Question

Equivalent conductivity of acetic acid at infinite dilution is \[{\text{390}}{\text{.7 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}\] and for \[{\text{0}}{\text{.1 M}}\] acetic acid is \[{\text{5}}{\text{.2 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}\] . Calculate degree of dissociation, \[{{\text{H}}^ + }\] ion concentration and dissociation constant of the acid.

Answer 1

Hint: To Calculate the degree of dissociation \['\alpha '\] ,we will be dividing the equivalent conductivity at concentration of \[{\text{0}}{\text{.1 M}}\] to the equivalent conductivity at infinite dilution.
  \[\alpha = \dfrac{\Lambda }{{{\Lambda ^\infty }}}\]
To calculate the hydrogen ion concentration ,we will be multiplying the degree of dissociation with the concentration of acetic acid.
\[\left[ {{{\text{H}}^ + }} \right] = \alpha \times C\]
We will calculate the equilibrium constant by using the following relationship.
\[K = \dfrac{{{\alpha ^2}C}}{{1 - \alpha }}\]

Complete step by step answer:
Equivalent conductivity of acetic acid at infinite dilution is \[{\text{390}}{\text{.7 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}\] and for \[{\text{0}}{\text{.1 M}}\] acetic acid is \[{\text{5}}{\text{.2 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}\] .
We can calculate the degree of dissociation \['\alpha '\] by dividing the equivalent conductivity at concentration of \[{\text{0}}{\text{.1 M}}\] to the equivalent conductivity at infinite dilution.
  \[
  \alpha = \dfrac{\Lambda }{{{\Lambda ^\infty }}} \\
  \alpha = \dfrac{{{\text{5}}{\text{.2 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}}}{{{\text{390}}{\text{.7 mho c}}{{\text{m}}^{\text{2}}}{\text{ gm }}{\text{. equi}}{{\text{v}}^{\text{2}}}}} \\
  \alpha = 0.0133 \\
  \alpha = 1.33\% \\
 \]
Hence, the degree of dissociation of acetic acid is 0.0133.

The concentration ‘C’ of acetic acid is \[{\text{0}}{\text{.1 M}}\] .
We can calculate the hydrogen ion concentration by using the following relationship
\[
  \left[ {{{\text{H}}^ + }} \right] = \alpha \times C \\
  \left[ {{{\text{H}}^ + }} \right] = 0.0133 \times 0.1 \\
  \left[ {{{\text{H}}^ + }} \right] = 0.00133{\text{ M}} \\
 \]
Hence, the hydrogen ion concentration is equal to \[0.00133{\text{ M}}\] .
We can calculate the equilibrium constant by using the following relationship.
\[
  K = \dfrac{{{\alpha ^2}C}}{{1 - \alpha }} \\
  K = \dfrac{{{{\left( {0.0133} \right)}^2} \times 0.00133{\text{ }}}}{{1 - 0.0133}} \\
  K = 2.38 \times {10^{ - 5}} \\
 \]
Hence, the value of the equilibrium constant is \[2.38 \times {10^{ - 5}}\] .

Note: Acetic acid is a weak acid and is partially dissociated in aqueous solution. The hydrogen ion concentration in the aqueous solution depends on two factors. One is the degree of dissociation of acetic acid and the other is the initial concentration of acetic acid.