Question

A solution of sodium chloride in water has a vapor pressure of 19.6 torr at 25 degrees Celsius. What is the mole fraction of NaCl solute particles in this solution?

Answer 1

`chi_"NaCl" = 0.175`

Explanation:

We're asked to find the mole fraction of a solute in solution, given the solution's vapor pressure at `25^"o""C"`.

To do this, we can use Raoult's law:

`P_"soln" = (P_ ("H"_2"O")^"o")(chi_ ("H"_2"O"))`

where

• `P_"soln"` is the vapor pressure of the solution

• `P_ ("H"_2"O")^"o"` is the vapor pressure of the pure solvent (water) at a given temperature

• `chi_ ("H"_2"O")` is the mole fraction of water, which we can use to calculate the mole fraction of `"NaCl"` since that is the only other component of the solution

We need to know the vapor pressure of pure water at `25^"o""C"`, which we can find in any online list:

We see that the vapor pressure of water at `25.0^"o""C"` is `23.756` `"torr"`.

Our variables:

`P_"soln" = 19.6` `"torr"`

`P_ ("H"_2"O")^"o" = 23.756` `"torr"`

`chi_ ("H"_2"O") = ?`

Plugging in known values:

`19.6color(white)(l)"torr" = (23.756color(white)(l)"torr")(chi_ ("H"_2"O"))`

`chi_ ("H"_2"O") = color(red)(0.825`

Which means the mole fraction of `"NaCl"` is

`chi_"NaCl" = 1.000 - color(red)(0.825) = color(blue)(0.175`