Benzene and toluene form ideal solutions. Consider a solution of benzene and toluene prepared at 25∘C. As suming that the mole fractions of benzene and toluene in the vapor phase are equal, calculate the composition of the solution. At 25∘C the vapor pressures of benzene and toluene are 95 and 28 torr, respectively.

Xtoluene = 0.77

Xbenzene = 0.23

Explanation:

Step 1: Data given

Temperature = 25.0 °C

the mole fractions of benzene and toluene in the vapor phase are equal

At 25∘C the vapor pressures of benzene and toluene are 95 and 28 torr.

Step 2:

Xtoluene + Xbenzne = 1

Since the mol fractions are equal, the partial pressure also will be equal.

pToluene = pbenzene

Xtoluene *pToluene = Xbenzene *pBenzene = (1.00 - Xtoluene)*pBenzene

⇒with X toluene = mol fraction of toluene

⇒pbenzene = vapor pressure benzene = 95 torr

⇒Xbenzene = mol fraction benzene = 1.0 -0.5

⇒ptoluene = 28 torr

Xtoluene * 28 torr = (1.0 - Xtoluene)*95 torr

Xtoluene = 0.77

Xbenzene = 1.0 - 0.77 = 0.23