# At 55.0 C, what is the vapor pressure of a solution prepared by dissolving 57.6 g of LiF in 259 g of water? The vapor pressure of water at 55.0 C is 118 mmHg. Assume complete dissociation of the solute.

Dec 5, 2015

$\text{90.2 mmHg}$

#### Explanation:

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 the same temperature.

color(blue)(P_"sol" = chi_"solvent" * P_"solvent"^@)" ", where

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

Now, the most important thing to realize here is that lithium fluoride, $\text{LiF}$, a soluble ionic compound, will dissociate completely in aqueous solution to form lithium cations and fluoride anions.

${\text{LiF"_text((aq]) -> "Li"_text((aq])^(+) + "F}}_{\textrm{\left(a q\right]}}^{-}$

Notice that every mole of lithium fluoride produces one mole of lithium cations and one mole of fluoride anions.

This means that you get a total of two moles of ions for every one mole of lithium fluoride in the solution.

Use lithium fluoride's molar mass to determine how many moles would be found in the given sample

57.6 color(red)(cancel(color(black)("g"))) * "1 mole LiF"/(25.94color(red)(cancel(color(black)("g")))) = "2.221 moles LiF"

This means that the solution will contain

2.221 color(red)(cancel(color(black)("moles LiF"))) * "2 moles ions"/(1color(red)(cancel(color(black)("mole LiF")))) = "4.442 moles ions"

Now, water's mole fraction in this solution will be equal to the number of moles of water divided by the total number of moles present in the solution.

To get the number of moles of water, use its molar mass

259 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015 color(red)(cancel(color(black)("g")))) = "14.377 moles H"_2"O"

This means that water's mole fraction will be

chi_"water" = (14.377 color(red)(cancel(color(black)("moles"))))/( (14.377 + 4.442) color(red)(cancel(color(black)("moles")))) = 0.7640

The vapor pressure of the solution will thus be

P_"sol" = 0.7640 * "118 mmHg" = color(green)("90.2 mmHg")

The answer is rounded to three sig figs.