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Buffer Solutions

Two buffer so...

Question

Two buffer solutions, A and B, each made with acetic acid and sodium acetate differs in their pH by one unit, A has salt: acid = $x : y$ , B has salt: acid = $y : x$ . If $x > y$ , then the value of $x : y$ is

A

3.17

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B

5.8

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C

5.34

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D

8.68

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Solution

The correct option is B $3.17$
$p H = p K_{a} + l o g \frac{[s a l t]}{[a c i d]}$
As given $p H = p K_{a} + l o g \frac{x}{y}$
$p H - 1 = p K_{a} + l o g \frac{y}{x}$ as x > y
Simplifying,
$1 = l o g \frac{x}{y} - l o g \frac{y}{x}$
$1 = l o g \frac{x}{y} + l o g \frac{x}{y} = 2 l o g \frac{x}{y}$
$\frac{1}{2} = l o g \frac{x}{y}$
$\frac{x}{y} = 3.17$

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