At a certain temperature the vapor pressure of pure benzene is measured to be 322. torr . Suppose a solution is prepared by mixing 138.g of benzene and 91.2g of heptane .
Calculate the partial pressure of benzene vapor above this solution. 3 sig figs!
Steps/equations are appreciated...!
To calculate the partial pressure of benzene vapor above the solution, we can use Raoult's Law, which states that the vapor pressure of a component in a solution is directly proportional to its mole fraction in the solution.
Here are the steps to calculate the partial pressure of benzene vapor above the solution:
1. Calculate the moles of benzene (C6H6) and heptane (C7H16) in the solution using their respective masses and molar masses.
Moles of benzene = Mass of benzene / Molar mass of benzene
= 138. g / 78.11 g/mol
= 1.77 mol
Moles of heptane = Mass of heptane / Molar mass of heptane
= 91.2 g / 100.21 g/mol
= 0.910 mol
2. Calculate the mole fraction of benzene (Xbenzene) and heptane (Xheptane) in the solution.
Mole fraction = Moles of component / Total moles in solution
Xbenzene = Moles of benzene / (Moles of benzene + Moles of heptane)
= 1.77 mol / (1.77 mol + 0.910 mol)
= 0.660
Xheptane = Moles of heptane / (Moles of benzene + Moles of heptane)
= 0.910 mol / (1.77 mol + 0.910 mol)
= 0.340
3. Use Raoult's Law to calculate the partial pressure of benzene vapor (Pbenzene).
Pbenzene = Xbenzene * Vapor pressure of benzene
= 0.660 * 322. torr
= 212.5 torr
Therefore, the partial pressure of benzene vapor above the solution is 212.5 torr (rounded to 3 significant figures).
To calculate the partial pressure of benzene vapor above the solution, we will use Raoult's law, which states that the vapor pressure of each component in a solution is directly proportional to its mole fraction.
First, we need to find the mole fraction of benzene in the solution. The mole fraction (X) of a component is calculated by dividing the moles of that component by the total moles of all components in the solution.
Step 1: Calculate the moles of benzene and heptane.
Moles of benzene = mass of benzene / molar mass of benzene
Molar mass of benzene = 78.11 g/mol
Moles of benzene = 138 g / 78.11 g/mol
Moles of heptane = mass of heptane / molar mass of heptane
Molar mass of heptane = 100.2 g/mol
Moles of heptane = 91.2 g / 100.2 g/mol
Step 2: Calculate the total moles of all components in the solution.
Total moles = moles of benzene + moles of heptane
Step 3: Calculate the mole fraction of benzene.
Mole fraction of benzene = moles of benzene / total moles
Step 4: Use Raoult's law to calculate the partial pressure of benzene vapor.
Partial pressure of benzene vapor = mole fraction of benzene * vapor pressure of pure benzene
The vapor pressure of pure benzene is given as 322 torr.
Now, let's plug in the numbers and calculate the partial pressure of benzene vapor.
Moles of benzene = (138 g / 78.11 g/mol) = 1.766 mol
Moles of heptane = (91.2 g / 100.2 g/mol) = 0.909 mol
Total moles = 1.766 mol + 0.909 mol = 2.675 mol
Mole fraction of benzene = 1.766 mol / 2.675 mol = 0.6598
Partial pressure of benzene vapor = 0.6598 * 322 torr
Calculating the partial pressure gives us:
Partial pressure of benzene vapor = 212.4 torr (rounded to 3 significant figures)
Therefore, the partial pressure of benzene vapor above this solution is 212.4 torr.
n benzene = grams/molar mass
n heptane = grams/molar mass
Xbenzene = n benzene/totalmols
pbenzene = Xbenzene*Pobenzene