AIIMS 2005 Chemistry Titration Curves MCQ Question

To determine the pH at the equivalence point of the titration of acetic acid with ammonia, we first need to understand the nature of the reactants and the resultant solution at equivalence.

Step 1: Understanding the Reaction

Acetic acid ($CH_3COOH$) is a weak acid, and ammonia ($NH_3$) is a weak base. The titration reaction can be represented as:

$$CH_3COOH + NH_3 \rightleftharpoons CH_3COO^- + NH_4^+$$

At the equivalence point, all of the acetic acid has reacted with ammonia to form the acetate ion ($CH_3COO^-$) and the ammonium ion ($NH_4^+$).

Step 2: Analyzing the Resultant Solution

At the equivalence point, we have a solution containing both $CH_3COO^-$ (the conjugate base of acetic acid) and $NH_4^+$ (the conjugate acid of ammonia). The pH of the solution will depend on the balance between these two ions.

Step 3: Calculating the pH at Equivalence Point

The pH at the equivalence point can be derived from the hydrolysis of the ions in solution.

1. Hydrolysis of $NH_4^+$: The ammonium ion can donate a proton to water, forming $NH_3$ and $H^+$:

   $$NH_4^+ + H_2O \rightleftharpoons NH_3 + H_3O^+$$

   The equilibrium expression is given by:

   $$K_a = \frac{[NH_3][H_3O^+]}{[NH_4^+]}$$

   Where $K_a$ for $NH_4^+$ can be calculated using:

   $$K_w = K_a \cdot K_b$$

   Given that $K_b$ for ammonia ($NH_3$) can be derived from $pK_a$:

   $$K_b = 10^{-14} / K_a = 10^{-14} / 10^{-5} = 10^{-9}$$

   Thus, $pK_b$ for ammonia is approximately 9.0.

2. Hydrolysis of $CH_3COO^-$: The acetate ion can also undergo hydrolysis:

   $$CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$$

   The equilibrium expression for this reaction is:

   $$K_b = \frac{[CH_3COOH][OH^-]}{[CH_3COO^-]}$$

   Since $K_b$ for $CH_3COO^-$ can also be calculated similarly as above:

   $$K_b = 10^{-14} / K_a = 10^{-14} / 10^{-5} = 10^{-9}$$

   Thus, $pK_b$ for acetate ion is also approximately 9.0.

Step 4: The Resulting pH

Since both ions produce equal concentrations of $H^+$ and $OH^-$ at equivalence, the resulting solution will act as a buffer system. However, because the $K_b$ values are equal, the resulting solution will not be neutral. Given that $NH_4^+$ is a stronger acid than $CH_3COO^-$ as a base, the pH will be slightly less than 7.

After evaluating the contributions of both ions to the pH, we determine that the pH at the equivalence point is around 6.0, leaning towards basicity due to the presence of acetate.

Conclusion

Thus, the correct answer to the question is not 5.0 or 9.0, but rather the closest neutral point accounting for the weak acid-weak base titration, which is:

Correct Answer: C) 6.0

Why Other Options Are Incorrect:

• Option A (5.0): This would imply a highly acidic solution which does not account for the basic nature of the acetate ion.
• Option C (7.0): This is the neutral point of pure water and does not consider the presence of the weak acid and base.
• Option D (9.0): This suggests a strongly basic solution which is not supported by the reaction's equilibrium.

In conclusion, the pH at the equivalence point of the titration of ac