Question

Calculate the degree of dissociation \[\left( \alpha \right)\] of acetic acid if its molar conductivity \[{\Lambda _m}\] is \[39.05Sc{m^2}{\left( {mol} \right)^{ - 1}}\]
Given \[{\lambda _0}\left( {{H^ + }} \right) = 349.6Sc{m^2}{\left( {mol} \right)^{ - 1}}\] ; \[{\lambda _0}\left( {C{H_3}CO{O^ - }} \right) = 40.9Sc{m^2}{\left( {mol} \right)^{ - 1}}\]

Answer 1

Hint: The degree of dissociation gives the value about the number of moles dissociated at a given time. It can be determined from the molar conductivity and molar conductance at infinite dilution. The molar conductance at infinite dilution can be calculated from the molar conductance of ions.
Formula used:
\[\alpha = \dfrac{{{\Lambda _m}}}{{{\lambda _0}}}\]
\[\alpha \] is degree of dissociation
\[{\Lambda _m}\] is molar conductivity
\[{\lambda _0}\] is molar conductance at infinite dilution

Complete answer:
Acetic acid is a weak acid with the molecular formula of \[C{H_3}COOH\], it can be dissociated into ions of carboxylate and proton.
The dissociation will be as follows:
\[C{H_3}COOH \rightleftharpoons C{H_3}CO{O^ - } + {H^ + }\]
The molar conductance of carboxylate ion and proton at infinite dilution were given.
Thus, the molar conductance of acetic acid at infinite dilution can be equal to the sum of the molar conductance of carboxylate ion and proton at infinite dilution.
By substituting the values, we will get
\[{\lambda _0}\left( {C{H_3}COOH} \right) = {\lambda _0}\left( {C{H_3}COOH} \right) + {\lambda _0}\left( {{H^ + }} \right) = 349.6 + 40.9 = 390.5Sc{m^2}{\left( {mol} \right)^{ - 1}}\]
Thus, the molar conductance at infinite dilution is
\[{\lambda _0}\left( {C{H_3}COOH} \right) = 390.5Sc{m^2}{\left( {mol} \right)^{ - 1}}\]
Given molar conductivity \[{\Lambda _m}\] is \[39.05Sc{m^2}{\left( {mol} \right)^{ - 1}}\]
Substitute the values of molar conductance and molar conductivity at infinite dilution in the formula of degree of dissociation.
\[\alpha = \dfrac{{39.05}}{{390.5}} = 0.1\]
Thus, the degree of dissociation of acetic acid is \[0.1\].

Note:
The molar conductance at infinite dilution of the substances can be calculated from the ions present in it. Kohlrausch law will be used to find out the molar conductance of acids or bases at infinite dilution from the molar conductance of ions and salt at infinite dilution. The degree of dissociation of weak acids can be known from this law.