# 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"#?

##### 1 Answer

I got

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 *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

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)#