Question

The acid dissociation constant of $ {{\text{H}}_2}\;{\text{S}} $ and $ {\text{H}}{{\text{S}}^ - } $ are $ {10^{ - 7}} $ and $ {10^{ - 13}} $ respectively. The pH of $ 0.1{\text{M}} $ aqueous solution of $ {{\text{H}}_2}\;{\text{S}} $ will be
(A) $ 2 $
(B) $ 3 $
(C) $ 4 $
(D) $ 5 $

Answer 1

Hint: The negative logarithm of $ {{\rm H}^ + } $ ion concentration is defined as pH. The meaning of the pH name is therefore justified by the power of hydrogen. We shall calculate the molarity of the hydrogen ions from the acid dissociation constant given using the equilibrium constant and thus, find the pH.

Formula Used
We can find out the pH value of any substance by the following formula
 $ pH = - \log \left[ {{H^ + }} \right] $
Where
 $ pH $ is the required pH value
 $ \left[ {{H^ + }} \right] $ is the concentration of $ {H^ + } $ ions.

Complete Step-by-Step Solution
According to the question, the following information is provided to us:
The acid dissociation constant of $ {{\text{H}}_2}\;{\text{S}} $ is $ {10^{ - 7}} $
The acid dissociation constant of $ {\text{H}}{{\text{S}}^ - } $ is $ {10^{ - 13}} $
The molarity of the aqueous $ {{\text{H}}_2}\;{\text{S}} $ is $ 0.1 M $
The following compound $ {{\text{H}}_2}\;{\text{S}} $ can be broken down as
 $ {H_2}S \to H{S^ - } + {H^ + } $
 $ {K_a} = \dfrac{{{x^2}}}{{\left( {{{10}^{ - 1}} - x} \right)}} $
Where
 $ {K_a} $ is the acid dissociation constant
We can see that $ x < < {10^{ - 1}} $
Therefore, we can neglect $ x $ since it is very small quantity
Such that $ {10^{ - 1}} - x \approx {10^{ - 1}} $
Now,
 $ {10^{ - 1}} \times {10^{ - 7}} = {x^2} $
Upon further solving, we get
 $ \therefore x = {10^{ - 4}} $
Now, we will determine the value of pH of $ {{\text{H}}_2}\;{\text{S}} $
That is,
 $ pH = - \log \left[ {{H^ + }} \right] $
Upon substituting the values, we get
 $ pH = - \log \left[ {{{10}^{ - 4}}} \right] $
 $ \Rightarrow pH = 4log10 $
On solving, we get
 $ \therefore pH = 4 $
Hence, the correct option is (C).

Additional Information
pH is a measure of the acidic/basic nature of substances. With $ 7 $ being neutral, the range goes from $ 0 $ to $ 14 $ . Acidity is indicated by a pH of less than $ 7 $ , whereas a base is indicated by a pH greater than $ 7 $ . Actually, pH is a measure of the relative amount in the water of free hydrogen and hydroxyl ions. Acidic water with more free hydrogen ions is acidic, while water with more free hydroxyl ions is basic.

Note
The pH is a measure of the hydrogen ion concentration, the acidity or alkalinity of a solution. Normally, the pH-scale is between $ 0 $ and $ 14 $ . Aqueous solutions are acidic at $ {25^ \circ }C $ with a pH of less than $ 7 $ and basic or alkaline solutions are those with a pH of more than $ 7 $ .