A solution, that we may consider to be ideal, is composed of a 100⋅g masses EACH of ethanol and methanol....what is the vapour pressure of the solution?

A solution, that we may consider to be ideal, is composed of a 100⋅g masses EACH of ethanol and methanol. If the vapour pressures of each PURE solvent at a given temperature are 44.5⋅mm⋅Hg and 88.7⋅mm⋅Hg respectively, what is the vapour pressure of each component, and the vapour pressure of the solution?

1 Answer
anor277
Nov 23, 2016

Psolution≅60⋅mm⋅Hg

Explanation:

The partial pressure of each component in solution is proportional to its mole fraction.

Thus PMeOH=χMeOH×Ppure MeOH

χMeOH=Moles of MeOHMoles of MeOH + Moles of EtOH

= 100⋅g32.04⋅g⋅mol−1(100⋅g32.04⋅g⋅mol−1)+(100⋅g46.07⋅g⋅mol−1)

= 3.12⋅mol3.12⋅mol+2.17⋅mol=0.590. χ is dimensionless; why?

We could do the same thing to get χEtOH, however this is a binary solution, and the mole fractions of each component must sum to 1.

Thus χEtOH=1−χMeOH=1−0.590=0.410

And thus Psolution=PMeOH+PEtOH

= χMeOH×88.7⋅mm⋅Hg+χEtOH×44.5⋅mm⋅Hg

= 0.410×88.7⋅mm⋅Hg+0.590×44.5⋅mm⋅Hg

= ??⋅mm⋅Hg

As is typical in these solutions, the vapour is enriched with respect to the more volatile component, here methyl alcohol.

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