Single Choice

Resistance of $$0.2\ M$$ solution of an electrolyte is $$ 50\ \Omega $$. The specific conductance of the solution is $$ 1.4\ S$$ $$ m^{-1}$$. The resistance of $$ 0.5\ M$$ solution of the same electrolyte is $$ 280\ \Omega $$. The molar conductivity of $$ 0.5\ M$$ solution of the electrolyte in $$ S$$ $$ m^{2}$$ $$ mol^{-1}$$ is:

A$$ 5\times 10^{3}$$
B$$ 5\times 10^{2}$$
C$$ 5\times 10^{-4}$$
Correct Answer
D$$ 5\times 10^{-3}$$

Solution

We know,

R=
1
K

×
l
A



50=
1
1.4

×
l
A



l
A

=70m−1

Again,

280=
1
K

×70

K=
1
4

Sm−1

Now,
Λm=
k×1000
M

×(10−2)3

Λm=
1
4

×(
1000
M

)(10−2m)3

=
1
4

×
1000
0.5

×10−6

=500×10−6

=5×10−4Sm2mol−1

Hence, option C is correct.

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