Question

A solution of 10 g of a nonvolatile binary electrolyte (mat. wt. = 100) in 500 g of water freezes at -0.74${}^o$C. What is the degree of ionisation?

[$k_f$ of water $=1.85Kmolalit{y}^{-1}$]

• A. 50%
• B. 75%
• C. 100%
• D. 0%

Answer 1

The correct option is C 100%

Number of moles of solute $=\frac{10g}{100g/mol}=0.1mol$
Molality of solution $=\frac{0.1\times 1000}{500}=0.2m$
$\Delta T_f=i{K}_{f}m$
$0.74=i\times 1.85\times 0.2$
The van't Hoff's factor $i=2$
The degree of ionisation $\alpha =\frac{i-1}{n^{\prime }-1}$
For binary electrolyte, $n^{\prime }=2$
$\alpha =\frac{2-1}{2-1}=1$
The degree of ionisation is 100%.