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JEE Advanced levelSingle correct optionDifficulty 3 of 3g2091

A buffer has pH 6.2. For imidazole (pKa of imidazolium = 7.0), the ratio $[imidazolium] / [imidazole]$ in this buffer is closest to

A6.3
B0.16
C63
D0.6

Answer: A

From the Henderson-Hasselbalch equation,

pH = p K_{a} + lo g \frac{[ B ]}{[ BH X ^{+} ]}

, so

lo g \frac{[ BH X ^{+} ]}{[ B ]} = p K_{a} - pH = 7.0 - 6.2 = 0.8

and the ratio is

1 0^{0.8} = 6.3

.

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