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Chemistry Question on Buffer Solutions

The dissociation constant of a weak acid is 1×10−41 \times 10^{-4} in order to prepare a buffer solution with a pH=5pH = 5 the [salt] / [Acid] ratio should be :

A

4 : 5

B

10 : 1

C

5 : 4

D

1 : 10

Answer

10 : 1

Explanation

Solution

pH=pKa+log⁡[Salt][Acid] 5=−log⁡Ka+log⁡[Salt][Acid][∵pKa=−log⁡Ka] 5=−log⁡[1×10−4]+log⁡[Salt][Acid] 5=4+log⁡[Salt][Acid] 5−4=log⁡ [Salt] [Acid] 1=log⁡[Salt][Acid] [Salt][Acid]=10 i.e., 10:1\begin{array}{l} pH = p K_{a}+\log \frac{[ Salt ]}{[ Acid ]} \\\ 5=-\log K_{a}+\log \frac{[ Salt ]}{[ Acid ]} \quad\left[\because p K_{a}=-\log K_{a}\right] \\\ 5=-\log \left[1 \times 10^{-4}\right]+\log \frac{[ Salt ]}{[ Acid ]} \\\ 5=4+\log \frac{[ Salt ]}{[ Acid ]} \\\ 5-4=\log \frac{\text { [Salt] }}{[ Acid ]} \\\ 1=\log \frac{[ Salt ]}{[ Acid ]} \\\ \frac{[ Salt ]}{[ Acid ]}=10 \text { i.e., } 10: 1 \end{array}