Question

The pH of $ 0.01M $ solution of acetic acid is $ 5.0 $ . What are the values of $ \left[ {{H^ + }} \right] $ and $ {K_a} $ respectively?
(A) $ 1 \times {10^{ - 4}}M,1 \times {10^{ - 8}} $
(B) $ 1 \times {10^{ - 5}}M,1 \times {10^{ - 9}} $
(C) $ 1 \times {10^{ - 5}}M,1 \times {10^{ - 8}} $
(D) $ 1 \times {10^{ - 3}}M,1 \times {10^{ - 8}} $

Answer 1

Hint: pH is defined as the negative logarithm of the hydrogen ion $ \left[ {{H^ + }} \right] $ concentration. By substituting the given value of pH in the below formula, the value of $ \left[ {{H^ + }} \right] $ can be determined. The formula of pH can be written in terms of acid dissociation constant $ \left( {{K_a}} \right) $ and concentration.

Complete Step By Step Answer:
Acetic acid is a weak acid with the molecular formula of $ C{H_3}COOH $ , as it is a weak acid it has the value of pH nearer to $ 7 $ . pH is one of the useful concepts which was introduced by Sorensen.
pH can be useful to know the nature of chemical compounds like acidic, basic, or neutral compounds. Given that the pH of $ 0.01M $ solution of acetic acid is $ 5.0 $
the formula of pH can be written as $ pH = - \log \left( {{H^ + }} \right) $
by substituting the value of pH in the above formula, $ 5.0 = - \log \left( {{H^ + }} \right) $
Then the value of hydrogen Ion concentration $ \left[ {{H^ + }} \right] $ will be $ 1 \times {10^{ - 5}}M $
Given concentration of acetic acid is $ 0.01M $
The pH equation can be written as $ pH = - \log \left( {\sqrt {{K_a} \times } C} \right) $
By substituting the value of pH, and concentration in the above formula,
 $ 5.0 = - \log \left( {\sqrt {{K_a} \times 0.01} } \right) $
By further simplification, the value of $ {K_a} $ will be $ 1 \times {10^{ - 8}} $
Thus, the value of $ \left[ {{H^ + }} \right] $ and $ {K_a} $ will be $ 1 \times {10^{ - 5}}M,1 \times {10^{ - 8}} $

Note:
As the hydrogen ion concentration is also a concentration, it has the units of moles per liter which is known as molarity and represented by $ M $ . Whereas the acid dissociation constant tells about the strength of the acid which is a constant value in general and has no units.