Question

Useful buffer range of weak acid HA ${K_a} = {10^{ - 5}}$ is:
A. 5 to 7
B.4 to 6
C.3 to 5
D.None of these

Answer 1

vHint: ${K_a}$is the acid dissociation constant. It helps to determine the strength of the acid. The $pH$range where the buffer neutralizes the added acids and bases is called buffer range. While doing so, the buffer tries to maintain the constant$pH$.
Formula used:

$$pH = p{K_a} + \log \dfrac{{[conjugateBase]}}{{[acid]}} \\\ p{K_a} = - {\log _{10}}{K_a} \\\$$

Complete step by step answer:
Given,${K_a} = {10^{ - 5}}$
Using the relation, $p{K_a} = - {\log _{10}}{K_a}$
We get $p{K_a} = - {\log _{10}}{K_a} = - {\log _{10}}{10^{ - 5}} = 5$
Now, we will use this value to determine the potential of hydrogen$pH$by using the formula:
$pH = p{K_a} + \log \dfrac{{[conjugateBase]}}{{[acid]}}$
For an acid HA,
Case 1: $\dfrac{{[conjugateBase]}}{{[acid]}} = \dfrac{1}{{10}}$
Substituting this value,
$pH = p{K_a} + \log \dfrac{1}{{10}}$
We get,$pH = 5 + \log 0.1$
$pH$=5-1=4 …(I)
Case 2: $\dfrac{{[conjugateBase]}}{{[acid]}} = \dfrac{{10}}{1}$
Substituting this value
$pH = 5 + \log \dfrac{{10}}{1}$
We get,
$pH$=5+1=6 …..(II)
So, Useful buffer range of weak acid is 4 to 6.

Hence, option B. (4 to 6) is the correct option to the given question.

Note:
Lesser the value of$p{K_a}$, stronger is the acid. Temperature and concentration can affect the$p{K_a}$ Buffer usually maintains the$pH$ of the system and resists the change in the concentration of ${H^ + }$ ions in the system or solution.