Raoults Law Calculating Vapor Pressure of Volatile Solutions

This example problem demonstrates how to use Raoults Law to calculate the vapor pressure of two volatile solutions mixed together. Raoult's Law Example What is the expected vapor pressure when 58.9 g of hexane (C6H14) is mixed with 44.0 g of benzene (C6H6) at 60.0 Â °C?Given:Vapor pressure of pure hexane at 60 Â °C is 573 torr.Vapor pressure of pure benzene at 60 Â °C is 391 torr. Solution Raoults Law can be used to express the vapor pressure relationships of solutions containing both volatile and nonvolatile solvents. Raoults Law is expressed by the vapor pressure equation:Psolution ÃŽ §solventP0solventwherePsolution is the vapor pressure of the solutionÃŽ §solvent is mole fraction of the solventP0solvent is the vapor pressure of the pure solventWhen two or more volatile solutions are mixed, each pressure component of the mixed solution is added together to find the total vapor pressure.PTotal Psolution A Psolution B ...Step 1 - Determine the number of moles of each solution in order to be able to calculate the mole fraction of the components.From the periodic table, the atomic masses of the carbon and hydrogen atoms in hexane and benzene are:C 12 g/molH 1 g/mol Use the molecular weights to find the number of moles of each component:molar weight of hexane 6(12) 14(1) g/molmolar weight of hexane 72 14 g/molmolar weight of hexane 86 g/molnhexane 58.9 g x 1 mol/86 gnhexane 0.685 molmolar weight of benzene 6(12) 6(1) g/molmolar weight of benzene 72 6 g/molmolar weight of benzene 78 g/molnbenzene 44.0 g x 1 mol/78 gnbenzene 0.564 molStep 2 - Find mole fraction of each solution. It doesnt matter which component you use to perform the calculation. In fact, a good way to check your work is to do the calculation for both hexane and benzene and then make sure they add up to 1.ÃŽ §hexane nhexane/(nhexane nbenzene)ÃŽ §hexane 0.685/(0.685 0.564)ÃŽ §hexane 0.685/1.249ÃŽ §hexane 0.548Since there are only two solutions present and the total mole fraction is equal to one:ÃŽ §benzene 1 - ÃŽ §hexaneÃŽ §benzene 1 - 0.548ÃŽ §benzene 0.452Step 3 - Find the total vapor pressure by plugging the values into the equation:PTotal ÃŽ §hexaneP0hexane ÃŽ §benzeneP0benzenePTotal 0.548 x 573 torr 0.452 x 391 torrPTotal 314 177 t orrPTotal 491 torr Answer: The vapor pressure of this solution of hexane and benzene at 60 Â °C is 491 torr.