Single Choice

A $$0.1$$ M solution of a monobasic acid has a specific resistance of 'r' ohm-cm. Its molar conductivity is:

A$$\dfrac{10}{r}$$
B$$10r$$
C$$\dfrac{10^{4}}{r}$$
Correct Answer
D$$\dfrac{10^{4}}{2r}$$

Solution

The specific conductance is inversely proportional to the specific resistance $$ \left( k=\cfrac { 1 }{ r }\right) $$. The relationship between the molar conductivity and the specific conductance is $$ { \Lambda }_{ m }=\cfrac { \kappa \times 1000 }{ M } $$.
Substitute $$ k=\cfrac { 1 }{ r } $$ and $$ M=0.1 M $$ in the above equation,
$$ { \Lambda }_{ m }=\cfrac { \cfrac { 1 }{ r } \times 1000 }{ 0.1 } =\cfrac { { 10 }^{ 4 } }{ r }$$

Hence, option $$C$$ is correct.

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