Colligative Properties Properties that depend only on the number of solute particles and not on their identity. (intensive physical property: does not depend on amt.)

Quick Review Solvent Solute Solute + solvent = solution Does the dissolving Doesn’t change state Largest amount in the solution Gets dissolved Changes state Present in the lesser amount

Exception… Isn’t there always an exception? You can determine solutes & solvents by amounts, most of the time… Some very soluble salts, like LiCl, more than 5 g of salt can be dissolved in 5 mL of water. Water is still considered the solvent because it had not changed state.

Remember, solutions are homogeneous mixtures (same is true of solid solutions – alloys) Mixing is physical process; chemical properties don’t change Properties of solutions are similar to those of the pure substances Addition of a foreign substance to water alters the properties slightly

Colligative: particles are particles Colligative comes from colligate – to tie together Colligative properties depend on amount of solute but do NOT depend on its chemical identity Solute particles exert their effect merely by being rather than doing The effect is the same for all non-volatile solutes The volatility of a substance refers to the readiness with which it vaporizes.

What does non-volatile mean? The volatility of a substance refers to the readiness with which it vaporizes. Typically, substances with a boiling point below 100 °C are considered volatile and all others are called nonvolatile. Ethyl alcohol and pentane are examples of volatile substances; sugar and sodium chloride are considered nonvolatile.

Another explanation of volatile solutions with a nonvolatile solute produce a vapor which is pure solvent solutions with a volatile solute produce a vapor which is a mixture of both solvent and solute. a nonvolatile solute does not appear as a component of the vapor above the solution. a volatile solute does appear as a component of the vapor above the solution.

Colligative Properties These are the effects that a solute has on a solvent. When water has something dissolved in it, its physical properties change. It will no longer boil at 100oC and it will no longer freeze at 0oC like pure water.

Colligative Properties Examples Vapor pressure lowering Boiling point elevation Freezing Point depression

Colligative properties for nonvolatile solutes: Take it to the bank! Vapor pressure is always lower Boiling point is always higher Freezing point is always lower Osmotic pressure drives solvent from lower concentration to higher concentration

Recall the kinetic molecular theory… 1. Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion. 2. These particles move in a straight line until they collide with another particle or the walls of the container. 3. These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.

4. There is no force of attraction between gas particles or between the particles and the walls of the container. 5. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container. 6. The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

What is vapor pressure? The vapor pressure of a liquid is the equilibrium pressure of a vapor above its liquid (or solid) the pressure of the vapor resulting from evaporation of a liquid (or solid) above a sample of the liquid (or solid) in a closed container.

Vapor Pressure Lowering The particles of solute are surrounded by and attracted to particles of solvent. Now the solvent particles have less kinetic energy and tend less to escape into the space above the liquid. (Refer to figure 14.20 in the text on page 499) So the vapor pressure is less.

Vapor Pressure

Vapor Pressure Graph

Psolution = (χsolvent) (P°solvent) P – pressure, χ – mole fraction Raoult’s Law In the mid-1800s, it was discovered that the vapor pressure of a solution was lowered and that the amount was more-or-less proportional to the amount of solute. In the early 1880s, Francios Marie Raoult was able to determine the equation which governs this property: Psolution = (χsolvent) (P°solvent) P – pressure, χ – mole fraction

Mole Fraction Another way of expressing the concentration of a solution or mixture Moles of one component = mole fraction (χ) Total moles in the solution or mixture Must know the number of moles of each component present in the solution!

Raoult’s Law: Example #1 What is the vapor pressure of an aqueous solution that has a solute mole fraction of 0.1000? The vapor pressure of water is 25.756 mmHg at 25 °C. Solution: χsolvent = 1.0000 - 0.1000 = 0.9000 Use Raoult's Law: Psolution = (χsolvent) (P°solvent) Psolution = (0.900) (25.756) Psolution= 23.18 mmHg

Raoult’s Law: Example #2 The vapor pressure of an aqueous solution is found to be 24.90 mmHg at 25 °C. What is the mole fraction of solute in this solution? The vapor pressure of water is 25.756 mm Hg at 25 °C. Solution: Psolution = (χsolvent) (P°solvent) 24.90 = (χsolvent) (25.756) χsolvent = 0.966765 χsolute = 1 - 0.966765 = 0.033235 χsolute = 0.03324 (to four sig figs)

Raoult’s Law: Example #3 How many grams of nonvolatile compound B (molar mass= 97.80 g/mol) would need to be added to 250.0 g of water to produce a solution with a vapor pressure of 23.756 torr? The vapor pressure of water at this temperature is 42.362 torr.

We will assume that B does not ionize in solution. 1) Determine mole fraction of solvent that produces a solution vapor pressure of 23.756 torr: Psolution = (χsolvent) (P°solvent) 23.756 torr = (χsolvent) (42.362 torr) χsolvent = 0.5608 2) Determine moles of compound B needed to produce the above solvent mole fraction: 0.5608 = 13.88 / (13.88 + B)7.7839 + 0.5608B = 13.88 0.5608B = 6.0961 B = 10.87 mol 3) Determine mass of B 10.87 mol times 97.80 g/mol = 1063 g Note: this is a completely ridiculous amount to dissolve in 250.0 g of water, but that's not the point. The point is to solve the problem.

Molality The volume of a solution changes with temperature as it expands or contracts. This change alters the Molarity of the solution. However, masses DO NOT change with temperature. Hence we use molality. molality (m) = moles of solute kg of solvent 1 m solution would be read as “one molal solution”

How are vapor pressure & boiling point connected? If a liquid has a high vapor pressure at a particular temperature, it means that its molecules are escaping easily from the surface. If, at the same temperature, a second liquid has a low vapor pressure, it means that its molecules aren't escaping so easily.

What does that mean about the boiling point of the two liquids? If the molecules are escaping easily from the surface then intermolecular forces are relatively weak. So you won't have to supply so much heat to break them (the IM forces) completely and boil the liquid. At a particular temperature… Higher vapor pressure = lower boiling point

Boiling Point Elevation Boiling-point elevation describes the phenomenon that the boiling point of a liquid (a solvent) will be higher when another compound is added A solution has a higher boiling point than a pure solvent.

Boiling Point Elevation The boiling point of a solution is ALWAYS higher than the pure liquid. Explains why you use antifreeze in your car’s radiator in the summer – the boiling point is higher so that it can absorb heat from the engine without boiling – hopefully! Explains why you use a pressure cap on your radiator – the higher the pressure, the higher the boiling point. Explains why chefs add salt to boiling water – higher temperature cooks faster.

Calculate the Boiling Point Elevation ΔTb = i Kbm ΔTb : increase in the boiling point i: van’t Hoff factor (only used with electrolytic solutions) Kb : boiling point elevation constant (0.512°C/m for water) m : molality of particles **Solvents other than water have a different boiling point constant **If the solution is electrolytic (ionic), then the equation is ΔTb = iKbm

What is the “i”?? The van 't Hoff factor is symbolized by the lower-case letter i. It is a unitless constant directly associated with the degree of dissociation of the solute in the solvent. Substances which do not ionize in solution, like sugar, have i = 1. Substances which ionize into two ions, like NaCl, have i = 2. Substances which ionize into three ions, like MgCl2, have i = 3. And so on. . . .

Boiling Point Elevation Example #1 What is the boiling point of a 0.75 m solution of urea in water? Kb for water is 0.52°C/m. Urea is a nonelectrolyte. ΔTb = mKb ΔTb = (0.75) (0.52°C/m) = 0.39°C 100°C + 0.39°C = 100.39°C

Boiling Point Elevation Example #2 What is the boiling point elevation, ΔTb, of a 1.50 m solution of CaCl2 in water? Kb for water is 0.52°C/m. Calcium chloride, CaCl2, is an electrolyte. Each formula unit forms three ions in solution. The molality of the solute particles (ions) is 3 x 1.50 m = 4.50 m. ΔTb = imKb ΔTb = (3)(1.50 m)(0.52°C/m) = 2.34°C

Another way to look… Liquids boil when their vapor pressure becomes equal to the external pressure. High vapor pressure = less heat to reach external pressure Low vapor pressure = more heat to reach external pressure higher vapor pressure = lower boiling point

Freezing Point Depression Solutions freeze at lower temperatures than the solvents used to prepare them Antifreeze added to the water in your car’s radiator will allow the solution to remain a liquid far below the normal freezing point of water Salt & calcium chloride spread on snow-covered roads dissolve the snow by allowing that solution to stay liquid longer

Freezing Point Depression Calculation ΔTf = freezing point of solvent – freezing point of solution ΔTf = i m Kf Kf for water = 1.86°C/m

Freezing Point Depression Example #1 At what temperature would a 0.50 m methyl alcohol solution in water freeze? Kf for water is 1.86°C/m. Methyl alcohol is a nonelectrolyte. ΔTf = 0.50m (1.86°C/m) = 0.93°C Fpsolution = Fpwater – ΔTf Fpsolution = 0°C – 0.93°C = -0.93°C

Freezing Point Depression Example #2 What is the freezing temperature of a 0.50 m NaOH solution in water? Kf for water is 1.86°C/m. NaOH is an electrolyte. ΔTf = i m Kf ΔTf = 2 (0.50 m) (1.86°C/m) = 1.86°C **Note: “i” was used in this equation because the solution was electrolytic. Therefore the solute would dissipate into ions.

Osmotic Pressure Osmosis: diffusion of a solvent through a semipermeable membrane (think Biology again!) Osmotic Pressure: amount of additional pressure caused by the water molecules that moved into the concentrated solution

Osmotic pressure depends on the number of solute particles in a given volume of solution (Hmmm…sounds like another colligative property!)

Calculating Osmotic Pressure

Osmotic Pressure Example #1 How much glucose (C6H12O6) per liter should be used for an intravenous solution to match the 7.65 atm at 37 °C osmotic pressure of blood? Π = i M R T 7.65 atm = (1) (M) (0.0821 L-atm/ mol-K) (310K) M = 0.301 0.301 M = mol 0.301 mol x 180 g = 54.18 g 1 L 1 mol glucose

Osmotic Pressure Example #2 What is the osmotic pressure of a solution prepared by adding 13.65 g of sucrose (C12H22O11) to enough water to make 250 mL of solution at 25 °C? Π = i M R T 13.65 g x 1 mol = 0.040 mol 0.040 mol = 0.16 M 342 g 0.250 L Π = (1) (0.16 M) (0.0821 L-atm/mol-K) (298 K) Π= 3.91 atm

What does osmotic pressure have to do with…? Salting food to preserve it?  Any harmful bacteria on the meat  will dehydrate, since  water will flow out of the cell to try and  lower the free energy and establish  equilibrium.  This extends the  life of the food without need for refrigeration. Keeping fish alive in a fish tank?  Some fish are salt‐water fish,  some are fresh‐water fish.   If a salt‐water fish is placed in fresh,  purified water (meaning the concentration of electrolyte inside the fish  cells is higher than in the aquarium water) water will  enter the cells to try  and establish an equilibrium. Fish cells can only contain a  certain amount  of pressure, and if too much water enters the cell, it will burst. On the other hand, if a fresh‐water fish is placed in salt water, water will  exit the  cells until the cells ‘shrivel’ up.  

Given a person “saline” solution intravenously when they  are dehydrated? Most dehydration in humans is “isotonic” dehydration, meaningcells are equally deficient in both water and electrolytes  (typically sodium ion). Typical saline solutions are essentially equal (in sodium) to the  salt concentration in human blood.   Hypotonic dehydration  occurs when sodium loss is greater than water loss and the  osmotic pressure is greater inside the cells, which pulls more fluid  out of the blood  and into the cells. Hypertonic dehydration occurs when water loss is greater than  sodium loss Higher blood sodium levels combined with decreased water inside  cells increases  the osmotic pressure in the bloodstream, which, in  turn, pulls more fluid out of the  cells.

Reverse Osmosis https://www.youtube.com/watch?v=mZ7bgkFgqJQ&t=55s