Question
The specific conductance of a $$0.1$$ $$N$$ $$KCl$$ solution at $${23^ \circ }C$$ is $$0.012\,{\Omega ^{ - 1}}\,c{m^{ - 1}}.$$ The resistance of cell containing the solution at the same temperature was found to be $$55\,\Omega .$$ The cell constant will be
A.
$$0.142\,c{m^{ - 1}}$$
B.
$$0.66\,c{m^{ - 1}}$$
C.
$$0.918\,c{m^{ - 1}}$$
D.
$$1.12\,c{m^{ - 1}}$$
Answer :
$$0.66\,c{m^{ - 1}}$$
Solution :
$$\eqalign{
& {\text{Specific conductivity,}} \cr
& k = 0.012\,{\Omega ^{ - 1}}\,c{m^{ - 1}};{\text{Resistance}} = 55\,\Omega \cr
& k = \frac{1}{{{\text{resistance}}}} \times \frac{l}{a}\left[ {G = \frac{1}{R}} \right] \cr
& \frac{l}{a} = {\text{cell constant}} \cr
& \frac{l}{a} = 55 \times 0.012 \cr
& \,\,\,\,\,\, = 0.66\,c{m^{ - 1}} \cr} $$