11.4 Colligative Properties Properties that depend on the number of particles, not the identity of it MOLE fractions Vapor Pressure Lowering Boiling Point Elevation Freezing Point Depression Osmotic Pressure

Vapor Pressure Lowering The presence of nonvolatile solute lowers the vapor pressure of a solvent The dissolved solute decreases the number of solvent molecules per unit volume.

Psolution= (ᵪsolvent)(Pᵒsolvent) Raoult’s Law Psolution= (ᵪsolvent)(Pᵒsolvent) Psolution= observed vapor pressure of the solvent in the solution ᵪsolvent = mole fraction of solvent Pᵒsolvent = vapor pressure of the pure solvent i = Van’t Hoff factor For nonelectrolytes =1; for electrolytes = number of particles formed when solute dissolves.

Example Calculate the vapor pressure caused by the addition of 100.g of sucrose, C12H22O11, to 1000.g of water if the vapor pressure of pure water at 25C is 23.8 torr.

Problem 2 with nonelectrolytes Predict the vapor pressure of a solution prepared by mixing35.0g solid Na2SO4 (molar mass = 142 g/mol) with 175g water at 25C. The vapor pressure of pure water is 23.76 torr.

BellRinger A solution is made by dissolving 50.0 grams of glucose with 600.0 grams of water. What is the vapor pressure of this solution at 80C where the vapor pressure for water is 355.1 torr. A solution is made of 20. g ofNaOH in 150g of water. What is the vapor pressure of this solution at 80C

VP from Mass % Assume you have 100g. Use the percent as your grams Example: What is the vapor pressure at 25C of a 15% non-electrolyte with a molar mass of 121.3 in water?

Molar Mass from VP Solve for mole fraction from P equation X=nsolvent/nsolvent + ncompound Find moles of solvent Plug in and solve for n of compound MM = g/mol

Example A solution made by mixing 50 grams of a compound with 500g of water has a vapor pressure of 22.8 torr (VP of pure water is 23.8 torr)

Non Ideal Solutions Liquid – liquid solutions both components are volatile Ptotal = PA + PB = ᵪAPAᵒ + ᵪBPBᵒ

Example A solution is prepared by mixing 5.81g acteone (C3H6O, molar mass = 58.1 g/mol) and 11.9 g chloroform (HCCl3, molar mass = 119.4 g/mol). At 35C, this solution has atotal vapor pressure of 260. torr. Is this an ideal solution? The vapor pressures of pure acetone and pure chloroform at 35C are 345 and 293 torr, respectively.

Calculating Mole Fraction from Pressures Mole Fraction total =1 Set one as x and the other as 1-x Set up equation with unknowns and solve for x

Example The vapor pressure of toluene at 90 C is 380 torr and the vapor pressure of water is 525.8 torr. What is the mole fraction of toluene if the total pressure is 475torr.

Boiling Point Elevation Because vp is lowered by adding solute, E must be added to the system, so BP increases ΔTb= iKbm ΔT= change in Temperature i = Van’t Hoff factore Kb = Molal boiling point elevation constant M= concentration in molality

Freezing Point Depression ΔT= iKfm

Example Calculate the freezing point and boiling point of a solution of 100.g ethylene glycol in 900.g of water

Calculating Molar Mass Solute concentration must be low Solve for m using freezing or boiling point equation Solve for moles from molality MM=grams/moles

Example A solution was prepared by dissolving 18.00g glucose in 150.0g water. The resulting solution was found to have a boiling point of 100.34C. Calculate the molar mass of glucose

Osmotic Pressure The pressure that must be applied to a solution to prevent the net movement of water from solvent to solution π= MRTi or =(n/V)Rti We can also calculate MM if given osmotice pressure MM= dRT π

Example What concentration of sodium chloride in water is needed to produce an aquaeous solution isotonic with blood (π = 7.70 atm at 25C)

Example The concentration of hemoglobin in blood is roughly 15.0g/100ml of solution. Assume that a solution contains 15.0 g of hemoglobin dissolve in water to make a 100mL of solution and that the osmotic pressure is found to be 0.0500atm at 25C. What is the molecular mass of hemoglobin? (the osmotic pressure of a 1m solution at 25C is 25.45 atm)

Example The observed osmotic pressure for a 0.10 M solution of Fe(NH4)2(SO4)2 is 10.8 atm. Compare the expected and experimental values for i.