Question

A cell, with cell constant $0.4\, cm ^{-1}$, has the resistance of $40 \,ohm$ of a $0.01 \,M$ solution of an electrolyte, then the molar conductivity in $ohm ^{-1} \,cm ^{2} \,mol ^{-1}$ will be

• A. $ 10^{4} $
• B. $ 10^{3} $
• C. $ 10^{2} $
• D. $ 1 $

Answer 1

Answer: (B)

Cell constant $=0.4 \,cm ^{-1}$ Resistance $=40\, ohm$
$\therefore $ Conductivity $=\frac{1}{40} \,ohm ^{-1}$
Concentration of solution $=0.01 \,M$
Specific conductivity $=$ conductivity $\times$ cell Constant
$=\frac{1}{40} \,ohm ^{-1} \times 0.4 \,cm ^{-1}$
$\therefore $ Specific conductivity $=0.01 \,ohm ^{-1}\, cm ^{-1}$
Molar conductivity $=\frac{\text { specific conductivity } \times 1000}{\text { concentration }(\text { molarity })}$
$=\frac{0.01 \times 1000}{0.01}\, ohm ^{-1\,} cm ^{2}\, mol ^{-1}$
$\therefore $ Molar conductivity $=1000\, ohm ^{-1} \,cm ^{2} \,mol ^{-1}$