Pentane (C 5 H 12 ) and hexane (C 6 H 14 ) form an ideal solution. At 25°C the vapor pressures of pentane and hexane are 511 and 150. torr, respectively. A solution is prepared by mixing 25 mL pentane (density, 0.63 g/mL) with 45 mL hexane (density, 0.66 g/mL). a. What is the vapor pressure of the resulting solution? b. What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?

Interpretation: The vapor pressure of solution along with mole fraction composition of Pentane in the vapor has to be calculated.

Concept Introduction: Raoult’s law for ideal solution states that the mole fraction of the solvent is directly proportional to the vapor pressure of an ideal solution. Raoult’s law can be expressed by the equation,

Psolution=χsolventP°solvent

Where, Psolution   = observed vapor pressure of the solution

χsolvent    = mole fraction of solvent

            P°solvent = vapor pressure of pure solvent

Record the given info

Vapor pressure of Pentane= 511 torr

Vapor pressure Hexane = 145 torr

Density of Pentane = 0.63 g ml-1

Volume of Pentane = 25 mL

Density of Hexane = 0.66 g ml-1

Volume of Pentane = 45 mL

To calculate the total moles of solution

Molecular weight of Pentane = 72.15 g

Molecular weight of Hexane = 86.17 g

Moles of Pentane = 25 mL C5H12×0.63 gmL×1 mol72.15 g

                           = 0.22 mol

Moles of Hexane = 45 mL C6H14×0.66 gmL×1 mol86.17 g

                           = 0.34 mol

Total moles = 0.34 mol+0.22 mol

                   = 0.56 mol

Total moles in solution = 0.56 mol

To calculate the mole fraction of Pentane and Hexane

Mole fraction of Pentane = Mole pentane in solutionTotal moles in solution

                                      = 0.22 mol0.56 mol

                                      = 0

Interpretation: The vapor pressure of solution along with mole fraction composition of Pentane in the vapor has to be calculated.

Concept Introduction: Raoult’s law for ideal solution states that the mole fraction of the solvent is directly proportional to the vapor pressure of an ideal solution. Raoult’s law can be expressed by the equation,

Psolution=χsolventP°solvent

Where, Psolution   = observed vapor pressure of the solution

χsolvent    = mole fraction of solvent

            P°solvent = vapor pressure of pure solvent