Colligative PropertiesPt. 3

By Shawn P. Shields, Ph.D.

This work is licensed by Shawn P. Shields-Maxwell under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Colligative Properties

A physical property of a solution that depends only on the ratio of the number of particles of solute to solvent in the solution, not the identity of the solute.

Describes a nonvolatile solute dissolved in a solvent.

Four Colligative Properties

Boiling point elevation

Freezing point depression

Vapor pressure lowering

Osmotic pressure

How can we explain these?

Recall: Pressure-Temperature Phase Diagrams

PT

TT

1 atm

vapor

liquidsolid

triple point

X mp X bp

T (C)

P (atm)

Effect of Colligative Properties on the Phase Diagram

T (C)

P (atm)1 atm

Dotted lines indicate the new phase boundaries for the solution.

The solid-liquid coexistence line is now shifted to lower temperatures.

The liquid-vapor line shifts to higher temperatures.

Effect of Colligative Properties on the Phase Diagram

T (C)

P (atm)1 atm

new mpX

new bpX

Boiling point elevation

Melting point depression

Vapor pressure lowering (come back to this)

Boiling Point ElevationRecall: The boiling point of a substance is the temperature where the vapor pressure equals the external (usually atmospheric) pressure.

The external pressure doesn’t change, but the temperature required to attain that vapor pressure is increased!

Tb = kbmTb is the increase in boiling temperaturekbis the molal boiling point elevation constant (look it up for a given solvent)m is the molality of the solute

molality= moles solutekg of solvent

Freezing Point DepressionWhen the freezing point is depressed, this means the temperature must be lower before a given substance freezes.

Tf = kfm

Tf is the decrease in freezing temperaturekfis the molal freezing point depression constant (look it up for a given solvent)m is the molality of the solutemolality (m)=

moles solutekg of solvent

Calculating Solvent Mass

Use the volume of the solvent and its density to find the mass of solvent for molality (m).

𝐦𝐨𝐥𝐚𝐥𝐢𝐭𝐲 (𝐦)=𝐦𝐨𝐥𝐞𝐬𝐬𝐨𝐥𝐮𝐭𝐞𝐤𝐠𝐨𝐟 𝐬𝐨𝐥𝐯𝐞𝐧𝐭

𝐝𝐞𝐧𝐬𝐢𝐭𝐲 ( 𝐠𝐦𝐋 )= 𝐦𝐚𝐬𝐬

𝐯𝐨𝐥𝐮𝐦𝐞

Recall: Equilibrium Vapor Pressure

Molecules in the liquid phase continuously vaporize and condense in a closed container.rate of evaporation = rate of condensation

The partial pressure of the gas is constant at equilibrium.

Liquid molecule

Vapor Pressure Lowering

The vapor pressure of the solution is lower than the pure solvent.

T (C)

P (atm)1 atm

Normal bp of pure solvent

VP at bp of pure solvent

X VP of solution

Raoult’s LawThe vapor pressure of the solution depends on the mole fraction of the solvent.

is the vapor pressure of the solution

is the mole fraction of the solvent

is the vapor pressure of the pure solvent

Raoult’s Law

The vapor pressure of the solution depends on the mole fraction of the solvent.

Liquid moleculeNonvolatile solute

Osmosis

The two regions are separated by a semipermeable membrane that allows solvent to pass, but not solute particles.

Osmosis By OpenStax College [CC BY 3.0 (http://creativecommons.org/licenses/by/3.0)], via Wikimedia Commons

The net movement of solvent molecules from a region of lower solute concentration to one with a higher concentration.

Osmotic Pressure ()Osmotic pressure is the amount of pressure required to stop the flow of solvent. A similar equation to the Ideal Gas law can be written for the osmotic pressure:

Where is the osmotic pressure (in the same units as the gas constant, R)V is the volume in L, n is moles of solute, and T is temperature in K

Osmotic Pressure ()

We can rearrange this equation to a more useful form

Where C is the concentration (M, molarity)

Example Problemswill be posted separately.