Problem 87 - A Complete Resource Book in Chemistry for JEE Main

Question

When \(10 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) acetic acid \((\mathrm{pKa}=5.0)\) is titrated against \(10 \mathrm{~mL}\) of \(0.1 \mathrm{M}\) ammonia solution \((\mathrm{pKb}=5.0\) ) the equivalence point occurs at \(\mathrm{pH}\) (a) \(5.0\) (b) \(6.0\) (c) \(9.0\) (d) \(7.0\)

Step-by-Step Solution

Answer

The pH at the equivalence point is 5.0, so the correct answer is (a).

Step 1: Understand the reaction

When acetic acid, a weak acid, reacts with ammonia, a weak base, they form ammonium acetate. The reaction reaches the equivalence point when equal moles of acid and base have reacted.

Step 2: Calculate the equivalence point pH using pKa and pKb

The pH at the equivalence point in the titration of a weak acid with a weak base is given by the equation \[\text{pH} = \frac{\text{pKa} + \text{pKb}}{2}\]For this problem, both pKa and pKb are 5.0.

Step 3: Substitute values into the formula

Substitute pKa and pKb into the formula:\[\text{pH} = \frac{5.0 + 5.0}{2} = 5.0\]

Step 4: Identify the correct answer

Based on the calculations, the pH at the equivalence point is 5.0, which corresponds to option (a).

Key Concepts

Equivalence Point

The equivalence point in a titration is the moment in the experiment where the quantity of titrant added is exactly enough to completely neutralize the analyte solution. This means that the moles of acid involved in the reaction are equal to the moles of the base. Understanding this concept is crucial in titrations because it marks the point where the mixture has completely reacted and neither reactant is in excess.
In the case of a weak acid reacting with a weak base, like acetic acid with ammonia, an interesting phenomenon occurs. The solution can turn into a buffer system, which might influence the pH changes during the reaction. Knowing this can help in predicting or calculating the pH at the equivalence point. Titrations of weak acids and bases typically reach an equivalence point that requires special consideration, as their resulting pH differs from titrations involving strong acids and bases.

pKa and pKb Calculation

pKa and pKb are intrinsic properties of acids and bases that determine their strength and the extent to which they dissociate in water. The pKa value tells us about how strong an acid is; a lower pKa indicates a stronger acid, meaning it dissociates more completely in water. Conversely, pKb indicates the strength of a base, with a lower pKb meaning a stronger base that more readily accepts protons.

• pKa and pKb are logarithmic measures. Therefore, small changes in their values denote significant changes in acid or base strength.
• The relationship between pKa and pKb also allows us to understand the behavior of acids and bases in solution, particularly during titration processes.

For our problem, the acetic acid has a pKa of 5.0 while the ammonia, acting as a base, has a pKb of 5.0. At the equivalence point, where the acid has been neutralized by the base, the pH can be calculated by averaging the pKa and pKb. The formula used is \[\text{pH} = \frac{\text{pKa} + \text{pKb}}{2}. \] Substituting the known values, the pH turns out to be 5.0, suggesting that the equivalence point pH is influenced equally by the acidic and basic components.

Weak Acid-Weak Base Titration

Understanding the titration between a weak acid and a weak base requires grasping how these substances interact differently from their strong counterparts. When titrating a weak acid like acetic acid with a weak base such as ammonia, the pH at the equivalence point deviates significantly from neutral.

• Both the weak acid and weak base only partially dissociate in solution, which affects the chemistry of the titration. The process can create a buffer solution when both reactants are present in similar concentrations.
• The pH of the solution at equivalence is not 7, as it would be with strong acids and strong bases; instead, it is defined by the pKa and pKb values of the reactants.
• This makes it necessary to use the average of the pKa and pKb to determine the equivalence point pH, as seen in the formula \(\text{pH} = \frac{\text{pKa} + \text{pKb}}{2}.\)

Such titrations can be particularly useful for preparing buffer solutions, given that the resulting solution tends to resist changes in pH due to the balanced nature of the weak acid and weak base pairing. Overall, the process provides valuable insight into the behavior of acidic and basic solutions, demonstrating the importance of knowing the dissociation properties of the chemicals involved.