# Question #53001

##### 1 Answer

#### Explanation:

Notice that the problem provides you with the **volume** of water and its **density** at

This should automatically tell you that you can find its **mass** by using the definition of density

#color(blue)("density" = "mass"/"unit of volume")#

Water is said to have a density of **every** milliliters of water will have a mass of

If that's the case, then

#643.5 color(red)(cancel(color(black)("mL"))) * overbrace("0.9971 g"/(1color(red)(cancel(color(black)("mL")))))^(color(purple)("density")) = "641.634 g"#

Now, the **vapor pressure** of the solution will depend on the **mole fraction** of the solvent in the solution, *pure solvent*, **Raoult's Law**.

#color(blue)(P_"solvent" = chi_"solvent" xx P_"solvent"^@)#

In order to find the mole fraction of the solvent, you need to know the **number of moles** of solvent and the **total number of moles** present in solution.

Since you have the mass of water used to make this solution, use water's **molar mass** to help you find the number of moles it contains

#641.634 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "35.617 moles H"_2"O"#

To find the total number of moles present in solution, find the number of moles of *solute* first

#158.0 color(red)(cancel(color(black)("g"))) * "1 mole sucrose"/(342.3 color(red)(cancel(color(black)("g")))) = "0.4616 moles sucrose"#

The solution will thus contain a total number of

#n_"total" = "35.617 moles" + "0.4616 moles" = "36.079 moles"#

The mole fraction of water will be

#chi_"water" = (35.617color(red)(cancel(color(black)("moles"))))/(36.079color(red)(cancel(color(black)("moles")))) = 0.9872#

Therefore, the vapor pressure of the solution will be

#P_"sol" = 0.9872 * "23.76 torr"#

#P_"sol" = color(green)("23.46 torr") -># rounded to four sig figs