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) = 0.990, = 0.010
B) = 0.940, = 0.060
C) = 0.960, = 0.040
D) = 0.910, = 0.090
E) = 0.900, = 0.100

Question

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) = 0.990, = 0.010 
B) = 0.940, = 0.060 
C) = 0.960, = 0.040 
D) = 0.910, = 0.090 
E) = 0.900, = 0.100

Quizplus · Accepted Answer

Using Raoult's law, the total vapour pressure of the solution can be calculated as:

P_total = P_methanol * x_methanol + P_water * x_water

where P_methanol and P_water are the vapour pressures of pure methanol and water respectively, and x_methanol and x_water are the mole fractions of methanol and water in the solution.

Substituting the given values, we get:

248 = 256 * x_methanol + 55.3 * x_water

Solving the above equation for x_methanol and x_water, we get:

x_methanol = (248 - 55.3 * x_water) / 256

Substituting the values one by one from the given answer choices, we find that only choice C satisfies the above equation:

x_water = 0.04 => x_methanol = (248 - 55.3 * 0.04) / 256 = 0.96

Therefore, the predicted mole fractions of methanol and water in the solution are 0.96 and 0.04, respectively.

A Solution of Methanol and Water Has a Vapour Pressure