Formulas for Colligative Properties

Molality Formula Lowering Elevating Depression moles of solute of the Molality = of the Osmotic kilograms of solvent Vapor Pressure BOILING Point FREEZING Point Pressure

m = moles kg

Vapor Pressure For calculating changes in colligative properties the van’t Hoff factor (i) is used. Op = M R T Example: LiCl dissociates into Li+ and Cl- so i = 2

BaCl2 dissociates into Ba+ and 2Cl- so i = 3 P = X Po This allows the researchers to account for the number of solute particles without being concerned Op = Osmotic about the type of particle being used. Pressure atm

The boiling point and freezing point change according to the number of particles that go into the P = vapor pressure of the M = molarity of solution. solvent the solution The boiling point elevates and the freezing point becomes depressed.

X = the mole fraction of the Note: R = gas constant solvent • Nonpolar substances don’t dissociate into ions so they are given a factor of 1.

• Ionic substances will dissociate into ions and so each ion must be counted. T = temperature Po = vapor pressure of the in Kelvin (K) Units pure solvent (a book value, CRC reference)

 T = i kb m  T = i kf m

 T = change in temperature  T = change in temperature Reference Only Reference Only i = the van’t Hoff factor i = the van’t Hoff factor kb = the boiling point elevation constant kf = the freezing point depression constant (a book value, CRC reference tables) (a book value, CRC reference tables) for for the solvent. the solvent.

Example: Example:

What is the boiling point of a 2 m solution of NaCl in water What is the freezing point of a 2 m solution of NaCl in water o if the boiling point elevation constant is 0.5o C / m? if the freezing point elevation constant is -1.858 C /m?

Solution: Solution:

+ - i = 2 Na+ and CL- i = 2 Na and CL

o o  T = i kb m = (2) (0.5o C m) (2m) = 2oC  T = i kf m = (2) (0.5 Cl m) (2m) = 2 C

o Note: The boiling point of water is 100o C so ADD the value Note: The freezing point of water is 0 C so SUBTRACT the to obtain the elevated boiling point. value to obtain the elevated boiling point.

Notes/ J. Haugh Visual Notes/ X Drive/Chemistry/2012