Help with vapor pressure, osmotic pressure, and freezing point?

Question

I need help with three questions for chemistry. I do not need the answer but I would like to know how to work them out/what equations to use. 1. calculate the vapor pressure of a solution of .39 mol of cholesterol in 5.4 mol of toluene at 32 degrees celcius. pure toluene has a vapor pressure of 41 torr at 32...

Answer 1

These are all colligative properties, which means they only depend on the number of particles in solution. Here we go:

1. Amazingly I couldn't remember this formula off the top of my head, but I've done some nice and quick Googling. The formula seems to be:
V.P. = (Vapor Pressure of Pure)(Mole Fraction of Solute)
the mole fraction of the solute is given by:
Moles Solute / Moles Total (including the moles of solute)
You should be able to solve that fine. (.39/(5.4+.39))*41
2. dT = kf * i * m
Where dT is the change in freezing temperature, kf is the freezing point depression constant, m is molality (moles solute / kg solvent), and i is the Van't Hoff factor (the number of particles the solute in question breaks into. For instance: organic compounds are nonionic, and don't break down, so the value for i = 1. NaCl on the other hand breaks into 2 particles, i = 2)
dT = ((5/MMC10...)/.444kg) * 1 * 4.90
3. pi = iMRT
Where pi is the osmotic pressure, i is the Van't Hoff factor, R is the Ideal Gas constant .0821 L * atm / mol * K, T is the temperature is Kelvin, and M is the molarity (moles / L)
pi / i * R * T = mol/L
mol/L * L = mol
g / MM = mol ---> g / mol = MM

I hope this helps.

Answer 2

1) Use the Clausius-Clapeyron equation:
It's a bit messy to type here so: http://en.wikipedia.org/wiki/Clausius-Cl...
(scroll down to Applications > Chemistry) It's the first one.

2) delta T(freezing point) = i*m*Kfp
i = van Hoff factor = number of ions/particles the solute dissolves into
m = molality
T(new) - T(initial) = i*m*Kfp
mol C10H8 = (5.5 / 128.18) = 0.029 mol
m = 0.029 mol / 0.444kg = 0.09664 m
T(new) = 1*(0.09664m)*(4.90 C/m) + 5.5C
T(new) = 5.974 C

3) osmotic pressure = Π = iMRT
M = molarity = mol/liters = (grams sample/MM sample) / liters solution
R = ideal gas constant = 0.0821
T = temp = 25+273 = 298K
i = 1

Set the right side equal to 0.272 atm and solve for MM

Hope this helps! =)