Colligative properties are those that depend on the number of solute particles.
ID: 979330 • Letter: C
Question
Colligative properties are those that depend on the number of solute particles. Because electrolytes dissociate into ions, the concentration of particles in the solution is greater than the formula-unit concentration of the solution. For example, if 1 mol of Na2SO4 totally dissociates, 3 mol of ions are produced (2 mol of Na+ ions and 1 mol of SO42ions). Thus, a colligative property such as osmotic pressure will be three times greater for a 1 MNa2SO4 solution than for a 1 M nonelectrolyte solution.
However, complete dissociation of electrolytes does not always occur. The extent of dissociation is expressed by the van't Hoff factor, i:
i = moles of particles in solutionmoles of solute dissolved
The equations for colligative properties can be written to include i. For example,
Tf = Kfmi
Tb = Kbmi
Part A
Assuming complete dissociation of the solute, how many grams of KNO3 must be added to 275 mL of water to produce a solution that freezes at 14.5 C? The freezing point for pure water is 0.0 C and Kf is equal to 1.86 C/m.
Express your answer to three significant figures and include the appropriate units.
Explanation / Answer
Volume of water = 275 mL
Freezing point of the solution = - 14.5 0C
Freezing point of the pure solvent = 00C , kf of water = 1.86 0 C / m
We use following formula
Delta Tf= i m kf
Here delta Tf is freezing point depression = Freezing point of the solvent – freezing point of the solution
. i is Vant’hoff factor here for KNO3 = 2 since KNO3 dissociates into two ions.
Kf is freezing point constant of pure solvent and m is molality.
Lets plug given values.
14.50C = 2 x m x 1.86 0C/m
m = 3.898 mol / kg
We have to find moles of solute ( KNO3)
Molality = moles of solute / mass of solvent in kg.
Mass of solvent in kg = Mass of water = ( 275 mL x 1.g/ mL x 1kg / 1000 g ) = 0.275 kg
Lets plug this value in molality.
3.898 mol = moles of KNO3 / 0.275 kg
n KNO3 = 1.07195
mass of KNO3 = moles x molar mass
= 1.07195 mol x 101.1032 g /mol
= 108.38 g
So the mass of KNO3 = 108.32 g