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# Colligative Properties III

Colligative Properties III

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### Colligative Properties III

1. 1. Colligative Properties Pt. 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.
2. 2. 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.
3. 3. Four Colligative Properties Boiling point elevation Freezing point depression Vapor pressure lowering Osmotic pressure How can we explain these?
4. 4. Recall: Pressure-Temperature Phase Diagrams PT TT 1 atm vapor liquid solid triple point X mp X bp T (C) P (atm)
5. 5. 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.
6. 6. Effect of Colligative Properties on the Phase Diagram T (C) P (atm) 1 atm new mp X new bp X Boiling point elevation Melting point depression Vapor pressure lowering (come back to this)
7. 7. Boiling Point Elevation Recall: 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 = kbm Tb is the increase in boiling temperature kbis the molal boiling point elevation constant (look it up for a given solvent) m is the molality of the solute molality = moles solute kg of solvent
8. 8. Freezing Point Depression When the freezing point is depressed, this means the temperature must be lower before a given substance freezes. Tf = kfm Tf is the decrease in freezing temperature kfis the molal freezing point depression constant (look it up for a given solvent) m is the molality of the solute molality (m) = moles solute kg of solvent
9. 9. Calculating Solvent Mass Use the volume of the solvent and its density to find the mass of solvent for molality (m). 𝐦𝐨𝐥𝐚𝐥𝐢𝐭𝐲 (𝐦) = 𝐦𝐨𝐥𝐞𝐬 𝐬𝐨𝐥𝐮𝐭𝐞 𝐤𝐠 𝐨𝐟 𝐬𝐨𝐥𝐯𝐞𝐧𝐭 𝐝𝐞𝐧𝐬𝐢𝐭𝐲 𝐠 𝐦𝐋 = 𝐦𝐚𝐬𝐬 𝐯𝐨𝐥𝐮𝐦𝐞
10. 10. 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
11. 11. 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
12. 12. Raoult’s Law The vapor pressure of the solution depends on the mole fraction of the solvent. Psoln = χsolventPsolvent ο Psoln is the vapor pressure of the solution  is the mole fraction of the solvent Psolvent ο is the vapor pressure of the pure solvent
13. 13. Raoult’s Law The vapor pressure of the solution depends on the mole fraction of the solvent. χ 𝐬𝐨𝐥𝐯𝐞𝐧𝐭 = moles 𝐬𝐨𝐥𝐯𝐞𝐧𝐭 moles solute + moles solvent Liquid molecule Nonvolatile solute
14. 14. 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.
15. 15. 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: Π V = nRT 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
16. 16. Osmotic Pressure () We can rearrange this equation to a more useful form Π V = nRT Π = n V RT = CRT Where C is the concentration (M, molarity)
17. 17. Example Problems will be posted separately.