solutions, weak acids and bases dissociate more due to their inverse relationship between concentration and dissociation. The degree of dissociation ((alpha)) increases with the dilution, affecting the pH. Furthermore, the extent to which the pH changes also depends on buffer capacity and the presence of salts or conjugal pairs.

In the context of the given exercise, dilution of a mixture of NaOH and acetic acid (Scenario P and Q) results in no significant change in [H^+] because NaOH, the strong base, reacts completely with acetic acid, and the ratio of their concentrations determines the system's buffering capacity. Conversely, the dilution of a saturated solution of a weak base in equilibrium with its solid (Scenario S) initially seems to decrease the [H^+] concentration, but the presence of excess solid maintains the solubility product, keeping the [H^+] concentration relatively unchanged.

Weak Acid and Base Reaction

When a weak acid reacts with a weak base, the process is governed by the principles of acid-base equilibrium. Weak acids and bases do not dissociate completely in water, which is indicated by their small dissociation constants. The reaction between a weak acid and a weak base generally results in a salt and water, with the equilibrium favoring the reactants due to their low dissociation.

For example, when acetic acid reacts with ammonia, the resulting products are ammonium acetate and water. Since both reactants are weak, their reaction is not driven to completion, and the mixture's pH depends on the relative strengths and concentrations of the acid and base involved.

In Scenario R from the exercise, the reaction between HCl, a strong acid, and ammonia, a weak base, is noteworthy. Strong acids completely dissociate, increasing the [H^+] concentration, while weak bases only partially accept protons. Upon dilution, the dissociation of the weak base (ammonia) increases slightly, but this effect is minimal compared to the fully dissociated strong acid. Consequently, the dilution of R increases the pH only marginally, leading to a decrease in [H^+].

Le Chatelier's Principle

Le Chatelier's principle is a fundamental concept in chemical equilibrium, stating that if a dynamic equilibrium system undergoes a change in concentration, temperature, volume, or pressure, the system will adjust itself to counteract the imposed change and achieve a new equilibrium state.

Applying Le Chatelier's principle to acid-base reactions, when a system at equilibrium is diluted, it responds by shifting the equilibrium to increase the concentration of the dissociated ions, trying to restore the original conditions. This is particularly relevant in Scenario S from our exercise, which involves a saturated solution of a sparingly soluble weak base, (Ni(OH)_2), in equilibrium with its solid. When this system is diluted, the equilibrium shifts to produce more hydroxide ions, thus, increasing the solubility of (Ni(OH)_2). However, the presence of excess solid means the solubility product will remain constant, and the dissolution continues until it reestablishes equilibrium. As a result, the hydroxide ion concentration increases, potentially lowering the [H^+] concentration, but to a lesser extent due to the solid's buffering effect.