# Question ea75e

Jun 17, 2017

$\text{225 mmHg}$

#### Explanation:

The idea here is that the vapor pressure of a solution that contains a non-volatile solute will depend on the mole fraction of the solvent and on the vapor pressure of the pure solvent at a given temperature.

${P}_{\text{sol" = chi_"solv" * P_"solv"^@" }} \to$ the equation for Raoult's Law

Here

• ${P}_{\text{sol}}$ is the vapor pressure of the solution
• ${\chi}_{\text{solv}}$ is the mole fraction of the solvent
• ${P}_{\text{solv}}^{\circ}$ is the vapor pressure of the pure solvent

Now, in order to calculate the mole fraction of the solvent, convert the mass of calcium chloride and the mass of water to moles by using the molar masses of the two compounds

125 color(red)(cancel(color(black)("g"))) * "1 mole CaCl"_2/(110.98color(red)(cancel(color(black)("g")))) = "1.126 moles CaCl"_2

522 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "28.976 moles H"_2"O"

The mole fraction of water, your solvent, is equal to the number of moles of water divided by the total number of moles present in solution

chi_"water" = (28.976 color(red)(cancel(color(black)("moles"))))/((28.976 + 1.126)color(red)(cancel(color(black)("moles")))) = 0.9626

You can thus say that the vapor pressure of the solution at ${70}^{\circ} \text{C}$ is equal to

${P}_{\text{sol" = 0.9626 * "233.77 mmHg}}$

P_"sol" = color(darkgreen)(ul(color(black)("225 mmHg")))#

The answer is rounded to three sig figs.