A solution of methanol and water has a vapour pressure of 248 Torr.What would you predict as the mole fractions of each component,assuming ideal behaviour? The vapour pressures of methanol and water are 256 Torr and 55.3 Torr,respectively.
A) $\chi \text { methanol }$ = 0.990,$\chi \text { water }$ = 0.010
B) $\chi \text { methanol }$ = 0.940,$\chi \text { water }$ = 0.060
C) $\chi \text { methanol }$ = 0.960,$\chi \text { water }$ = 0.040
D) $\chi \text { methanol }$ = 0.910,$\chi \text { water }$ = 0.090
E) $\chi \text { methanol }$ = 0.900,$\chi \text { water }$ = 0.100

Question

Quizplus · Accepted Answer

We can use Raoult's law to calculate the mole fractions of each component.

For methanol: 
P_methanol = X_methanol * P^o_methanol 
X_methanol = P_methanol/P^o_methanol 
X_methanol = 248/256 = 0.9688

For water: 
P_water = X_water * P^o_water 
X_water = P_water/P^o_water 
X_water = 248/55.3 = 4.477

Now we need to normalize these mole fractions:

X_total = X_methanol + X_water 
X_total = 0.9688 + 4.477 = 5.4468

X_methanol(normalized) = X_methanol/X_total 
X_methanol(normalized) = 0.9688/5.4468 = 0.1779

X_water(normalized) = X_water/X_total 
X_water(normalized) = 4.477/5.4468 = 0.8221

Therefore, the mole fractions are: 
X_methanol = 0.1779 
X_water = 0.8221

The answer closest to this result is C: $\chi \text { methanol }$ = 0.960,$\chi \text { water }$ = 0.040.

A Solution of Methanol and Water Has a Vapour Pressure χ methanol \chi \text { methanol }χ methanol

A Solution of Methanol and Water Has a Vapour Pressure $\chi \text { methanol }$