Pentane (C5H12) and hexane (C6H14) form an ideal solution. At 25oC 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).
What is the vapor pressure of the resulting solution?
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Pentane (C5H12) and hexane (C6H14) form an ideal solution. At 25oC 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).
What is the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution?
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To find the vapor pressure of the resulting solution:
1. Start by converting the given volumes of pentane and hexane to mass:
Volume of pentane = 25 mL
Density of pentane = 0.63 g/mL
Mass of pentane = Volume * Density = 25 mL * 0.63 g/mL
Volume of hexane = 45 mL
Density of hexane = 0.66 g/mL
Mass of hexane = Volume * Density = 45 mL * 0.66 g/mL
2. Calculate the total mass of the solution:
Total mass of the solution = Mass of pentane + Mass of hexane
3. Calculate the mole fraction of pentane:
Mole fraction of pentane = Moles of pentane / Total moles of the solution
To calculate the moles of pentane, divide its mass by its molar mass:
Molar mass of pentane (C5H12) = 5 * atomic mass of carbon + 12 * atomic mass of hydrogen
4. Use Raoult's law to calculate the vapor pressure of the resulting solution:
Raoult's law states that the vapor pressure of an ideal solution is equal to the sum of the partial pressures of each component.
Partial pressure of pentane = Mole fraction of pentane * Vapor pressure of pentane
Partial pressure of hexane = Mole fraction of hexane * Vapor pressure of hexane
Total vapor pressure of the solution = Partial pressure of pentane + Partial pressure of hexane
You can now plug in the values and calculate the vapor pressure of the resulting solution.
To find the composition by mole fraction of pentane in the vapor that is in equilibrium with this solution:
1. Calculate the mole fraction of pentane (as shown above).
2. Use the equation for the vapor pressure of an ideal solution to determine the mole fraction of pentane in the vapor:
Vapor pressure of the solution = Mole fraction of pentane * Vapor pressure of pentane + Mole fraction of hexane * Vapor pressure of hexane
Rearrange the equation to solve for the mole fraction of pentane:
Mole fraction of pentane = (Vapor pressure of the solution - Mole fraction of hexane * Vapor pressure of hexane) / Vapor pressure of pentane
Plug in the given values and the vapor pressure of the solution previously calculated to find the composition by mole fraction of pentane in the vapor.