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Question: The molar conductivity of acetic acid at infinite dilution is \(387\;S\;c{m^2}mo{l^{ - 1}}\) At the ...

The molar conductivity of acetic acid at infinite dilution is 387  S  cm2mol−1387\;S\;c{m^2}mo{l^{ - 1}} At the same temperature, 0.0010.001M solution of acetic acid, molar conductivity is 55  S  cm2mol−155\;S\;c{m^2}mo{l^{ - 1}} ,α\alpha is the degree of dissociation of 0.1 N acetic acids What is the value of 600α600\alpha ?
Assume 1−α=11 - \alpha = 1 for 0.10.1 N acid

Explanation

Solution

Molar conductivity is the conductance property of a solution containing one mole of the electrolyte or it is a function of the ionic strength of a solution or the concentration of salt. It is therefore not a constant.

Degree of dissociation α\alpha
= molar conductance at the particular concentration molar conductance at infinite dilution

Complete step-by-step answer: We have been given the molar conductivity at infinite dilution.
And the molar conductivity of acetic acid.
So for 0.001M  CH3COOH0.001M\;C{H_3}COOH ,α=ΔmΔ∞\alpha = \dfrac{{{\Delta _m}}}{{{\Delta _\infty }}}
∴α=55387=0.142\therefore \alpha = \dfrac{{55}}{{387}} = 0.142or 14.2%14.2\%
Kα=cα21−α{K_\alpha } = \dfrac{{c{\alpha ^2}}}{{1 - \alpha }}
Kα=0.001×(0.142)21−0.142=2.35×10−5{K_\alpha } = \dfrac{{0.001 \times {{(0.142)}^2}}}{{1 - 0.142}} = 2.35 \times {10^{ - 5}}
For 0.1N0.1N acid,Kα=cα2{K_\alpha } = c{\alpha ^2}
2.35×10−5=0.1×α22.35 \times {10^{ - 5}} = 0.1 \times {\alpha ^2}
∴α=0.015  or  1.5%\therefore \alpha = 0.015\;or\;1.5\%
Therefore
600α=600×0.015=9600\alpha = 600 \times 0.015 = 9

Additional information: When the solution is dilute the number of ions available per unit volume reduces, resulting in the reduction of the conductivity. ... The molar conductivity of both weak and strong electrolytes increases with a decrease in concentration or dilution. Molar conductance is dependent on the concentration of the electrolyte. When the solution is dilute the number of ions available per unit volume reduces, resulting in reduction of the conductivity.

Hence the correct answer is 9.

Note: the molar conductivity of an electrolytic solution is the conductance of the volume of the solution containing a unit mole of electrolyte that is placed between two electrodes of unit area cross-section or at a distance of one-centimetre apart. The molar conductivity of both weak and strong electrolytes increases with a decrease in concentration or dilution.