The vapor pressure of benzene (C6H6) at 25 degrees C is 95.1 mm Hg. What is the vapor pressure of benzene above a solution in which 5.05 g C6H5COOH (benzoic acid) is dissolved in 25 g C6H6?
Answer should be 93.9 mmHg
mols C6H6 = grams/molar mass
mols C6H5COOH = grams/molar mass
XC6H6 = mols C6H6/total mols
Psoln = XC6H6*Pobenzene
but I don't get 93.9
To find the vapor pressure of benzene above the solution, we need to use Raoult's law, which states that the vapor pressure of a component of an ideal solution is proportional to its mole fraction in the solution.
First, let's calculate the mole fraction of benzene (C6H6) and benzoic acid (C6H5COOH) in the solution.
Step 1: Convert the given masses of benzene and benzoic acid into moles.
Molar mass of C6H6 (benzene) = 78.11 g/mol
Molar mass of C6H5COOH (benzoic acid) = 122.12 g/mol
Moles of benzene (C6H6) = mass / molar mass = 25 g / 78.11 g/mol
Moles of benzoic acid (C6H5COOH) = mass / molar mass = 5.05 g / 122.12 g/mol
Step 2: Calculate the mole fraction of benzene and benzoic acid.
Mole fraction of benzene (Xbenzene) = moles of benzene / (moles of benzene + moles of benzoic acid)
Mole fraction of benzoic acid (Xbenzoic acid) = moles of benzoic acid / (moles of benzene + moles of benzoic acid)
Now that we have the mole fractions, we can use Raoult's law to find the vapor pressure of benzene above the solution.
Vapor pressure of benzene above the solution (Pbenzene) = Xbenzene * Pvapour benzene
Given: Pvapour benzene = 95.1 mmHg
Substituting the values:
Pbenzene = Xbenzene * 95.1 mmHg
To find the vapor pressure of benzene, we need to find the mole fractions of benzene and benzoic acid in the solution:
Xbenzene = moles of benzene / (moles of benzene + moles of benzoic acid)
Xbenzoic acid = moles of benzoic acid / (moles of benzene + moles of benzoic acid)
Let's calculate the mole fractions:
moles of benzene = 25 g / 78.11 g/mol
moles of benzoic acid = 5.05 g / 122.12 g/mol
Xbenzene = (25 g / 78.11 g/mol) / ( (25 g / 78.11 g/mol) + (5.05 g / 122.12 g/mol) )
Xbenzoic acid = (5.05 g / 122.12 g/mol) / ( (25 g / 78.11 g/mol) + (5.05 g / 122.12 g/mol) )
Calculating the mole fractions gives:
Xbenzene ≈ 0.853
Xbenzoic acid ≈ 0.147
Now we can find the vapor pressure of benzene using Raoult's law:
Pbenzene = Xbenzene * Pvapour benzene
Pbenzene = 0.853 * 95.1 mmHg
Pbenzene ≈ 81.1 mmHg
Therefore, the vapor pressure of benzene above the solution is approximately 81.1 mmHg.