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Question #99914

Difficulty: 8/10 | 🟢 Free

The Question

A $50.0\text{ mL}$ sample of $0.20\text{ M}$ aqueous solution of a weak monoacidic base, \ce{BOH} ( $K_b = 2.0 \times 10^{-5}$ ), is titrated against $0.10\text{ M}$ \ce{HCl}(aq) at $298\text{ K}$ . An indicator \ce{HIn} is used to detect the endpoint. The indicator transitions from its basic color to its acidic color, and the endpoint is visually detected when the concentration of the acidic form is exactly 10 times that of the basic form. Assuming ideal behavior, what must be the exact $pK_{In}$ of the indicator to perfectly coincide with the equivalence point of this titration?

(Given: $\log 3 = 0.48$ , $K_w = 1.0 \times 10^{-14}$ )

Options

A.
$6.24$
B.
$5.24$
C.
$8.00$
D.
$6.00$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Exception_Exposure

Learn to identify edge cases and boundary exceptions that JEE examiners hide in math problems.

Concepts Behind This Question

Limiting Reagent Stoichiometry|Salt Hydrolysis Logic|Titration Indicators

Why This Question Is Tricky

Examiner Levers

Logical Assertion

Tests the causal relationship between two true statements.

Difficulty Boost : +4

Common Mistakes

This problem tests the intersection of limiting reagent stoichiometry, salt hydrolysis, and indicator theory.

The 'Trap' is threefold: (1) Students often assume stoichiometric equivalence implies a neutral pH ( $pH = 7$ ), leading to $pK_{In} = 8.00$ . (2) Students fail to account for the volume expansion during titration, using the initial concentration of the base for the salt, leading to $pH = 5.00$ and $pK_{In} = 6.00$ . (3) Students calculate the correct pH (5.24) but forget to apply the indicator transition ratio ( $[\ce{HIn}] = 10[\ce{In^-}]$ ), selecting 5.24 directly.

The core concept requires recognizing that the limiting reagent leaves a conjugate acid that dictates the acidic pH, forcing a specific indicator choice.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Some Basic Concepts of Chemistry - Class 11 Part 1
Concept	Limiting Reagent Stoichiometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free