Question

Indicator	${\text{pH range}}$
Methyl violet	$0.3 - 1.8$
Methyl orange	$2.8 - 3.8$
Congo red	$2.8 - 4.8$
Methyl red	$3.8 - 6.1$
Bromothymol blue	$6.0 - 7.9$
Phenol red	$6.8 - 8.6$

The table above shows the ${\text{pH}}$ ranges of some common indicators. Given that ${K_a}$ is $7.3 \times {10^{ - 10}}$ for boric acid $({H_3}B{O_3})$ , Choose an indicator that can be used for the titration of $0.10M{\text{ }}K{H_2}B{O_3}$ with $0.10M{\text{ }}HCl$
(A) Methyl orange
(B) Congo Red
(C) Methyl Red
(D) Phenol Red

Answer 1

Hint : To solve this, we have to write down the chemical reaction of $K{H_2}B{O_3}$ with $HCl$ and the products formed. Then find concentration of products at the equivalence point with the help of ${K_a}$ value given in the question. With the help of concentration of the hydronium ion, find the $pH$ . Then check in which indicator range the $pH$ lies.

Complete Step By Step Answer:
The reaction of $K{H_2}B{O_3}$ with $HCl$ is as follows:
$K{H_2}B{O_3} + HCl \to {H_3}B{O_3} + KCl$
At equivalence point the concentration of ${H_3}B{O_3}$ produced $= 0.050M{\text{ }}{H_3}B{O_3}$ then ionizes so:
${H_3}B{O_3} + {H_2}O \to {H_3}B{O_3} + {H_3}{O^ + }$
$0.05M$ $x$ $x$
${k_a} = \dfrac{{[{H_3}{O^ + }][{H_3}B{O_3}]}}{{[{H_3}B{O_3}]}} = \dfrac{{{x^2}}}{{0.05}}$
i.e. $7.3 \times {10^{ - 10}} = \dfrac{{{x^2}}}{{0.05}}$
$x = 6.04 \times {10^6}$
Using the concentration of hydronium ion, we can find the $pH$ i.e.
$pH = - \log (6.04 \times {10^6}) = 5.22$
This $pH$ is in the range of methyl red indicators which will be suitable for the given titration.
Therefore, the correct option is C.

Note :
The substances that change color when they are added to alkaline or acidic solutions are called indicators. Methyl orange is a $pH$ indicator used in titrations due to its clear and distinct color variance at different values of $pH$ . It shows red color in acidic medium and yellow color in basic medium. As it changes its color at the $p{K_a}$ of a mid-strength acid, it is used in titration of acids. Congo red serves as an acid-base indicator as it turns red in the presence of alkalies and blue in the presence of acids.