Answer:
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
