Final answer:
Raoult's Law is used to calculate the vapor and liquid compositions in equilibrium by multiplying the mole fraction of component A in the liquid with its pure component vapor pressure. The mole fractions are found using the amount of each component and the total pressure. Dalton's Law is applied to relate the partial pressure with the mole fraction in the vapor phase.
Step-by-step explanation:
To calculate the vapor and liquid compositions in equilibrium for a system of components A/B using Raoult's Law, you first need to determine the mole fractions of each component in the liquid phase. According to Raoult's Law, the vapor pressure of a component (PA) in a mixture is equal to the product of its mole fraction in the liquid phase (XA) and its pure component vapor pressure (P°A).
We have PA = XA*P°A for component A. If we have a binary solution with component A and a nonvolatile solute B, we can use the relation XA + XB = 1. Knowing PA and the total pressure PTOT (101.3 kPa), you need to solve for the mole fraction of A in the liquid (XA) and the vapor phase (YA). The mole fraction of B in the liquid (XB) can be found using XB = 1 - XA. To find the mole fraction in the vapor phase (YA), you would use Dalton's Law to relate the partial pressure of A (PA) to the total pressure after which YA can be expressed as PA/PTOT.
For a given mixture, the mole fractions are calculated using the number of moles of each component. For example, if a mixture contains 0.50 mol A and 1.00 mol B, then XA = 0.5/(0.5+1.0) = 0.33. Similarly, XB = 1 - XA = 0.67. By substituting these values into Raoult's Law, we can determine the partial pressures and from there the composition of the vapor phase.