Question
At $${100^ \circ }C$$ the vapour pressure of a solution of $$6.5\,g$$ of a solute in $$100\,g$$ water is $$732\,mm.$$ If $${K_b} = 0.52,$$ the boiling point of this solution will be
A.
$${100^ \circ }C$$
B.
$${102^ \circ }C$$
C.
$${103^ \circ }C$$
D.
$${101^ \circ }C$$
Answer :
$${101^ \circ }C$$
Solution :
$$\eqalign{
& {\text{From Raoult's law of partial pressure,}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\frac{{p_A^ \circ - {p_S}}}{{{p_S}}} = \frac{{{n_B}}}{{{n_A}}} \cr
& \Rightarrow \frac{{760 - 732}}{{732}} = \frac{{{W_B} \times {M_A}}}{{{M_B} \times {W_A}}} \cr
& \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{28}}{{732}} = \frac{{6.5 \times 18}}{{{M_B} \times 100}} \cr
& \Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{M_B} = 30.6 \cr
& \therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\Delta {T_b} = 0.52 \times \frac{{6.5 \times 1000}}{{30.6 \times 100}} \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 1.10 \cr
& \therefore \,\,{\text{Boiling point}} = 100 + 1.10 \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {101.1^ \circ }C \approx {101^ \circ }C \cr} $$