AIPMT PRELIMS 2004 Chemistry Indicators MCQ Question

In acid-base titrations, indicators are used to visually signal the endpoint of the titration, where the pH of the solution changes rapidly. The relationship between the pH of the solution and the concentrations of the acid (HIn) and base (In⁻) forms of the indicator can be described using the Henderson-Hasselbalch equation. This equation is crucial for understanding how indicators work in terms of their color change at specific pH ranges.

Correct Answer Explanation

The correct option is: A) log $\frac{[HIn]}{[In^-]} = pK_a - pH$

This equation is a rearranged form of the Henderson-Hasselbalch equation, which is given by:

$$pH = pK_a + \log \frac{[In^-]}{[HIn]}$$

To derive option A from this equation, we can rearrange it as follows:

1. Start with the original equation:

   $$pH = pK_a + \log \frac{[In^-]}{[HIn]}$$

2. Rearranging gives:

   $$\log \frac{[In^-]}{[HIn]} = pH - pK_a$$

3. Taking the reciprocal on the left-hand side (which changes the sign of the logarithm):

   $$\log \frac{[HIn]}{[In^-]} = pK_a - pH$$

Thus, option A is indeed correct, as it accurately describes the relationship between the pH of the solution and the ratio of the concentrations of the conjugate acid and base forms of the indicator.

Incorrect Options Explanation

Now, let's analyze why the other options are incorrect:

B) log $\frac{[HIn]}{[In^-]} = pH - pKₐ$

This option incorrectly states the relationship. It suggests that the logarithmic expression equals the difference of pH and $pK_a$. Based on our derivation, we see that it should be $pK_a - pH$, not $pH - pK_a$.

C) log $\frac{[In^-]}{[HIn]} = pH - pKₐ$

This option is incorrect as it maintains the original form of the Henderson-Hasselbalch equation but fails to match the sign correctly. The expression on the left should represent the ratio of base to acid, and as derived, the right side should indeed be $pH - pK_a$, but it does not match the question being posed.

D) log $\frac{[In^-]}{[HIn]} = pKₐ - pH$

This option is also incorrect as it states the opposite of what we derived. It suggests that the log of the base to acid ratio equals $pK_a - pH$. However, from the rearrangement, this expression is true for the opposite ratio, $\frac{[HIn]}{[In^-]}$, as we corrected in our derivation.

Summary

In conclusion, the correct understanding of the relationship between pH, the concentrations of the indicator forms, and the $pK_a$ is represented accurately in option A. The other options fail to align with this fundamental relationship, either by incorrect rearrangement or by misrepresenting the logarithmic ratios.

This understanding is essential for effectively utilizing indicators in acid-base titrations and ensuring accurate readings during experiments.