Question

At a certain temperature, the dissociation constants of formic acid and acetic acid are ${{1}}{{.8 \times 1}}{{{0}}^{{{ - 4}}}}$ and ${{1}}{{.8 \times 1}}{{{0}}^{{{ - 5}}}}$ respectively. The concentration of acetic acid solution in which the hydrogen ion has the same concentration as in ${{0}}{{.001M}}$ formic acid solution is equal to
a) ${{0}}{{.001M}}$
b) ${{0}}{{.01M}}$
c) ${{0}}{{.1M}}$
d) none of these

Answer 1

Hint: The smaller the dissociation constant the weaker the acid or base would be. Dissociation constant depends on the way the substances would split apart. The concentration of the reactant will be equal to the concentration of each of the products formed.

Complete step by step answer:
Given:
We have two acids here: formic acid and acetic acid which are both weak acids.
The dissociation constant of formic acid, ${{{K}}_{{{a1}}}}{{ = 1}}{{.8 \times 1}}{{{0}}^{{{ - 4}}}}$
The dissociation constant of acetic acid, ${{{K}}_{{{a2}}}}{{ = 1}}{{.8 \times 1}}{{{0}}^{{{ - 5}}}}$
The concentration of formic acid, ${{{C}}_{{1}}}{{ = 0}}{{.001M}}$
We must find out the concentration of acetic acid,${{{C}}_{{2}}}{{ = ?}}$
The concentration of hydrogen ion, $\left[ {{{{H}}_{{3}}}{{{O}}^{{ + }}}} \right]{{ = }}\sqrt {{{{K}}_{{a}}}{{ \times C}}} $
The concentration of hydrogen ion ${{(}}{{{H}}_{{3}}}{{{O}}^{{ + }}}{{)}}$ is same in both the solutions.
So, $\sqrt {{{{K}}_{{{a1}}}}{{ \times }}{{{C}}_{{1}}}} {{ = }}\sqrt {{{{K}}_{{{a2}}}}{{ \times }}{{{C}}_{{2}}}} $
$ \Rightarrow \sqrt {{{1}}{{.8 \times 1}}{{{0}}^{{{ - 4}}}}{{ \times 0}}{{.001}}} $= $\sqrt {{{1}}{{.8 \times 1}}{{{0}}^{{{ - 5}}}}{{ \times }}{{{C}}_{{2}}}} $
$ \Rightarrow {{{C}}_{{2}}}{{ = }}\dfrac{{{{1}}{{.8 \times 1}}{{{0}}^{{{ - 4}}}}{{ \times 0}}{{.001}}}}{{{{1}}{{.8 \times 1}}{{{0}}^{{{ - 5}}}}}}{{ = 0}}{{.01}}$

So, the correct answer is Option b.

Additional Information:
The dissociation constant of strong acids:
For example, ${{HCl}} \to {{{H}}^{{ + }}}{{ + C}}{{{l}}^{{ - }}}$. Hydrochloric acid is a strong acid but when it splits into hydrogen ion and chlorine ion, the concentration of ${{HCl}}$would be same as the concentration of ${{{H}}^{{ + }}}$ and ${{C}}{{{l}}^{{ - }}}$ ions.
So, the dissociation constant ${{(}}{{{K}}_{{a}}}{{)}}$ of ${{HCl = }}\dfrac{{\left[ {{{{H}}^{{ + }}}} \right]{{ + }}\left[ {{{C}}{{{l}}^{{ - }}}} \right]}}{{\left[ {{{HCl}}} \right]}}$
The dissociation constant of weak acids:
For example, ${{C}}{{{H}}_{{3}}}{{COOH}}$ (acetic acid) $ \to {{C}}{{{H}}_{{3}}}{{CO}}{{{O}}^{{ - }}}{{ + }}{{{H}}^{{ + }}}$ (${{C}}{{{H}}_{{3}}}{{CO}}{{{O}}^{{ - }}}$ is a conjugate base of acetic acid)
${{{K}}_{{a}}}{{ = }}\dfrac{{\left[ {{{C}}{{{H}}_{{3}}}{{CO}}{{{O}}^{{ - }}}} \right]{{ + }}\left[ {{{{H}}^{{ + }}}} \right]}}{{\left[ {{{C}}{{{H}}_{{3}}}{{COOH}}} \right]}}$

Note: Dissociation constant is also known as ‘Equilibrium constant’ or ‘Ionization constant’ and is represented as ${{{K}}_{{a}}}$ for acids and as ${{{K}}_{{b}}}$ for bases. The larger the equilibrium constant the stronger the acid will be and it’ll have more ${{{H}}^{{ + }}}$ ion concentration at equilibrium. Equilibrium constant doesn’t depend on the initial concentrations of reactants or products.