# Chapter 13: Physical Properties of Solutions

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1 Chapter 13: Physical Properties of Solutions Key topics: Molecular Picture (interactions, enthalpy, entropy) Concentration Units Colligative Properties terminology: Solution: a homogeneous mixture Solute: the component that is dissolved in solvent -- usually in smaller amount Solvent: medium (often water) into which solutes are mixed -- usually in greater amount concentration: describes how much solute there is -- dilute: small amount of solute -- concentrated: large amount of solute -- saturated: contains as much solute as can be dissolved -- unsaturated: can dissolve more solute -- supersaturated: more than saturated, unstable -- solubility: amount of solute dissolved in a given volume of a saturated solution a supersaturated solution can be prepared by forming a saturated solution at a high temperature, and then cooling it (many solutes are more soluble at higher temperature)

2 Some of the solute will fall out of solution (as a solid) if the solution is disturbed (vibration, dust, etc) Addition of a crystal (nucleation site) causes precipitation from a supersaturated solution. Molecular view of a soluble ionic compound in water. Molecular view of the solution process: Ultimately, we can say that any process is governed by ΔG = ΔH - TΔS (Equation 14.10, ΔG < 0 for spontaneity) ΔH < 0 helps (exothermic, H = enthalpy) ΔS > 0 helps (increased disorder, S = entropy) ΔH > 0 (endothermic) is possible if ΔS compensates

3 First examine ΔH: Since ΔH soln is a state function, we can think of it as: ΔH 1 > 0; ΔH 2 > 0; ΔH 3 < 0 where, in terms of intermolecular forces, we have ΔH 1 = disruption of solute-solute interactions ΔH 2 = disruption of solvent-solvent interactions ΔH 3 = formation of solute-solvent interactions ΔH soln = ΔH 1 + ΔH 2 + ΔH 3 = heat of solution For a gas dissolving in a liquid, ΔH soln is usually exothermic because ΔH 1 = 0 (gas molecules don t interact)

4 The saying like dissolves like is useful in predicting solubility. This expression is about the intermolecular forces present in the solute vs. solvent. CCl 4 dissolves in benzene (C 6 H 6 ) : both nonpolar water (H 2 O) and methanol (CH 3 OH) dissolve in each other : both polar ionic compounds dissolve in polar solvents due to solvation ionic compounds are not soluble in nonpolar solvents example: vitamin C and vitamin D: water or fat soluble? Two liquids that are soluble in each other in all proportions are called miscible (opposite is immiscible) Next examine ΔS: ΔS > 0 helps (increased disorder, S = entropy) in solution formation, and there is a natural tendency for entropy to increase in any process. A solution is usually more disordered than the separate solute and solvent molecules.

5 Schematic depiction of the mixing of solvent and solute. Concentration Units: molarity = M = moles of solute liters of solution molality = m = moles of solute mass of solvent (in kg) For very dilute aqueous solutions, molarity and molality are equal since 1 L of H 2 O weighs 1 kg. mole fraction of A = A = moles of A sum of moles of all components

6 mass of solute percent by mass = mass of solute + solvent 100% mass of solute = 100% = parts per hundred mass of solution If we multiply by 10 6 instead of 100 we get parts per million (ppm); if we multiply by 10 9 we get parts per billion (ppb). e.g., the drinking water standard for arsenic is 10 ppb (EPA s Maximum Contaminant Level) Choice of units depends on the purpose of the experiment: w Mole fraction: used for gases and vapor pressures of solutions w Molarity: commonly used since volumes of solutions are easy to measure w Molality: temperature independent w Percent by Mass: temperature independent and we don t need to know the molar mass Unit Conversions: e.g., Determine the molality of an aqueous solution that is 4.5% urea by mass. Solution:

7 The molar mass of urea is g/mol. There are different ways to approach this: we will assume we have 1 kg of water. Then, with the mass of urea as x, x 4.5 = 100 ) 100x =4.5(x +1kg); ) 95.5x =4.5kg x +1kg Which gives x = g. The molality is then (47.12 g)/(60.06 g/mol) 1kg =0.78 m e.g., At 20.0 C, a m aqueous solution of glucose (C 6 H 12 O 6 ) has a density of g/ml. Calculate the molarity of this solution. Solution: In 1 kg of water, we have mol glucose. Also, mol glucose weights (0.258 mol)( g/mol) = g. Therefore we have (1 kg) + (46.48 g) = g solution. This occupies ( g) / ( g/ml) = ml. Thus the molarity is (0.258 mol) / ( L) = M. Factors that affect solubility: We can sometimes rationalize solubility using Le Chatelier's principle. e.g., dissolving oxygen in water releases heat: O 2 (g) O 2 (dissolved) + heat

8 Therefore raising the temperature (adding heat) shifts the equilibrium to the left, which means that less oxygen dissolves at higher temperature. Solubility of some compounds vs temperature. For an endothermic process, heat + solute(undissolved) solute(dissolved) raising the temperature shifts the equilibrium to the right, which means that more solute dissolves. But in general other factors (e.g. entropy) make it hard to predict the effect of temperature on solubility.

9 For gases, pressure also affects the solubility. P1 < P2 gas + solution(little gas) solution(more gas) Increasing the pressure will result in a shift of equilibrium to the right to reduce the pressure (remove gas). e.g., open a can of soda (pressure drops, shift to left) Henry s Law makes this quantitative: c = kp c molar concentration (mol/l) of dissolved gas k Henry s Law constant P gas pressure (atm) e.g., Calculate the molar concentration of O2 in water at 25ºC under atmospheric conditions (air contains 22% oxygen). k = 1.3 x 10-3 mol/l atm.

10 Solution: c = (1.3 x 10-3 mol/l atm)(1 atm x 22/100) = 2.9 x 10-4 mol/l e.g., Calculate the pressure of O 2 necessary to generate an aqueous solution that is 3.4 x 10-2 M in O 2 at 25ºC. Solution: From the previous problem, we know that a pressure of 0.22 atm O 2 gives a solution of 2.9 x 10-4 M. From Henry s Law, we know that doubling the pressure also doubles the amount of dissolved gas. Therefore, = atm = 25.8 atm Colligative Properties: Properties that depend only on the number of solute particles in solution and not the nature of the solute. Non-volatile solute interferes with the solvent s liquid-vapor equilibrium (from chemwiki.ucdavis.edu).

11 1. Vapor-Pressure Lowering For a non-volatile solute, the vapor pressure of the liquid decreases. Another way to think of it: solute shifts equilibrium to the left solvent (l) solvent (g) Raoult s Law makes this quantitative: P 1 = 1 P o 1 P 1 partial pressure of a solvent over a solution 1 mole fraction of the solvent in the solution P o 1 vapor pressure of the pure solvent Note: If there is only one solute, χ 1 = (1-χ 2 ) where χ 2 is the mole fraction of the solute, and thus P 1 =(1 2)P o 1 ) P o 1 P 1 = P = 2 P o 1 e.g., Calculate the mass of urea that should be dissolved in 225 g of water at 35ºC to produce a solution with a vapor pressure of 37.1 mmhg. (At 35ºC, P o H 2 O = 42.2 mmhg ) Solution #1: How many moles of water do we have? 225 g g/mol = mol 1 = P mmhg P1 o = 42.2 mmhg =0.879 = mol water x mol urea mol water Thus moles of urea is The mass of urea needed is (1.72 mol)(60.06 g/mol) = 103 g.

12 Solution #2: 2 = P x mol urea P1 o = =0.121 = 42.2 x mol urea mol water If both components are volatile, the vapor will contain both substances, and Raoult s Law still applies: P A = A PA o P B = B PB o P T = P A + P B (Dalton, s Law of Partial Pressures) P T = A PA o + B PB o Ideal hexane-octane solution (from Ross Church). Note that when the solution mole fractions are equal (0.5), the vapor above the solution is enriched in the more volatile species. This is the principle behind fractional distillation.

13 2. Boiling-Point Elevation Boiling-point is when vapor pressure = atm pressure Non-volatile solute lowers the solvent vapor pressure Thus need higher temperature to reach boiling point quantitative expression: ΔT b = K b m K b m T b = T b Tb o boiling-point elevation molal boiling-point elevation constant molality of the solution 3. Freezing-Point Depression Solute interferes with the formation of an ordered solid In order to form a solid, a lower temperature is required quantitative expression: ΔT f = K f m K f m T f = T o f T f freezing-point depression molal freezing-point depression constant molality of the solution

14 Phase diagram illustrating boiling-point elevation and freezing-point depression. (from e.g., Determine the boiling point and freezing point of a solution prepared by dissolving 678 g of glucose in 2.0 kg of water. For water, K b = 0.52 C/m and K f = 1.86 C/m. Solution: moles of glucose: (678 g) / ( g/mol) = 3.76 mol m = (3.76 mol) / (2.0 kg) = 1.88 ΔT b = K b m = (0.52 C/m)(1.88 m) = 0.98 C T b = 101 C ΔT f = K f m = (1.86 C/m)(1.88 m) = 3.50 C T f = -3.5 C

15 4. Osmotic Pressure Osmosis is the selective passage of solvent molecules through a semipermeable membrane which blocks the passage of solute molecules. It occurs from a more dilute solution to a more concentrated one. quantitative expression: π = MRT π M R T osmotic pressure (atm) molarity of the solution gas constant ( L atm/k mol) temperature (K) Two solutions of equal concentration have the same osmotic pressure and are said to be isotonic to each other.

16 Osmotic pressure. Beginning with equal levels of pure solvent and solution (left), the solution level rises as a result of the net flow of solvent from left to right. The osmotic pressure π, required to stop osmosis, can be measured directly from the difference in the final liquid levels. Electrolyte Solutions Colligative properties depend only on the number of dissolved particles, not on the type of particle. Therefore, a 0.1 m solution of NaCl has twice the freezing-point depression of a 0.1 m nonelectrolyte solution.

17 Solution Ions Theoretical ΔT f 1.00 m NaCl Na +, Cl - (1.86)(2.00 m) = 3.72 C 1.00 m (NH 4 ) 2 SO 4 2 NH + 2-4, SO 4 (1.86)(2.00 m) = 5.58 C The theoretical freezing-point depression is usually an overestimate because the ions can form pairs. To be quantitative we introduce the van t Hoff factor i: i = actual number of particles in solution after dissociation number of formula units initially dissolved in solution and we modify the equations for colligative properties: ΔT b = ik b m ΔT f = ik f m π = imrt Free ions and ion pairs in solution. Ion pairing reduces the number of dissolved particles in solution, affecting the colligative properties.

18 The more dilute a solution is, the closer i is to the expected value. e.g., What mass of naphthalene (128.2 g/mol) must be dissolved in 2.00 x 10 2 g of benzene (K f = 5.12 C/m) to give a solution with a freezing point 2.50 C below that of pure benzene? Solution: ΔT f = K f m m = ΔT f / K f = 0.49 mol/kg. Now, 0.49 mol kg g 1kg 10 3 g =0.098 mol Then, (0.098 mol)(128.2 g/mol) = 12.6 g.

19 e.g., What mass of insulin must be dissolved in 50.0 ml of water to produce a solution with an osmotic pressure of 16.8 mmhg at 25 C? Solution: = MRT ) M = /RT = 16.8 mmhg 760 mmhg/atm K mol L atm K = mol/l Then, ( mol/l)(0.05 L) = mol Finally, ( mol)(5808 g/mol) = 0.26 g. e.g., An aqueous solution that is M in acetic acid (HC 2 H 3 O 2 ) is 3.5% ionized at 25 C. Calculate the osmotic pressure of this solution. Solution: π = MRT. Now, 3.5% ionized means that ( ) = 96.5% exists as a single species in solution while 3.5% exists as two species in solution. Thus i = =1.035 Then π = (1.035)(0.015 M)( L atm/k mol)(298 K) = 0.38 atm e.g., A solution made by dissolving 14.2 g of sucrose in 100 g of water (K f = 1.86 C/m) exhibits a freezing-point depression of 0.77 C. Calculate the molar mass of sucrose. Solution: ΔT f = K f m m = ΔT f / K f = 0.77 / 1.86 = mol/kg. Now, (0.414 mol/kg)(0.1 kg) = mol. Then, (14.2 g) / ( mol) = 343 g/mol.

20 Colloids A colloid is a dispersion of particles of one substance throughout another substance. It is intermediate between a homogenous and heterogeneous mixture. Paint (pigment particles in solvent) and milk (fat globules in water) are common examples of colloids. The particle size (1 103 nm) is much larger than in solution. Categories: o Aerosols (liquid or solid dispersed in gas) o Foams (gas dispersed in liquid or solid) o Emulsions (liquid dispersed in another liquid) o Sols (solid dispersed in liquid or in another solid) o Gels (liquid dispersed in solid)

21 One way to distinguish a colloid from a solution is by the Tyndall Effect : the scattering of light by dispersed particles. Tyndall effect. When the dispersing medium is water, we can classify colloids as hydrophilic or hydrophobic. Hydrophilic colloid (a globular protein).

22 Hydrophobic colloid stabilized by adsorbed ions. Common example: clay. An unstable colloid can be stabilized by the addition of an emulsifier. Soaps (sodium stearate) and detergents work by adsorbing to the surface of hydrophobic dirt/grease particles, allowing them to be dispersed in water and removed. Emulsification of grease by detergent molecules.

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