Solutions and Colligative Properties - Result Question 31
####2. What would be the molality of $20 %$ (mass/mass) aqueous solution of KI? (Molar mass of KI = $166 g mol^{-1}$ )
(2019 Main, 9 April I)
(a) 1.48
(b) 1.51
(c) 1.35
(d) 1.08
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Solution:
- The expression of elevation of boiling point,
$$ \begin{aligned} \Delta T _b & =K _b \times m \times i \ & =k _b \times \frac{w _2 \times 1000}{M _2 \times w _1} \times i \end{aligned} $$
where, $m=$ molality
$i=$ van’t Hoff factor $=1$ (for non-electrolyte/non-associable)
$w _2=$ mass of solute in $g=1 g$ (present in both of the solutions)
$M _2=$ molar mass of solute in $g mol^{-1}$ (same solute in both of the solutions)
$w _1=$ mass of solvent in $g=100 g$ (for both of the solvents $A$ and $B$ )
$K _b=$ ebullioscopic constant
So, the expression becomes,
$$ \begin{aligned} & \Delta T _b \propto K _b \ & \Rightarrow \quad \frac{\Delta T _b(A)}{\Delta T _b(B)}=\frac{K _b(A)}{K _b(B)}=\frac{1}{5} \quad\left[\text { Given } \frac{K _b(A)}{K _b(B)}=\frac{1}{5}\right] \end{aligned} $$
