Question

$8 \%$ aqueous solution of urea (by mass of solvent) has elevation in boiling point $x _{1} .20 \%$ aqueous solution of glucose (by mass of solvent) has elevation in boiling point $x_{2}$. If these two solutions are mixed then, elevation in boiling point is $x _{3}$. Then,

• A. $x_{1}+x_{2}=x_{3}$
• B. $3 x_{1}+x_{2}=x_{3}$
• C. $x_{1} < x_{2} < x_{3}$
• D. $x_{1}=x_{2}=x_{3}$

Answer 1

Answer: (D)

$6 \%$ urea solution, $\Delta T_{b}=\frac{1000 K_{b} w_{1}}{m_{1} w_{2}}$

$\Delta T_{b}($ urea $)=x_{1}=\frac{1000 \times K_{b} \times 8}{60 \times 100}=K_{b}$

$\Delta T_{b}($ glucose $)=x_{2}=\frac{1000 \times K_{b} \times 20}{60 \times 100}=K_{b}$

$\Delta T_{b}$ (mixture) $=\frac{1000(\text { total moles of solute }) K _{ b }}{\text { Total mass of solvent }}$

$=\frac{1000 \times K_{b} \times 25}{200}$

$x_{3}=K_{b}$

Thus, $x_{1}=x_{2}=x_{3}$