Question

The ionization constant of an acid,${{K}_{a}}$ is the measure of strength of an acid. The ${{K}_{a}}$ values of acetic acid, hypochlorous acid and formic acid are $1.74\times {{10}^{-5}}, 3.0\times {{10}^{-8}}$ $1.74\times {{10}^{-5}},3.0\times {{10}^{-8}}$ and $1.8\times {{10}^{-4}}$ respectively. Which of the following orders of $pH$ of $0.1mold{{m}^{-3}}$ solutions of these acids is correct?
A) Acetic acid $\rangle $ Hypochlorous acid $\rangle $ Formic acid
B) Hypochlorous acid $\rangle $ Acetic acid $\rangle $ Formic acid
C) Formic acid $\rangle $ Hypochlorous acid $\rangle $ Acetic acid
D) Formic acid $\rangle $ Acetic acid $\rangle $ Hypochlorous acid

Answer 1

Hint: Greater the value of ${{K}_{a}}$, stronger should be the acids.
The ionization constant of acids are inversely proportional to the $pH$ value.

Complete step by step answer:
So in the question, ionization constant value i.e. ${{K}_{a}}$ values for three acids acetic acid $\left( C{{H}_{3}}COOH \right)$, hypochlorous acid $\left( HClO \right)$ and formic acid $\left( HCOOH \right)$is given and we have compare the $pH$ values of the three acids and have to arrange it in a descending order and find the correct option from the question.
So for that we should know what ${{K}_{a}}$ value is and how they are related to the strength of an acid.
${{K}_{a}}$ value or the acid dissociation constant or ionization constant is mainly used to distinguish between the strong acid and weak acid. And the dissociation constant value gives whether it is a strong acid and has undergone complete dissociation or the solution contains undissociated ions through partial ionization, which is similar to the weak acids.
${{K}_{a}}$ value is the measure of the strength of an acid and simply it is an equilibrium constant in a chemical reaction.
${{K}_{a}}$ values are written as the product of the concentrations of the ions in the product side divided by the concentration of the reactant side.
So now we should know the relationship between the ${{K}_{a}}$ values of acids and the strength of the acids.
Greater value of ${{K}_{a}}$ means the extent of dissociation is more, i.e. the acid will be stronger since it can easily dissociate.
So greater the ${{K}_{a}}$ value, greater will be the strength of the acid.
${{K}_{a}}$ Value and the strength of acid is directly proportional,${{K}_{a}}\, \alpha \,strength\,\,of\,acid$
 ${{K}_{a}}\,\alpha \,\dfrac{1}{pH}$ ${{K}_{a}}\,\alpha \,strength\,\,of\,acid$
Let’s write the ${{K}_{a}}$ values of the acids given here,
$\left( C{{H}_{3}}COOH \right)$-$1.74\times {{10}^{-5}}$
$\left( HClO \right)$-$3.0\times {{10}^{-8}}$
$\left( HCOOH \right)$-$1.8\times {{10}^{-4}}$
So here the formic acid is having the greater ${{K}_{a}}$ value ,hence it will be the strongest acid ,then acetic acid and the least one is hydrochloric acid.
$HClO\rangle C{{H}_{3}}COOH\rangle HCOOH$ $HCOOH\rangle C{{H}_{3}}COOH\rangle HClO$
But \[pH\]values are inversely proportional to the ${{K}_{a}}$ values.
Since greater ${{K}_{a}}$ values indicate stronger the acid, and stronger the acid then lesser should be the \[pH\] values.
Acids with lower\[pH\] values represent the stronger acids.
Hence ${{K}_{a}}\,\alpha \,\dfrac{1}{pH}$

So the order will be,$HClO\rangle C{{H}_{3}}COOH\rangle HCOOH$
And the correct option is option (B).

Note: If in the question $p{{K}_{a}}$ values were given, then greater the $p{{K}_{a}}$ value the lesser is the strength of the acid. $p{{K}_{a}}$ value is usually used for denoting the ionization constant of weak acids.
$p{{K}_{a}}$ value and \[pH\] values are directly proportional, $p{{K}_{a}}$ values greater ,weaker the acid is and if \[pH\] values are greater, it denotes the acid is a weak acid.