Question

In a solution containing 0.01 M HCl and 0.1 M \[{H_2}C{O_3}\], ratio of \[\left[ {{H^ + }} \right]\] produced from strong acid and weak acid respectively is 1. Report your answer as \[\dfrac{x}{{500}}\]. Given: \[{K_{a1}}\] & \[{K_{a2}}\] of \[{H_2}C{O_3}\] are \[4 \times {10^{ - 7}}\] &
\[4 \times {10^{ - 11}}\]

Answer 1

Hint: Since HCl is a strong acid and \[{H_2}C{O_3}\] is a weak acid, the ratio of \[\left[ {{H^ + }} \right]\] produced from strong acid and weak acid respectively is given in the question to be 1. \[{K_a}\] is the acid ionization constant which is the equilibrium constant for chemical reactions involving weak acids in aqueous solution. The numerical value of \[{K_a}\] is used to predict the extent of acid dissociation.

Complete step by step Answer:
HCl is a strong Acid
 \[\left[ {{H^ + }} \right] = 0.01M\]
 \[{H_2}C{O_3}\] is a weak acid
 \[\left[ {{H^ + }} \right] = 2 \times {10^{ - 4}}M\]
 \[0.01 > > 2 \times {10^{ - 4}}\]
 \[{K_{a1}}\] & \[{K_{a2}}\] of \[{H_2}C{O_3}\] are given as,
 \[{K_{a1}} = 4 \times {10^{ - 7}}\]
 \[{K_{a2}} = 4 \times {10^{ - 11}}\]
For HCl
 \[\left[ {{H^ + }} \right] = \sqrt {{K_{a1}}} .c = \sqrt 4 \times {10^{ - 7}} \times 0.1 = \sqrt 4 \times {10^{ - 8}} = 2 \times {10^{ - 4}}\]
Therefore, we neglect \[2 \times {10^{ - 4}}\]
 \[\left\{ {{H^ + }} \right\}ratio\dfrac{{0.01}}{{2 \times {{10}^{ - 4}}}} = \dfrac{1}{2} \times {10^{ - 2}} \times {10^4} = 0.5 \times {10^2}\]

Note: According to the Arrhenius theory of acids and bases, when an acid is added to water, it donates an \[{H^ + }\] ion to water to form \[{H_3}{O^ + }\] (often represented by \[{H^ + }\] ). The higher the concentration of \[{H_3}{O^ + }\] (or \[{H^ + }\] ) in a solution, the more acidic the solution is. An Arrhenius base is a substance that generates hydroxide ions, \[O{H^ - }\], in water. The higher the concentration of \[O{H^ - }\] in a solution, the more basic the solution is. Also, a large \[{K_a}\] value indicates a stronger acid (more of the acid dissociates) and small \[{K_a}\] value indicates a weaker acid.