Colligative Properties

Various kinds of solutes (e.g. NaCl, ethylene glycol) added to H₂O result in a decrease in the freezing temperature, as well as an increase in the boiling temperature, of H₂O.

• Solutes added to H₂O are a useful mechanism with which to prevent water-cooled machines from freezing in winter and boiling over in summer
• Salt added to the roads can prevent the freezing of water in winter

These effects upon the physical properties of water are termed "colligative properties" and are primarily dependent upon the amount of solute added, and are relatively independent of the type of solute

Here's a weird experiment that demonstrates the colligative effects of solutes upon a solution

• We have two beakers. One contains H₂O, the other contains a salt solution (NaCl) in H₂O.
• Both beakers are placed into a sealed chamber:

• If we leave it for a couple of days and then come back and take a look, this is what it might look like:

What is going on here? The physical basis for this behavior is the effect of the solute upon the vapor pressure of the water

• Na⁺ and Cl^- ions are non-volatile ions. In other words, they will not leave and go into the vapor phase
• Those H₂O molecules with enough kinetic energy will leave the surface of the solutions and enter into the vapor phase
• The fact that Na⁺ and Cl^- ions are dissolved in H₂O indicates that there is an attractive interaction between the solutes and the H₂O.
• The interaction of the Na⁺ and Cl^- ions for H₂O will act to hinder the ability of the solvated H₂O molecules to leave and go into the vapor phase (Na⁺ and Cl^- ions are non-volatile)
• This hindrance of the H₂O molecules to enter the vapor phase will reduce the vapor pressure of the H₂O in the salt-containing solution
• The two beakers are in the same sealed container, thus, the vapor pressure above the solutions is identical
• The rate of H₂O entering the solutions by collisions from the vapor state will be identical
• The rate of H₂O leaving the liquid phase and entering the vapor phase is slower for the NaCl-containing solution

Raoult's Law

• An ideal solution is a solution that obey's Raoult's Law
• Variations in the strength of the solvent-solute and solvent-solvent interactions can result in vapor pressures that deviate from ideal solution behavior
• If solvent-solute interactions are really strong (e.g. involve Hydrogen bonding) then the vapor pressure of a solution might be lower than ideal
• If the solvent-solvent interactions are really strong then the vapor pressure of a solution might be higher than ideal

The vapor pressure of H₂O at 20°C is 17.5 torr. If sucrose (sugar, a non-volatile solute) is added to a mole fraction of 20%, what is the resulting vapor pressure of H₂O?

If the mole fraction of sucrose is 20%, then the mole fraction of H₂O in the sugar solution will be 80% (i.e. 0.80). Thus:

Here is a typical vapor pressure diagram for H₂O:

• The addition of a solute results in a lowering of the vapor pressure. At any given temperature, the vapor pressure of a solution of H₂O and a non-volatile solute will have a lower vapor pressure. What does this mean with regard to the liquid/gas phase transition?
• At any given temperature, the vapor pressure of the liquid is lower
• This means that bubbles that form will have a lower vapor pressure and will now collapse, where previously they remained (i.e. the sample boiled)
• The lower vapor pressure means the sample will boil at this temperature, but only if the pressure is lowered:

• Thus, at a constant pressure, the boiling point of an aqueous solution of a non-volatile solute will be higher than pure H₂O:

• The increase in the boiling point (DT_b) relative to that of the pure solvent is directly proportional to the number of solute particles per mole of solvent molecules
• Molality (m) represents the number of moles of solute per kg of the solvent component (whereas molarity, M, relates to volume of total solution). Thus, molality gives information about the number of moles of solute per mole of solvent
• Therefore, DT_b is proportional to molality (and not molarity):

DT_b = K_b * m

• K_b is called the molal boiling-point-elevation constant, and is dependent only upon the choice of solvent
• Boiling point elevation is dependent upon the concentration of solute. Thus, 1 mol of NaCl will raise the boiling point of water by a value twice as high as 1 mol of sucrose (because NaCl will dissociate into two ion, Na⁺ and Cl^-, wherease sucrose does not dissociate)

• If an aqueous solution of ethanol is frozen, the water selectively freezes as a pure substance and the ethanol (with a lower freezing point) is squeezed out as pure ethanol. Consequently the vapor pressure diagram representing the vapor/solid equilibrium (vapor pressure of solid) for an aqueous salt solution will be identical to that of pure H₂O:

• Thus, at a constant pressure, the melting point for a aqueous salt solution will be lower than pure H₂O:

• The decrease in the freezing point temperature, DT_f, is directly proportional to the molality of the solute:

DT_f = -K_f * m

• The value of K_f, the molal freezing-point-depression constant is a characteristic only of the solvent
• For water, the value of K_f is 1.86°C/m
• Thus, a 1 molal solution of solute will decrease the freezing point of water by 1.86°C (i.e. DT_f = -1.86°)
• A 0.5 molal solution of NaCl will produce 1.0 molal of solute (remember, it dissociates into two ions)

Some materials, like cellophane and some biological membranes, have tiny pores. These pores are large enough to allow solvent, like H₂O, to freely pass across the membrane, but may prevent the passage of larger solute molecules

• Such materials are termed semi-permeable membranes

If two solutions, with different solute concentrations, are separated by a semi-permeable membrane, there can be a net flow of solvent across the membrane

• Like effusion with gas molecules, the rate of movement of solvent across the membrane is a function of the concentration of solvent and the kinetic energy
• Both solutions are at the same temperature, thus have the same kinetic energy. However, solvation of solute molecules means there are less free solvent molecules to pass through the membrane (i.e. those solvent molecules involved in hydrating solute are not free to pass through the membrane)
• On the side with the pure solvent, more molecules of solvent per unit time can pass through the membrane

Here is how such an effect can be demonstrated:

• At the beginning of the experiment, here is how things might look in a 'U' shaped glass tube with two solutions separated by a semi-permeable membrane:

• After equilibrium is reached, here is how the apparatus and solutions might look:

The osmotic pressure behaves very much like pressure in the ideal gas equation:

pV = nRT

p = (n/V)RT

• Where n = moles of solute, T is temperature (K), R is the gas constant and V is the volume of solution
• (n/V) is the number of moles of solute per volume of solution. This is also the molarity of the solution (M). Thus:

p = MRT

• The osmotic pressure is just a function of the molar concentration of solute

Relative osmotic pressures

• Two solutions with equal osmotic pressures are termed isotonic
• If a solution has a lower osmotic pressure than another, it is termed hypotonic
• If a solution has a higher osmotic pressure than another it is termed hypertonic

1. Raoult's Law

2. Boiling Point Elevation

DT_b = K_b * m

3. Freezing Point Depression

DT_f = K_f * m

4. Osmotic Pressure

p = MRT

Colligative properties relate either the mole fraction, molal concentration, or molar concentration of a solute to a measurable change in a physical property of a solution

• Thus, we have a way to quantitate the number of moles of a solute based upon one of the four colligative properties
• If we know the quantity in grams of a solute added to a solution (to produce the measurable colligative effect), then we have both the number of moles of the solute and the associated mass
• Molar mass has the units of grams/mole; it describes the mass associated with 1 mole of the compound (i.e. solute)

An unknown solute is added to the solvent carbon tetrachloride (CCl₄). 0.370 grams of the solute was dissolved in 40.0g of CCl₄. The boiling point of the resulting solution increased by 0.443 °C. Calculate the molar mass of the solute. The molal boiling point elevation constant for CCl₄ is 5.02 °C/m.