What is the mol fraction of ethylene glycol in the solution phase for an aqueous solution with a vapor pressure of #"760 torr"# if the pure vapor pressure was #"1077 torr"#?

I got #0.294#.

Raoult's law states:

#P_j = chi_j^lP_j^"*"#,

where:

• #P_j# is the partial vapor pressure above the solution coming from the component #j# in solution.
• #P_j^"*"# is the vapor pressure above a sample of pure liquid #j# at the same #T# as the solution.
• #chi_j^l# is the mol fraction of #j# in the liquid phase.

Since the total vapor pressure of the solution was given, which is lower than the pure vapor pressure of water, there was a decrease in vapor pressure.

I assume however, that the #"1 atm"# #=# #"760 torr"# is for the WATER in the solution, not for the ENTIRE solution (though the question was written in such a way that it seemed to be for the overall solution...).

To track that change:

#DeltaP = P_i - P_i^"*"#,

where #P_i^"*"# was the vapor pressure of water before adding ethylene glycol, and #P_i# is the vapor pressure of water after adding ethylene glycol.

Then, plugging in Raoult's law:

#DeltaP = chi_i^lP_i^"*" - P_i^"*"#

#= P_i^"*"(chi_i^l - 1)#

#= -chi_j^lP_i^"*"#

The change in pressure was:

#"760 torr"# #-# #"1077 torr" = -"317 torr"#

So, the mol fraction of ethylene glycol in the solution (not in the vapor phase) would be:

#color(blue)(chi_j^l) = -(DeltaP)/(P_i^"*")#

#= -(-"317 torr")/("1077 torr")#

#= color(blue)(0.294)#