Question

The resistance of 1N solution of acetic acid is 250 ohm, when measured in a cell having a cell constant of \[1.15c{m^{ - 1}}\] .The equivalent conductance (in \[oh{m^{ - 1}}c{m^2}equ{i^{ - 1}}\]) of 1N acetic acid is:
A.2.3
B.4.6
C.9.2
D.18.4

Answer 1

Hint: Equivalent conductance of an electrolyte is defined as the conductance of a volume of solution containing one equivalent weight of dissolved substance when placed between two parallel electrodes 1 cm apart, and large enough to contain between them all of the solution.
Formula used:
\[Equivalence{\text{ }}conductance\] $ = \dfrac{{cell constant}}{{resistance}}$

Complete step by step answer:
In the above question,
Cell constant = $1.15c{m^{ - 1}}$
Resistance= $250$ ohm
Therefore, according to the given formula
\[Equivalence{\text{ }}conductance\] = $\dfrac{{1.15 \times 1000}}{{250}}$
\[ = \] $\dfrac{{1100}}{{250}}$ $ = 4.6 oh{m^{ - 1}}c{m^2}equ{i^{ - 1}}$

Hence, option B is correct.

Additional information:
At infinite dilution, when dissociation is complete, each ion makes a definite contribution towards equivalent conductance of the electrolyte irrespective of the nature of the ion with which it is associated and the value of equivalent conductance at infinite dilution for an electrolyte is the sum of contribution of its constituent ions i.e. anions and cations

Note:
A cell constant has a unit of 1/cm, where the number refers to the ratio of the distance between the electrode plates to the surface area of the plate. To determine the electrical conductivity, the measured current is multiplied by the cell constant.