Question

What fraction of an indicator $HIn$ is in basic form at a $pH$ of $5$ if the $p{K}_a$ of the indicator is $6$?
A. ${\displaystyle \frac{1}{2}}$
B. ${\displaystyle \frac{1}{11}}$
C. ${\displaystyle \frac{10}{11}}$
D. ${\displaystyle \frac{1}{10}}$

Answer 1

Hint: In an acidic or basic medium, an indicator is a substance that changes colour. Indicators are termed indicators because they show one colour in an acidic medium and different colour in a basic medium.

Complete answer:
Given:
$pH=5$
$p{K}_a=6$
The dissociation of $HIn$ takes place as follows:
$HIn\rightleftharpoons H^{+}+I{n}^{-}$
$pH=p{K}_a+\log {\displaystyle \frac{[salt]}{[acid]}}$
$5=6+\log {\displaystyle \frac{[I{n}^{-}]}{[HIn]}}$
$K_a={10}^{-6}={\displaystyle \frac{[H^{+}][I{n}^{-}]}{[HIn]}}$
$pH=5=[H^{+}]$
$[H^{+}]={10}^{-5}$
Therefore,
${\displaystyle \frac{[I{n}^{-}]}{[HIn]}}={\displaystyle \frac{{10}^{-6}}{{10}^{-5}}}$
${\displaystyle \frac{[I{n}^{-}]}{[HIn]}}={\displaystyle \frac{1}{10}}$

So, the correct answer is “Option D”.

Additional information:
 An acid-base titration is a method of obtaining information about a solution that contains an acid or a base. The acid-base indicator is commonly an organic compound that is a weak acid or weak base in itself. A known volume of acid is placed in a conical flask during the entire process. Two to four drops of an acid-base indicator are added, followed by a drop-by-drop addition of an alkali solution of unknown strength from a burette in the acid solution. A sharp colour change at the equivalence point denotes the neutralization point. The commonly used acid-base indicators are: Phenolphthalein – Colourless in (acid) and pink in (alkali) and Methyl orange – Pink in (acid) and yellow in (alkali)

Note:
The weak acid form ($HIn$) will have one colour and the weak acid negative ion ($I{n}^{-}$-) will have a different colour. The negative logarithm of $H^{+}$ ion concentration is used to calculate $pH$. As a result, the meaning of $pH$ is justified as hydrogen power. $p{K}_a$ is the negative base-$10$ logarithm of the acid dissociation constant ($K_a$) of a solution. The lower the $p{K}_a$ value, the stronger the acid.