Colligative Properties

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1 Colligative Properties Vapor pressures have been defined as the pressure over a liquid in dynamic equilibrium between the liquid and gas phase in a closed system. The vapor pressure of a solution is different than that of a pure liquid and is a colligative property Colligative Properties Changes in colligative properties depend only on the number of solute particles present, not on the identity of the solute particles. Among colligative properties are Vapor pressure lowering Boiling point elevation Melting point depression Osmotic pressure Vapor Pressure Because of solutesolvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase. Therefore, the vapor pressure of a solution is lower than that of the pure solvent. Notice the difference in pressures What do you think would happen to the vapor pressure for a solution containing a volatile solute? The extent to which a nonvolatile solute lowers the vapor pressure Is proportional to its concentration as described by Raoult s Law 1

2 Raoult s Law: P A = X A P o A Where: P A = vapor pressure of the solution X A = mole fraction of the solvent P o A = vapor pressure of the pure solvent (X A = n solvent / n solute + n solvent ) The vapor pressure of H 2 O over a solution depends on the number of H 2 O molecules per solute molecule. P solvent proportional to X solvent Because water molecules are involved in the hydration process, fewer are free for evaporation as is expressed by the increased mole fraction of solvent. The vapor pressure of solvent over a solution is always LOWERED! 1. Calculate the expected vapor pressure at 25 o C for a solution prepared by dissolving g of common table sugar (M.W g/mol) in cm 3 of water at 25 o C. The density of water is g/cm 3 and the vapor pressure of water is torr. 2. By how many atmospheres of pressure has the pressure been lowered? Raoult s Law describes only ideal solutions, not real solutions. Or, solutions that follow Raoult s Law are ideal solutions. An ideal solution is a solution with low concentration that assumes equal size and intermolecular forces for all species in solution An ideal solution also assumes no changes in volume during the solvation process No loss or gain of energy during the solvation process Raoult s Law is a poor prediction for volatile solutions or solutions where there is a large deviation in size or intermolecular forces 2

3 Raoult s Law is therefore valid only for VERY dilute solutions or some nonpolar - nonpolar solutions For the remainder of this chapter, we will assume ideal solutions. Lets evaluate a phase diagram of a pure solvent with the effects of a nonvolatile solute Other than vapor pressure lowering, what other effects can be observed by adding a solute to a pure solvent? Boiling Point Elevation and Freezing Point Depression Nonvolatile solute-solvent interactions also cause solutions to have higher boiling points and lower freezing points than the pure solvent. Boiling Point Elevation The change in boiling point is proportional to the molality of the solution: T b = K b m where K b is the molal boiling point elevation constant, a property of the solvent. T b is added to the normal boiling point of the solvent. Due to the shift in equilibrium that lowers the vapor pressure, more energy is required to raise the solvent of a solution to its boiling point Freezing Point Depression The change in freezing point can be found similarly: T f = K f m Here K f is the molal freezing point depression constant of the solvent. K b = 0.52 o C/m for water = K Kg / mol T f is subtracted from the normal freezing point of the solvent. 3

4 Boiling Point Elevation and Freezing Point Depression Note that in both equations, T does not depend on what the solute is, but only on how many particles are dissolved. T b = K b m T f = K f m 3.A solution was prepared by dissolving g of glucose in g of water. The resulting solution was found to have a boiling point of o C. Calculate the molar mass of glucose. It is a non-electrolyte 4. What is the temperature at which an ethylene glycol (the main constituent in antifreeze, M.W g/mol) solution in a car radiator will freeze if 7.76 kg is placed in 10.0 L of water. Assume the density of water to be exactly 1 g/ml. Osmosis Some substances form semipermeable membranes, allowing some smaller particles to pass through, but blocking other larger particles. In biological systems, most semipermeable membranes allow water to pass through, but solutes are not free to do so. Osmosis In osmosis, there is net movement of solvent from the area of higher solvent concentration (lower solute concentration) to the area of lower solvent concentration (higher solute concentration) across a semi-permeable membrane. 4

5 Solvent molecules move from pure solvent to solution in an attempt to make both have the same concentration of solute. The pressure required to stop ossmosis across the membrane is called the osmotic pressure (Π) Osmotic Pressure The pressure required to stop osmosis, known as osmotic pressure, π, is π = ( n )RT = MRT V where M is the molarity of the solution If the osmotic pressure is the same on both sides of a membrane (i.e., the concentrations are the same), the solutions are isotonic. Because pressures are easily and accurately measured, osmotic pressures are often used to determine the M.W. of a large molecule 5. A sample of 2.05 g of the plastic, polystyrene was dissolved in enough toluene to form 100 ml of solution. The osmotic pressure of this solution was found to be 1.21 kpa at 25oC. Calculate the M.W. of the polymer. The process of reverse osmosis is used to filter water by applying a pressure larger than the osmotic pressure of the solution to the solution side of the membrane, resulting in a shift in the equilibrium toward the solvent side. Osmosis in Cells If the solute concentration outside the cell is greater than that inside the cell, the solution is hypertonic. Water will flow out of the cell, and crenation results. 5

6 Osmosis in Cells If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic. Colligative Properties of Electrolytes Since colligative properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes. Water will flow into the cell, and hemolysis results. The van t Hoff Factor We modify the previous equations by multiplying by the van t Hoff factor, i T f = K f m i Because electrolytes dissociate or ionize in solution, they must be adjusted for the degree of their dissociation (or in some cases, ionization). van t Hoff Factor (i) i = moles of solute particles in solution moles of solute dissociated 5. Determine the van t Hoff factor (i) for each of the following: Compound NaCl MgSO 4 MgCl 2 FeCl 3 i 6. The observed osmotic pressure for a 0.10 molar solution of Fe(NH 4 ) 2 (SO 4 ) 2 at 25 o C is 10.8 atm. Compare the expected and experimental value for the Van t Hoff Factor. 6

7 Colligative Properties of Electrolytes van t Hoff Factor One mole of NaCl in water does not really give rise to two moles of ions. Some Na+ and Cl reassociate for a short time, so the true concentration of particles is somewhat less than two times the concentration of NaCl. However, a 1 M solution of NaCl does not show twice the change in freezing point that a 1 M solution of methanol does. The van t Hoff Factor Reassociation, or ion paring, is more likely at higher concentration. Therefore, the number of particles present is concentration dependent. Colloids: Suspensions of particles larger than individual ions or molecules, but too small to be settled out by gravity. 7. How would Ion Paring affect: Vapor pressure Freezing point depression Boiling point elevation Osmosis Van Hoff Factor Tyndall Effect Colloidal suspensions can scatter rays of light. This phenomenon is known as the Tyndall effect. 7

8 Colloids in Biological Systems Some molecules have a polar, hydrophilic (waterloving) end and a nonpolar, hydrophobic (waterhating) end. Sodium stearate is one example of such a molecule. For your exam, Read and Prepare to discuss the section on colloids. Including: Tyndall effect Coagulation Hydrophilic Hydrophobic 8

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