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Q.

Conductance of 0.1 M KCl (conductivity = ${X Ohm}^{- 1} {cm}^{- 1}$ ) filled in a conductivity cell is Y ${Ohm}^{- 1}$ If the conductance of 0.1 M NaOH filled in the same cell is Z ohm^-1 the molar conductance of NaOH will be

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a

$10^{3} \frac{XZ}{Y}$

b

$10^{4} \frac{XZ}{Y}$

c

$10 \frac{XZ}{Y}$

d

$0 .1 \frac{XZ}{Y}$

answer is B.

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Detailed Solution

$G = y Ω^{- 1}, k = x Ω^{- 1} {cm}^{- 1}, G = k (\frac{A}{l})$
$\frac{l}{A} = cell constant = \frac{k}{G} {cm}^{- 1} = \frac{x}{y}$
$\Rightarrow G = z = k (\frac{A}{l})$
Now, 0.1 M NaOH ,
$k = z \times (\frac{l}{A}), k = z (\frac{x}{y})$
Molar conductivity $= \frac{k}{M} \times 1000 = \frac{\frac{zx}{y} \times 1000}{0 .1} = \frac{z x}{y} \times 10^{4}$

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