Problem 76 - A Complete Resource Book in Chemistry for JEE Main

Question

The rapid change of \(\mathrm{pH}\) near the stoichiometric point of an acid- base titration is the basis of indicator detection. \(\mathrm{pH}\) of the solution is related to the concentrations of the conjugate acid (HIn) and base (In \(^{-}\)) forms of the indicator by the expression (a) \(\log \left[\frac{\operatorname{In}^{-}}{\mathrm{HIn}}\right]=\mathrm{pK}_{\mathrm{ln}}-\mathrm{pH}\) (b) \(\log \left[\frac{\mathrm{HIn}}{\mathrm{In}^{-}}\right]=\mathrm{pK}_{\mathrm{ln}}+\mathrm{pH}\) (c) \(\log \left[\frac{\mathrm{HIn}}{\mathrm{In}}\right]=\mathrm{pH}_{-} \mathrm{pK}_{\mathrm{ln}}\) (d) \(\log \left[\frac{\operatorname{In}}{\mathrm{HIn}}\right]=\mathrm{pH}_{-} \mathrm{pK}_{\mathrm{ln}}\)

Step-by-Step Solution

Answer

Choice (a): \( \log \left[ \frac{\text{In}^-}{\text{HIn}} \right] = \text{pK}_{\text{ln}} - \text{pH} \) is correct.

Step 1: Analyze the Given Expression

The question states that the expression relates \[ \log \left[ \frac{\text{In}^-}{\text{HIn}} \right] \text{ to } \text{pK}_{\text{ln}} - \text{pH}. \]We need to find which option matches this given relation.

Step 2: Examine Option (a)

Examine option (a):- The expression states: \[ \log \left[ \frac{\text{In}^-}{\text{HIn}} \right] = \text{pK}_{\text{ln}} - \text{pH} \]- This directly matches the provided expression format, implying option (a) fits.

Step 3: Verification of Other Options

- Check option (b): \[ \log \left[ \frac{\text{HIn}}{\text{In}^-} \right] = \text{pK}_{\text{ln}} + \text{pH} \] This does not match the given expression format.- Check option (c): \[ \log \left[ \frac{\text{HIn}}{\text{In}} \right] = \text{pH} - \text{pK}_{\text{ln}} \] This is a reversed format.- Check option (d): \[ \log \left[ \frac{\text{In}}{\text{HIn}} \right] = \text{pH} - \text{pK}_{\text{ln}} \] Also a reverse formation, aligning differently than stated.Only option (a) remains consistent with the initially provided expression.

Key Concepts

pH Indicator

In an acid-base titration, a pH indicator is vital. It helps us detect the endpoint where the equivalent amounts of acid and base have reacted. These indicators are substances that change color depending on the pH of the solution.
Different indicators operate in unique pH ranges. Choosing the right one is crucial because this affects when you'll notice the color change. The change happens because the pH of the solution influences the ratio of the indicator's conjugate acid (HIn) and base (In⁻) forms.
In the rapid pH change area of a titration, this color shift becomes visible, indicating you've reached the endpoint. Some popular indicators include phenolphthalein and bromothymol blue, each with its specific pH range for color transitions.

Stoichiometric Point

The stoichiometric point, often referred to as the equivalence point, is crucial in titrations. This is the point where the amount of acid equals the amount of base.
At this point, all reactants have reacted perfectly, making stoichiometry calculations more straightforward.
Reaching the stoichiometric point signals that the titration is complete. It's typically detected using a pH indicator or a pH meter. The choice between these two depends on the required precision. In an ideal titration process, the stoichiometric point will coincide with the sudden pH change.

Conjugate Acid-Base Pair

In chemistry, understanding conjugate acid-base pairs is essential. A conjugate acid-base pair consists of two substances. One donates a proton (an acid), and the other accepts it (a base).
For example, when an acid loses a proton, it forms its conjugate base. Conversely, when a base gains a proton, it forms its conjugate acid.

• Acid (HIn) ⟶ Conjugate Base (In⁻)
• Base (In⁻) ⟶ Conjugate Acid (HIn)

This relationship is pivotal for pH indicators, which rely on shifts in these conjugate states to change color. Understanding these pairs helps explain the mechanisms behind buffer solutions and many biological processes.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation is useful for understanding acid-base balance. It estimates the pH of a buffer solution using the concentration ratio of acid and base.
The equation is expressed as: \[ ext{pH} = ext{pK}_a + ext{log} rac{[ ext{Base} ]}{[ ext{Acid} ]} \]The equation offers insight into how buffers resist pH changes when acids or bases are added. It connects the idea of pH, pKa, and the concentration ratio, making it invaluable in many applications.
It’s important when working with titrations as it can help predict how the solution pH will change during an acid-base reaction.