# What is the vapor pressure of a #"1.00-molal"# sugar solution at #25^@"C"#? Sugar is nonvolatile, nonelectrolyte solute. The vapor pressure of water at #25^@"C"# is #"23.8 torr"#. The molar mass of water is #"18 g/mol"#

##### 1 Answer

#### Answer:

#### Explanation:

The idea here is that the vapor pressure of the solution will actually be **lower** than the vapor pressure of the pure solvent because of the presence of the nonvolatile solute **Raoult's Law** here.

The vapor pressure of the solution can be expressed as

#color(blue)(ul(color(black)(P_"sol" = chi_"solvent" * P_"solvent"^@)))#

Here

#P_"sol"# is the vapor pressure of the solution at the given temperature#chi_"solvent"# is themole fractionof the solvent in the solution#P_"solvent"^@# is the vapor pressure of thepure solventat the given temperature

Now, you know that your solution has a **molality** equal to **mole** of sugar for every

To make the calculations easier, let's pick a sample of this solution that contains exactly **molar mass** of water to convert the number of grams to *moles*

#1 color(red)(cancel(color(black)("kg"))) * (10^3 quad color(red)(cancel(color(black)("g"))))/(1color(red)(cancel(color(black)("kg")))) * ("1 mole H"_2"O")/(18 color(red)(cancel(color(black)("g")))) = "55.56 moles H"_2"O"#

The **mole fraction** of water is defined as the number of moles of water divided by the **total number of moles** present in your solution. Since the sample contains exactly **mole** of sugar, so the mole fraction of water will be

#chi_"solvent" = (55.56 color(red)(cancel(color(black)("moles"))))/((55.56 + 1.00)color(red)(cancel(color(black)("moles")))) = 0.98232#

You can thus say that the vapor pressure of the solution at

#P_"sol" = 0.98232 * "23.8 torr"#

#color(darkgreen)(ul(color(black)(P_"sol" = "23.4 torr")))#

The answer is rounded to three **sig figs**.