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?

1 Answer
Jul 14, 2017

Answer:

#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:

http://faculty.sdmiramar.edu

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#