Chem. 102 Outline

Chapter 13 Solutions

Vapor Pressure

Solvent Boiling Point and Freezing point Depression

Osmotic Pressure

Colloids

IV. Colligative Properties

The addition of a solute changes the solvents physical properties such as vapor pressure, melting and boiling point and it produces an osmotic pressure. It is best understood as the solute particles get in the way of solvent particles. The amount of change depends on the number of solute particles more than on the chemical nature of the solute. Colligative means “ depending of the collection”

A. Vapor Pressure

Vapor pressure is produced by molecules in the condensed phase having enough energy to escape the solid or liquid and enter the gas phase. If the molecules are returning to the condensed phase as fast as they are leaving it, we say the substance is in equilibrium with its vapor and a certain vapor pressure is produced. The vapor pressure depends on temperature and the intermolecular forces holding a substance together.

The presence of a solute can block solvent particles from entering the gas phase. Raoult’s law states that the vapor pressure of a component in a solution, P_A = the product of the mole fraction of the component (X_A) and the vapor pressure of the pure component (P_A°)

P_A = X_A P_A°

Raoult’s law works best for ideal solutions and when a solute concentration is low. An ideal solution is when the solute and solvent particle are similar in size and when they have similar intermolecular attractions.

What would be the vapor pressure of water at 100°C for a 50.wt. % ethylene glycol aqueous (CH₂OHCH₂OH, 62.0 g/mol) solution? Ethylene glycol is the main ingredient of antifreeze.

Well, a 50. wt% solution would be 50.g of water and 50.g of ethylene glycol. We can figure out the mole fraction of water as follows;

X_H2O = 2.78 mole H₂O / (2.78 mole H₂O + .81 mole ethylene glycol) = .773

P_H2O = .773 X 760 torr = 589 torr

I choose the normal boiling temperature of water to illustrate a point. The addition of ethylene glycol just reduced the vapor pressure of water. We will need a higher temperature for this solution to have a P_H2O = 760 torr, and so we have increased the normal boiling point of the water.

For a two component solution, if both solute A, and solvent B, are volatile, Raoult’s Law says

P_A = X_A P_A°

P_B = X_B P_B° and the total pressure will be the sum of the two partial pressures

P_total = P_A + P_B

As you might expect, the component with the higher vapor pressure is more likely to go into the vapor phase. The process of distillation is used to purify a low boiling point (high vapor pressure) substance by collecting the vapor which is enriched in the low boiling point substance. This is done to increase the ethyl alcohol in water to make different liquors out of wine, and is done to separate crude oil from the ground into a bunch of different products from natural gas to gasoline to waxes and asphalt.

The next example involves a lot of calculations, but what I am going to show is how the vapor above a ethyl alcohol / water solution is enriched in the lower boiling point alcohol.

Say I have a 12.0 wt % ethyl alcohol (C₂H₅OH, 46.0 g/mole, abbreviated as EtOH) in water solution. This is = to a

X_EtOH of .050 and X_H2O= 0.95. Compare the solution mole fraction of EtOH to the vapor above it at the normal boiling point of EtOH of 78°C. (78°C was chosen since it is the normal boiling point of EtOH which implies its vapor pressure is 760 torr)

P_EtOH = X_EtOH P°_EtOH = .050 X 760 torr = 38 torr

P_H2O = X_H2O P°_H2O = .95 X 327 torr (from a table) = 311 torr

Since X_gas = P_A / (P_A + P_B)

X_{EtOH, gas} = .11

Comparing X_EtOH,Soln = .050 and X_{EtOH, gas} = .11, we see that the mole fractor of ethyl alcohol has more than doubled. A series of this process can get us to about 90 wt % alcohol. Please note, the solution is not ideal, the actual vapor pressures are lower than that shown.

B. Solvent Boiling Point Elevation and Freezing Point Depression

Solute particles lower solvent vapor pressure, thus lower normal boiling point. Solute particles get in way of solvent freezing, so lower temperature needed to freeze. Net result, solute broadens liquid range.

DT_b = K_b m Boiling Pt Elevation (Works best for low m)

DT_b = T_{b, soln} – T_{b, solvent}

K_b molal boiling point constant (depends on solvent, not solute)

DT_f = K_f m Freezing Pt Depression

DT_f = T_{f, solvent} – T_{b, soln}

K_f molal freezing point constant (depends on solvent, not solute)

	Normal BP (°C)	Kb (°C/m)	Normal FP (°C)	Kf
H2O	100	.52	0.0	1.86
CCl4	76.8	5.02	-22.3	29.8

50.0 Wt% Ethylene Glycol in water (CH₂OHCH₂OH, molar mass = 62 g/mol) = 16 m

What T will this soln boil? ~115°C

What T will it freeze? ~ -30.°C

Antifreeze lets engines run hotter (more efficient) and lets coolant go to lower T before freezing.

Say 2.0 g of a 100. g/mol solute dissolved in 10.0 g of water. 2.0 m DT_b = 1.0°C and DT_f= 3.7°C

Which is easier to measure?

The variable Molar mass is in m (molality). Change in BP or FP can be used to measure molar mass, what K maximized to make change in BP/FP larger.

C. Osmotic Pressure

Semipermeable membrane separating two solutions, lets some particles pass and blocks others.

Osmosis lets only solvent through.

Dialysis lets solvent and small particles through, (Kidneys let water, urea and other small waste products through).

Osmosis – the net movement of solvent molecules toward solution with higher solute concentration

Osmotic Pressure – pressure required to prevent osmosis

p V = nRT

p = (n/V) RT = MRT

Sea Water ~ 3.6 g NaCl / 100 mL of water. What is osmotic pressure of sea water compared to pure water.

=.62 M

=>15 atm pressure.

Reverse Osmosis – Applying enough pressure to reverse osmosis and cause solvent molecules to move toward solution with lower concentration. Used to purify water.

Compare DT_f and p for .122 g of molar mass 1200 g/mole dissolved in 100. g water.

DT_f = .002°C and p = 2.5 X 10^-2 atm = 19 mm Hg ~ ¾ inch.

It is much, much easier to measure osmotic pressure of large molecules than DT_f. Imagine measuring 0.002°C versus 19 mm Hg.

Hypertonic Solution – Solution has higher concentration than other solution. If solution outside a cell is hypertonic, net flow of water out of cell will shrivel or crenate cell (kill cell). Used to preserve cucumbers and pears, peaches, etc. Osmosis partly responsible for moving water from ground through roots to tree tops.

Hypotonic Solution – Solution has a lower concentration that other solution. If solution outside cell is hypotonic, net flow of water into cell will swell cell (hemolysis) and can rupture cell. Used to study cell parts.

V. Colloids

Solutions are homogeneous mixtures made of small solute particles dispersed in a solvent. A suspension is like sand in water, where the particles are visible and will settle out soon after mixing. In between solutions and suspensions are colloids. Colloids have larger particle than solutions dispersed in a solvent and do not settle out. Colloid particles range in size between 10 – 2000 angstroms and larger (diatomic molecules are 2-3 angstroms across). When a particle is about the same size as light, that particle can cause light to be scattered in different direction from the propagation direction. This is called the Tyndall Effect. You see this when you drive in fog; the water droplets scatter your headlights back to your eyes, making night driving more challenging.

See table page 496

dispersing medium (solventlike)	dispersed substance (solutelike)	Example
gas	liquid	Fog, aerosol
liquid	gas	foam, whipped cream
liquid	liquid	milk, mayo
gas	solid	Smoke, dust, aerosol
liquid	solid	paint

The amount of aerosols particles in our atmosphere has been increasing and has the following effects.

1. Reduced Visibility – This is bad for tourist at locations like the Grand Canyon and can result in airplane and car crashes.

2. Health Effects – Large amounts can cause problems like coal miner’s black lung, asbestos workers getting lung cancer, and may be the cause of the increased asthma in children in the US.

3. Economic Effects - The San Joaquin Valley in California is currently in noncompliance with EPA aerosol standards and can lose federal highway money (~2 billion / year) if this we do not come into compliance.

4. Climate effects – aerosol particles can act as nucleation sites for water droplets affecting rainfall. The more aerosol particles could reduce rain by have a large number of small water droplets that stay in the air instead of a few droplets that grow large enough to fall out of the air as rain. Also different particles reflect and absorb light from the sun and from the earth differently and can effect climate.

Emulsions (Liquid dispersed in a liquid) can be hydrophilic (water loving) and hydrophobic (water fearing). A hydrophilic example would be a proteins with ionic groups or H-bonding groups on the outside that can strongly interact with the water. A hydrophobic emulsion needs stabilization or otherwise it will spontaneously separate. Fatty acids, called soaps, have a long hydrocarbon tail that can mix with a non-polar hydrophobic substance like an oil, and an ionic head that can strongly interact with water.

Soaps