Question

Calculate the vapour pressure of a solution at ${100}^{\circ }C$ containing $3g$ of cane sugar in $33g$ of water. $(At.wt.C=12g/mol,H=1g/mol,O=16g/mol)$

• A. $680.4mmHg$
• B. $756.3mmHg$
• C. $720.5mmHg$
• D. $540mmHg$

Answer 1

The correct option is B $756.3mmHg$

Vapour pressure of pure water (solvent) at ${100}^{\circ }C$, $p^o=760mm$

Vapour pressure of solution, p=?

Wt. of solvent, W $=33g$

Wt. of solute, w $=3g$

$\text{Mol. wt. of water}\left(H_{2}O\right),M=18g/mol$

Mol. wt. of sugar $\left(C_{12}{H}_{22}{O}_{11}\right)$,

$m=12\times 12+22\times 1+11\times 16=342g/mol$

According to Raoult's law,

$\frac{p^o-p}{p^o}=\frac{wM}{Wm}$

$\therefore p=p^o-\frac{w\times M}{m\times W}\times p^o$

$p=760-\frac{3\times 18}{342\times 33}\times 760(\therefore p^{o}for{H}_{2}O=760mm)$

$=760-3.36=756.3mmHg$