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. $\dfrac{1}{2}$
B. $\dfrac{1}{{11}}$
C. $\dfrac{{10}}{{11}}$
D. $\dfrac{1}{{10}}$

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:
$HIn \rightleftharpoons {H^ + } + I{n^ - }$
$pH = p{K_a} + \log \dfrac{{[salt]}}{{[acid]}}$
$5 = 6 + \log \dfrac{{[I{n^ - }]}}{{[HIn]}}$
${K_a} = {10^{ - 6}} = \dfrac{{[{H^ + }][I{n^ - }]}}{{[HIn]}}$
$pH = 5 = [{H^ + }]$
$[{H^ + }] = {10^{ - 5}}$
Therefore,
$\dfrac{{[I{n^ - }]}}{{[HIn]}} = \dfrac{{{{10}^{ - 6}}}}{{{{10}^{ - 5}}}}$
$\dfrac{{[I{n^ - }]}}{{[HIn]}} = \dfrac{1}{{10}}$

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.