# The vapor pressure of water at 20 C is 17.5mmHg. What is the vapor pressure of water over a solution prepared from 200g of sucrose (C_12H_22O_11) and 112.3 g of water?

Dec 28, 2016

We use $\text{Raoult's Law...........}$ and calculate a solution vapour pressure of $16 \cdot m m \cdot H g$.

#### Explanation:

$\text{Raoult's Law}$ tells us that in an ideal solution, the vapour pressure of a component is proportional to the mole fraction of that component in solution.

$\text{Mole fraction of sucrose:}$ $= \text{Moles of sucrose"/"Moles of sucrose + moles of water}$

${\chi}_{\text{sucrose}} = \frac{\frac{200 \cdot g}{342.13 \cdot g \cdot m o {l}^{-} 1}}{\frac{200 \cdot g}{342.13 \cdot g \cdot m o {l}^{-} 1} + \frac{112.3 \cdot g}{18.01 \cdot g \cdot m o {l}^{-} 1}} = 0.0857$

$\text{Mole fraction of water:}$

${\chi}_{\text{water}} = \frac{\frac{112.3 \cdot g}{18.01 \cdot g \cdot m o {l}^{-} 1}}{\frac{200 \cdot g}{342.13 \cdot g \cdot m o {l}^{-} 1} + \frac{112.3 \cdot g}{18.01 \cdot g \cdot m o {l}^{-} 1}} = 0.914$

Note that by definition, ${\chi}_{\text{sucrose"+chi_"water}} = 1$

Because sucrose is involatile, the vapour pressure of the solution is proportional to the mole fraction of water:

${P}_{\text{solution"=chi_"water}} \times 17.5 \cdot m m \cdot H g$

$= 0.914 \times 17.5 \cdot m m \cdot H g = 16 \cdot m m \cdot H g$

We might have got better results if we used ethyl alcohol or acetone as the solvent rather than water, given that these organic solvents would have expressed a REDUCED mole fraction with respect to water, and thus a GREATER diminution in vapour pressure with respect to that of the pure solvent....