Question

An acid base indicator has $Ka = 3 \times {10^{ - 5}}$,the acid form of indicator is red and the basic form of indicator is blue. By how much must the $pH$change in order to change the indicator from 75% red to 75% blue?
A. $7.91 \times {10^{ - 5}}$
B. $0.95$
C. $5 \times {10^{23}}$
D. $0.9$

Answer 1

Hint: To solve the given question 1st we need to find out the $pH$ at different concentrations, after finding out $pH$ we will subtract it and will get the final solution. The relationship between $pH$ and ${K_a}$ is given by:
$pH = p{K_a} + \log \dfrac{{[{{\ln }^ - }]}}{{[{\text{H}}\ln ]}}$
Here $p{K_a}$ represents the acidic strength, if lower is the value stronger is the acid and vice-versa..

Complete step by step answer:
According to the given question
The Final concentration of $[{\text{H}}\ln ]$ =75%
The Initial concentration of $[{\ln ^ - }]$ =25%
The Final concentration of $[{\text{H}}\ln ]$ =25%
The Initial concentration of $[{\ln ^ - }] $=75%
Therefore now by substituting the above formula in the above relationship, let us find out the value of $pH$ at two different concentrations.
$p{H_1} = - \log (3 \times {10^5}) + \log 75/25$
$ \Rightarrow p{H_1} = {\text{ }}5$
$ \Rightarrow [H_1^ + ] = {10^{ - 5}}M$ … (i)
$p{H_2} = - \log (3 \times {10^5}) + \log 25/75$
$ \Rightarrow p{H_2} = {\text{ - 4}}{\text{.045}}$
$ \Rightarrow [H_2^ + ] = 8.91 \times {10^{ - 5}}M$ … (ii)
Now subtracting equation (ii) and (i), we get
$[H_2^ + ] - [H_1^ + ] = 7.91 \times {10^{ - 5}}M$

So, the correct answer is Option A .

Additional Information:
$pK$ value: $p$ stands for negative logarithm. Just as ${H^ + }$ and $O{H^ - }$ ion concentration range over many negative power of 10, it is convenient to express them as $pH$or $pOH$, the dissociation constant $(K)$ value also range over many negative power of 10 and it is convenient to write them as $pK$. Thus, $pK$ is the negative logarithm of dissociation constant. Sometimes $pH$ of acid comes more than 7 and that of base comes less than 7. It shows that the solution is very dilute.

Note:
> Weak acids have higher $p{K_a}$ values. Similarly, weak bases have higher $p{K_b}$ values.
> A solution of $pH$ = 1 has a hydrogen ion concentration 100 times that of a solution of $pH$= 3.
> $pH$ of zero is obtained in 1N solution of strong acid. In case the concentration is 2N, 3N, 4N, etc. the respective $pH$ value will be negative.