Toluene and pyridine form ideal solutions. consider a solution of toluene and pyridine prepared at 25°c. assuming that the mole fractions of toluene and pyridine in the vapor phase are equal, calculate the composition of the solution. at 25°c the vapor pressures of toluene and pyridine are 28 and 21 torr, respectively.
a.χpyridine: b.χtoluene:

X pyridine = 0.57

X toluene =  0.43

Explanation:

We will solve this question utilizing Raoult´s law for ideal solution of two volatile componens.

When we are told that the mole fractions of toluene and pyridine in the vapor phase are equal that implies that their partial pressures are also equal since partial pressure = χ Ptotal .

We also know that according to Raoult´s law the partial pressure of a compound A above a solution is given by

PA = XA x PºA where PA is the patial P of A, Xa is the mol fraction of A in solution and PºA is its pure vapor pressure, therefore we have for the two components in this question:

Ppyridine = Xpyridine Pºpyridine

Ptoluene =  Xtoluene Pºtoluene

Ppyridine = Ptoluene ∴  XpyridinePºpyridine =  Xtoluene Pºtoluene

but for a 2 component solution Xtoluene = (1 - Xpyridine)

so we have an equation with one unknown and we can solve for the mole fraction of pyridine:

XpyridinePºpyridine = (1-Xpyridine)Pºtoluene

substituting with our values:

Xpyridine x (21 torr) = (1-Xpyridine) x (28torr) (We can cancel the torr units)

Xpyridine x (21 ) = 28 - Xpyridine (28)

Xpyridine x ( 21 + 28 ) = 28

Xpyridine = 28/ (28+21) = 0.57

Xtoluene = 1 - 0.43 = 0.43