Question

Conductance (Siemens, S) is directly proportional to the area of the vessel and the concentration of solution in it and is inversely proportional to the length of the vessel, then the unit of constant of proportionality is:

• A. $S \, m \,mol { }^{-1}$
• B. $S \,m ^2 mol ^{-1}$
• C. $S ^{-2} m ^1 mol$
• D. $S ^2 m ^2 mol ^{-2}$

Answer 1

Answer: (B)

$c \propto a$ and $c \propto$ molarity $\propto \frac{1}{1}$
$c \propto \frac{ a }{ l } \times$ molarity $= K \times \frac{ a }{ l } \times$ molarity
$\therefore$ Unit of $K = S \times \frac{ m }{ m ^2} \times \frac{\left( m ^3\right)}{ mol }= S m ^2\, mol ^{-1}$