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Question #44091

Difficulty: 8/10 | 🟢 Free

The Question

An analytical chemist prepares a buffer solution at $50^\circ\text{C}$ by mixing a weak base $B$ ( $pK_b = 5.0$ at $50^\circ\text{C}$ ) and its conjugate acid chloride $BHCl$ such that the solution exhibits maximum buffer capacity. Given that the ionic product of water at $50^\circ\text{C}$ is $K_w = 1.0 \times 10^{-13}$ , determine the exact $pH$ of this buffer solution and its relative basicity, defined as $\Delta pH = pH_{\text{buffer}} - pH_{\text{neutral}}$ , at this temperature.

Options

A.
8.0, +1.5
B.
9.0, +2.0
C.
8.0, +1.0
D.
9.0, +2.5

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Numerical_Precision

Improve calculation stamina and avoid rounding errors in high-stakes competitive examinations.

Concepts Behind This Question

Buffer Capacity and pH Range|Salt Hydrolysis Logic|Ionic Product of Water (Kw)

Why This Question Is Tricky

Common Mistakes

The 'Hidden Variable' being tested is the temperature dependence of the ionic product of water ( $K_w$ ).

Students habitually rely on the standard $25^\circ\text{C}$ values ( $pK_w = 14.0$ , neutral $pH = 7.0$ ).

At $50^\circ\text{C}$ , $pK_w$ drops to $13.0$ , which compresses the $pH$ scale and shifts the neutral point to $6.5$ .

Trap B assumes standard $25^\circ\text{C}$ conditions entirely ( $pH=9.0, \Delta pH=+2.0$ ).

Trap C correctly calculates the new buffer $pH$ ( $8.0$ ) but forgets that the neutral point has also shifted, incorrectly subtracting $7.0$ to get $+1.0$ .

Trap D uses the standard $pK_w$ for the buffer calculation but the shifted neutral point.

Quick Facts About This Question

Question Information

Subject	Chemistry
Chapter	Equilibrium - Class 11 Part 1
Concept	Buffer Capacity and pH Range
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free