Question

The mass of glucose that should be dissolved in $100$ g of water in order to produce the same lowering of vapour pressure as produced by dissolving $1g$ urea in $50g$ of water is?
A. $1g$
B. $2g$
C. $6g$
D. $12g$

Answer 1

The pressure exerted by vapours over a liquid under equilibrium conditions at a certain temperature is known as vapour pressure. A solvent's vapour pressure in a solution is always lower than the pure solvent's vapour pressure. The decrease in vapour pressure is proportional to the mole fraction of the solute.
Relative lowering of vapour pressure $= \dfrac{{{W_2}{M_{_1}}}}{{{W_1}{M_2}}}$
${W_1}$ = Mass of solute
${W_2}$ = Mass of solvent
${M_{_1}}$ = Molar mass of solute
${M_2}$ = Molar mass of solvent.

Complete Step By Step Answer:
Given:
For Glucose solution
Mass of water ( ${W_2}$ ) $= 100g$
For Urea solution
Mass of Urea ( ${W_1}$ ) $= 1g$
Mass of water ( ${W_2}$ ) $= 50g$
To find = Mass of glucose ( ${W_1}$ )
Molecular mass of glucose $= 180g$
Molecular mass of urea $= 60g$
From the question, we can say that
Mole fraction of solute in glucose = Mole fraction of solute in urea
Hence, vapour pressure lowering is same in both the cases
Using the above formula of Vapour pressure,
Relative lowering of vapour pressure $= \dfrac{{{W_2}{M_{_1}}}}{{{W_1}{M_2}}}$
We are given that
Relative lowering of vapour pressure of glucose = Relative lowering of vapour pressure of urea
${\left( {\dfrac{{{W_2}{M_{_1}}}}{{{W_1}{M_2}}}} \right)_{glu\cos e}} = {\left( {\dfrac{{{W_2}{M_{_1}}}}{{{W_1}{M_2}}}} \right)_{urea}}$
Substituting the given values in the above formula,
$\dfrac{{{W_1} \times 18}}{{100 \times 180}} = \dfrac{{1 \times 18}}{{50 \times 60}}$
${W_1} = \dfrac{{100 \times 180}}{{50 \times 60}}$
On solving the above equation, we get,
$\Rightarrow {W_1} = 6g$
Therefore, the mass of glucose that should be dissolved in $100$ g of water is $6g$ .
Hence, the correct option is C. $6g$ .

Note:
Colligative properties are the characteristics of dilute solutions of non-volatile solutes that are determined by the concentration of solute particles in the solution rather than the chemical composition of the solute. Relative lowering of vapour pressure is a colligative property. Other colligative properties are Elevation of boiling point, Depression in freezing point and osmotic pressure.