At a given temperature, you have a mixture of benzene (vapor pressure of pure be

Question

At a given temperature, you have a mixture of benzene (vapor pressure of pure benzene = 745 torr) and toluene (vapor pressure of pure toluene = 290 torr). The vapor is collected, condensed and the resulting liquid is allowed to equilibrate with its vapor. This vapor is collected, condensed and the resulting liquid is allowed to equilibrate with its vapor. The mole fraction of benzene in this vapor is 0.830. Assuming ideal behavior, calculate the mole fraction of toluene in the original solution.

Explanation / Answer

Xtol = 1 - Xbenz

Total pressure can be calculated via Raoult's law

Ptotal = Xbenz Pbenz + Xtol Ptol

= (0.830)(745) +(1-0.830)(290) = 667.65 torr

Partial vapour pressure of Toulene over the soln. fromn Raoult's law

P1tol = Xtol P tol = 49.3

From Dalton's law Ytol = P1 tol/P total = 0.073

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