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UT CH 302 - Colligative Properties
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Colligative Properties- Page 1 Lecture 4: Colligative Properties • By definition a colligative property is a solution property (a property of mixtures) for which it is the amount of solute dissolved in the solvent matters but the kind of solute does not matter. • Coming to grips with this concept should immediately remind you of kinetic molecular theory of gases—in that case we treated gas molecules as indistinguishable hard spheres and (ideally) it was the number of them, rather than the type of molecules, that determined gas properties. • This means that when considering the impact of solute on a colligative property, 1 mole of sugar ≡ 1 mole Na+ ≡ 1 mole O−2 ≡ 1 mole urea ≡ 1 mole pickles do exactly the same thing Listed below are the four colligative properties we will examine during this lecture—each is kind of fun because it is associated with fairly famous physical phenomena that you might like to explain to a friend . Colligative Properties For each of these properties you will be introduced to the physical phenomenon behind the property and learn how to perform simple calculations to determine the magnitude the change in solution state function associated with a colligative property. ♦Vapor Pressure Lowering—explains the value of putting antifreeze in your radiator to keep a car from overheating ♦Boiling Point Raising—explains how you can cook spaghetti faster in salt water ♦Freezing Point Lowering explains why salt is placed on roads to keep ice from forming ♦Osmotic Pressure explains why your little brother killed the family fish when he placed them in pure water while cleaning the tank.Colligative Properties- Page 2 Concentration and Colligative Properties If colligative properties depend on the amount of the solute in the solvent, then the equations defining them must include a concentration term, and sure enough, they do. Over the next few pages you will be introduced to the equations in the context of the specific properties, but for now, simply note the similarities in structure for the equations: each equation includes a colligative property on the left side of the equation that is set equal to a concentration term and a solvent constant. ΔP vapor pressure ΔT temperature raising or lowering π osmotic pressure ΔTf= -mKf ΔP = χP0 ΔTf= -mKf π = MRT Three properties set equal to three different concentrations terms times a solvent constant Let’s practice performing concentration calculations. Two of these, molarity, M, and mole fraction, X, should be familiar to you. A third, molality, m, may be new. But all are useful ways to define the amount of stuff in solution—the more stuff, the larger the concentration. Let’s start by imagining that we are placing 50 g (0.146 mole) of the solute, sugar, in 117 g (6.5 mole) of the solvent, H2O. ♦What is χ (mole fraction) of 50g of sugar in 117 g of water? χ = molesBmolesAmolesA+ = OHsugarsugar25.6146.0146.0+ = 0.022 mole fraction sugar ♦What is m (molality) of 50g of sugar in 117 g of water? Note that the moloaity calculation is similar to a molarity calculation except that we divide by the mass of the solvent in kg rather than the liters of solution. m = solventkgmolesA, = OHkgsugarmole2,117.0,146.0 = 1.25 molalColligative Properties- Page 3 ♦What is M (molarity) of 50g of sugar in 117 g of water? First we need to find the volume of solution from a density calculation. Vsolution = (mass)(density) = (50 g + 117 g)(gmL34.11) = 125 mL M = solutionVmolesA = Lmoles125.0146.0 = 1.17 Molar So we have 3 ways to describe 50g of sugar in 117 g of water, each of which is used in a colligative property calculation. 0.022 mole fraction ≡ 1.25 m ≡ 1.17 MColligative Properties- Page 4 Time out for the Van’t Hoff equation. Every test on colligative properties includes a question that employs the Van’t Hoff equation. Text books make this seem a lot harder than it is. Very simply, Van’t Hoff corrects for the fact that the number of particles you thrown into solution is not always the number of particles that determine the magnitude of the property. For example, think about what happens when you put the following one mole quantities into a liter of water. Which one raises the boiling point the most? 1. 1 mole NaCl 2. 1 mole Na2S 3. 1 mole CaS 4. 1 mole sugar You might think 1 mole is 1 mole is 1 mole, and they are all the same. But 1 mole NaCl 1 mole Na2S 1 mole CaS 1 mole sugar In fact each produces a different number of dissolved particles in solution. • 1mole of NaCl is 2 moles of particles in the solvent • 1 mole of Na2S is 3 moles of particles in the solvent • 1 mole of insoluble CaS is 0 moles of particles in the solvent • 1 mole of sugar is 1 mole of particles in solution What we need is a correction factor for each compound, i, the Van’t Hoff factor, which is i = 2, 3, 0 and 1, respectively for the four solutions. i is simply inserted into every colligative property equation to make the correction. Oh, and the answer to the original question about the change in boiling point for the four one mole samples? 1 mole Na2S > 1 mole NaCl > 1 mole sugar > 1 mole CaS 1 mole Na+ and 1 mole Cl− 2 moles Na+ 1 mole S−2 0 moles CaS insoluble 1 mole sugarColligative Properties- Page 5 So how big of an effect does a solute concentration have on a colligative property? Now time for some math with the four different equations for colligative properties. Suppose we wanted to measure just how much 50 grams of sugar in 117 grams of water changed the magnitude of a state function. Colligative property 1: Vapor pressure depression ΔP = P0χ mole fraction which is the amount of solute added depression constant which is the vapor pressure of pure solvent at a given T. of pure solvent in vapor pressure For H2O at 25oC the pure vapor pressure is 23.8 torr So the vapor pressure depression in ΔP = 23.8 torr (0.022) = 0.524 torr And the new vapor pressure is now about 23.3 torr. By the way, this equation is referred to as Raoult’s Law which says simply that the vapor pressure above a solution is proportional to the mole fraction of the solute.Colligative Properties- Page 6 Time out for a famous vapor


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UT CH 302 - Colligative Properties

Type: Miscellaneous
Pages: 15
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