To find the molal absolute humidity of an air-water vapor mixture, we need to understand the concept of partial pressure and total pressure.

Partial Pressure:
Partial pressure refers to the pressure exerted by a particular component of a mixture if it occupied the same volume alone. In this case, the partial pressure of air (A) is given as 5 Pa.

Total Pressure:
Total pressure refers to the sum of the partial pressures of all the components in a mixture. In this case, the total pressure of the system is given as 15 Pa.

Using these values, we can calculate the mole fraction of air (Xa) in the mixture using Dalton's law of partial pressures:

Xa = Pa / Ptotal

where Pa is the partial pressure of air and Ptotal is the total pressure of the system.

In this case, Xa = 5 Pa / 15 Pa = 1/3

Mole Fraction of Water Vapor:
Since the mixture is composed of air and water vapor, the mole fraction of water vapor (Xb) can be calculated as:

Xb = 1 - Xa

Xb = 1 - 1/3 = 2/3

Molal Absolute Humidity:
Molal absolute humidity is defined as the amount of water vapor in a mixture per unit mass of the solvent. In this case, water vapor is the solute and air is the solvent. The molal absolute humidity (Wb) can be calculated using the following formula:

Wb = Xb / mw

where Xb is the mole fraction of water vapor and mw is the molecular weight of water.

Using the given options, we can calculate the molal absolute humidity for each option:

a) Wb = (2/3) / 18 = 1/27
b) Wb = 1 / 18 = 1/18
c) Wb = (3/2) / 18 = 1/12
d) Wb = 2 / 18 = 1/9

Among the given options, option A (0.5) has the closest value to the calculated molal absolute humidity of 1/27. Therefore, the correct answer is option A.