# 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?

Jul 14, 2017

${\chi}_{\text{NaCl}} = 0.175$

#### Explanation:

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

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

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

where

• ${P}_{\text{soln}}$ 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

• ${\chi}_{\text{H"_2"O}}$ is the mole fraction of water, which we can use to calculate the mole fraction of $\text{NaCl}$ since that is the only other component of the solution

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

We see that the vapor pressure of water at ${25.0}^{\text{o""C}}$ is $23.756$ $\text{torr}$.

Our variables:

${P}_{\text{soln}} = 19.6$ $\text{torr}$

P_ ("H"_2"O")^"o" = 23.756 $\text{torr}$

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 $\text{NaCl}$ is

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