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?

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Answer 1 · 2017-07-14T03:40:32

$χ_{NaCl} = 0.175$ $chi_"NaCl" = 0.175$

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

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

$P_{soln} = (P_{H_{2} O}^{o}) (χ_{H_{2} O})$ $P_"soln" = (P_ ("H"_2"O")^"o")(chi_ ("H"_2"O"))$

where

$P_{soln}$ $P_"soln"$ is the vapor pressure of the solution
$P_{H_{2} O}^{o}$ $P_ ("H"_2"O")^"o"$ is the vapor pressure of the pure solvent (water) at a given temperature
$χ_{H_{2} O}$ $chi_ ("H"_2"O")$ is the mole fraction of water, which we can use to calculate the mole fraction of $NaCl$ $"NaCl"$ since that is the only other component of the solution

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

http://faculty.sdmiramar.edu

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

Our variables:

$P_{soln} = 19.6$ $P_"soln" = 19.6$ $torr$ $"torr"$

$P_{H_{2} O}^{o} = 23.756$ $P_ ("H"_2"O")^"o" = 23.756$ $torr$ $"torr"$

$χ_{H_{2} O} = ?$ $chi_ ("H"_2"O") = ?$

Plugging in known values:

$19.6 l torr = (23.756 l torr) (χ_{H_{2} O})$ $19.6color(white)(l)"torr" = (23.756color(white)(l)"torr")(chi_ ("H"_2"O"))$

$χ_{H_{2} O} = 0.825$ $chi_ ("H"_2"O") = color(red)(0.825$

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

$χ_{NaCl} = 1.000 - 0.825 = 0.175$ $chi_"NaCl" = 1.000 - color(red)(0.825) = color(blue)(0.175$