Question

For the titration between hydrochloric acid and sodium carbonate, the indicator used is:
a.) Potassium permanganate
b.) Phenolphthalein
c.) Phenol red
d.) Methyl orange

Answer 1

This titration is between a strong acid (Hydrochloric acid) and a weak base (sodium carbonate). This is a two-step reaction and the pH at the equivalence point is between the pH 3-4. Therefore the indicator to be used must also show the colour change close to this pH range.

Complete step by step answer:
First we need to know about standard solutions. A compound is called a primary standard if the impurities present in it are not greater than 0.01-0.02%. Its solution can be easily prepared by directly weighing the sample and dissolving it in a suitable solvent in order to get a definite volume of solution. A primary standard should also satisfy the following conditions:
-It should not be hygroscopic and should not lose its water of crystallization.
-It should be pure and should have high relative molecular mass.
-It should react instantaneously and stoichiometrically with the desired reactant.
-It should easily dissolve in water.
Sodium carbonate is a primary standard and hydrochloric acid is a secondary standard.

Now let us look into how the indicator is used to detect the end point of a titration:
Acid-base indicators are either weak acids or weak bases. Let us suppose HInd is an indicator such that it ionises in the following way:
$\begin{matrix} HInd(aq) \\\ Indicator \end{matrix}\rightleftharpoons \begin{matrix} { H }^{ + }(aq) \\\ proton \end{matrix}+\begin{matrix} { Ind }^{ - }(aq) \\\ conjugate\quad base \end{matrix}$
Where the HInd and the ${ Ind }^{ - }$ forms show different colours.
Now since it is a weak acid, we can write the expression for its ${ K }_{ a }$. Let us denote it by ${ K }_{ ind }$:
${ K }_{ ind }=\cfrac { \left[ { H }^{ + } \right] \left[ { Ind }^{ - } \right] }{ \left[ HInd \right] }$
When there is 50% dissociation of the indicator i.e. $\left[ { Ind }^{ - } \right] =\left[ HInd \right]$ then:
${ K }_{ ind }=\left[ { H }^{ + } \right]$
Therefore, ${ pK }_{ ind } = pH$

From the above equation it is clear that the change of colour for an indicator depends upon its ${ pK }_{ ind }$ value since it is the pH at which the indicator undergoes 50% dissociation. The pH range over which this colour change takes place is about 1 pH unit above and below this ${ pK }_{ ind }$ value.
The pH range for different indicators is given below:

Indicator	pH range
Phenolphthalein	8.3-10.0
Methyl orange	3.1-4.4
Phenol red	6.8-8.2

Potassium permanganate is not an acid-base indicator. Rather it is a redox indicator. The reaction between hydrochloric acid and sodium carbonate is a two-step process. In the first step, one mole of hydrochloric acid reacts with one mole of sodium carbonate to give one mole of sodium chloride and one mole of sodium bicarbonate. In the second step, one mole hydrochloric acid reacts with the one mole of sodium bicarbonate to give one mole of sodium chloride along with one mole of carbon dioxide and water.
$\begin{matrix} { Na }_{ 2 }{ CO }_{ 3 }(aq) \\\ Sodium\quad carbonate \end{matrix}+\begin{matrix} HCl(aq) \\\ Hydrochloric\quad acid \end{matrix}\longrightarrow \begin{matrix} NaHC{ O }_{ 3 }(aq) \\\ Sodium\quad bicarbonate \end{matrix}+\begin{matrix} NaCl(aq) \\\ Sodium\quad chloride \end{matrix}$

$\begin{matrix} { Na }H{ CO }_{ 3 }(aq) \\\ Sodium\quad bicarbonate \end{matrix}+\begin{matrix} HCl(aq) \\\ Hydrochloric\quad acid \end{matrix}\longrightarrow \begin{matrix} { CO }_{ 2 }(g) \\\ Carbon\quad dioxide \end{matrix}+\begin{matrix} NaCl(aq) \\\ Sodium\quad chloride \end{matrix}+\begin{matrix} { H }_{ 2 }O(l) \\\ water \end{matrix}$

Therefore the overall reaction will be:
$\begin{matrix} { Na }_{ 2 }{ CO }_{ 3 }(aq) \\\ Sodium\quad carbonate \end{matrix}+\begin{matrix} 2HCl(aq) \\\ Hydrochloric\quad acid \end{matrix}\longrightarrow \begin{matrix} { CO }_{ 2 }(g) \\\ Carbon\quad dioxide \end{matrix}+\begin{matrix} 2NaCl(aq) \\\ Sodium\quad chloride \end{matrix}+\begin{matrix} { H }_{ 2 }O(l) \\\ water \end{matrix}$
This reaction is between a strong acid (Hydrochloric acid) and a weak base (Sodium carbonate). The equivalence point for the overall reaction lies between the pH 3-4. Therefore, the indicator used must change its colour around this pH range. From the table given above, it is clear that only methyl orange changes its colour around this pH range. It is yellow above a pH of 4.4 and is red below a pH of 3.1. So, the correct answer is “Option D”.

Note: The type of indicator to be used for an acid-base reaction depends on whether the acids and bases to be used are weak or strong. For a strong acid-strong base titration; phenolphthalein, methyl orange and phenol red can be used as an indicator. For a strong acid-weak base titration, only methyl orange can be used. For a weak acid-strong base titration, phenolphthalein is used.