Chemistry 103A; Sections 5, 6, 7, 8; Lecture 41, 4 Dec 00

We were talking about:

Properties of Solutions

Solubility of Gases in liquids - Henry's Law

The solubility of a gas in a liquid is proportional to the pressure of the gas. The mathematical expression of this phenomenon is called "Henry's law." Henry's law has the form,

where Sg is the concentration of the gas in the solution (in mol/L) and pg is the pressure of the gas above the solution (in Torr). The constant, kH, is the proportionality constant and is called the Henry's law constant. The Henry's law constant depends on the solvent, the solute, and the temperature. These constants are measured and listed in data tables. There is at table of Henry's law constants for several gases in water on p. 653 in your text.

Example,

What is the concentration of oxygen in water open to the atmosphere at 25oC? (The partial pressure of O2 in air with a total pressure of one atmosphere is approximately 0.20 atm = 150 Torr. kH for oxygen in water at 25oC is 1.66 ´ 10-6 mol/Ltorr.)

Using Henry's law we find


which is about 8 mg per liter.

 The solubility of gases in liquids usually decreases with increasing temperature unless there is a reaction between the gas and the liquid (such as HCl and water). Boiling a liquid will generally drive the gases out of it. You would not want to use boiled water in your fish tank unless you first aerated it well.
 

Colligative Properties

Colligative means "depending on the number of particles and not on the nature of the particles." There are four properties of solutions that depend only on the fact that there are fewer molecules of solvent per unit volume in a solution than there are in the pure solvent. These properties are:

Vapor pressure reduction (Raoult's law)

Boiling point elevation

Freezing point depression

Osmotic pressure.


Raoult's Law

We know that the vapor pressure is caused by molecules escaping from the surface of a liquid into the gas phase. There is a competition between the intermolecular forces trying to keep the molecules in the liquid and the kinetic energy trying to release the molecules. At any given temperature there is a distribution of kinetic energies and some fraction of molecules will have enough energy to escape. If we increase the temperature that fraction is larger and the vapor pressure increases.

There is another way to influence the vapor pressure of a liquid. If we can reduce the number of molecules at the surface then here will be fewer molecules to escape and the vapor pressure of the solvent will decrease.

The number of molecules at the surface of a liquid is proportional to the mole fraction of the liquid, Xsolvent, so that the vapor pressure should be proportional to the mole fraction. Raoult's law makes this statement into an equation,

Where posolvent is the vapor pressure of the pure solvent. Raoult's law does not depend on what the solute is, only on the number of particles of solute relative to the number of particles of solvent.

For example, the vapor pressure of water is 23.8 Torr at 25oC. If we dissolve one mol of sugar (a nonionic compound) in nine mol of water the mole fraction of water is 0.90. The vapor pressure of water in the solution becomes,

Note that we are counting particles so that mole fraction has to be the mole fraction of particles. If we had used NaCl in the above example the one mol of NaCl would give two mol of particles (Na+ ions and Cl-ions) so that the mole fraction of water for purposes of Raoult's law - and the rest of the colligative properties - would be 9/11. This correction for ionic compounds is accounted for formally by the introduction of a factor, i, called the "van't Hoff factor." The van't Hoff factor is approximately the number of moles of particles that will be obtained in water solution from one mole of solute compound. For fairly dilute ionic solutions this approximation is reasonable. As we go to higher concentrations the approximation becomes less valid and the van't Hoff factor must be calculated some other way. For our purposes we will regard the van't Hoff factor for NaCl to be 2, that for Na2SO4 to be 3, and so on.


Boiling Point Elevation

Boiling point elevation is relatively easy to understand from Raoult's law. If the vapor pressure goes down then we have to heat it to a higher temperature to get it to boil. The solvent vapor pressure in a solution is lower than the vapor pressure of the pure solvent so we have to heat the solution higher to make it boil.

You can write an equation for boiling point elevation in terms of mole fraction of the solvent, but it customary to write it in terms of molality of the solute instead. The equation for boiling point elevation is,

The kbp is the boiling point elevation constant and there is a table of such constants in the text on page 661. Note that the boiling point elevation constant depends only on the solvent and not on the solute. The only reference to the solute is in its molality. Once again, the molality has to be the molality of particles so that in an ionic solution we would include the van't Hoff factor, i,
Example, Calculate the boiling point of 188. g of K2SO4 in 1.0 L (very nearly 1.0 kg) of water. 188 g of K2SO4 is 1.08 mol which, in 1.0 kg, of water gives a 1.08 molal solution. However, one mol of K2SO4 gives three mol of particles so that the van't Hoff factor, i is approximately 3. From the table, the boiling point elevation constant for water is 0.5121 oC/m. The boiling point elevation is,
 


The boiling point of this solution is 101.7oC.
 

 Freezing Point Depression

Freezing point depression of a solvent by the addition of a solute is the principle behind the old-fashioned hand-cranked ice cream freezers. The container of cream and flavorings is placed in a slush of ice and salt (NaCl) and stirred until it is frozen. Plain ice will not produce the desired result. The last lowers the freezing point of the water to the place that it will freeze the cream mixture.

The vapor pressure lowering argument is still valid, but it is not as simple as it was in boiling point elevation. We have to add two bits of new information.

One, ice has a vapor pressure, too.

Two, if ice and water are in equilibrium then the vapor pressures of the ice and water must be the same. (Otherwise the higher vapor pressure stuff would evaporate and condense out as the lower vapor pressure stuff and we would lose one component.)

 We lower the pressure of the liquid by adding a solute. To stay in equilibrium the solid vapor pressure must decrease, too. But we can't dilute the solid with a solute. The only way to lower the vapor pressure of the solid is to decrease the temperature. So the temperature goes down to keep the solid and liquid phases in equilibrium.

All of this is expressed in a freezing point equation, with a new constant, kfp, the freezing point lowering constant,

or
in the case of ionic solutes.

In this situation the freezing point constant is negative so that DT is negative. Here, again, the freezing point constant depends only on the properties of the solvent. The only solute dependence comes from the molality of the solvent (and we count the molality of particles).

Example,

Let's calculate the lowest temperature we could obtain with an ice/salt slush in water. The solubility of NaCl in water at 0oC is about 35.7 g/100mL and the freezing point constant for water is - 1.86 oC/mol.

35.7 g/100mL is 357 g/L or approximately 6.1 molal.
 

23oC below freezing is 41 Fahrenheit degrees below freezing, or - 9 oF (- 23oC). That should be plenty cold enough to freeze ice cream.

Freezing point depression is often used to measure the formula weights of compounds. Placing a weighed amount of solute in a known mass of solvent one measures the freezing point depression. With this information you can calculate the molality of the solution and then you can what the formula weight of the compound must be to give that molality. The formula would look like this,

in which everything is known except the formula weight, FW.
 
 

Osmotic Pressure

There are other ways to influence the vapor pressure of a liquid or solution other than changing the temperature or adding a solute. If we "squeeze" the liquid (of either a pure solvent or a solution) by adding and external pressure we increase the vapor pressure. (One way to apply and external pressure is to expose the liquid to the atmosphere, where it will be pressed by one atmosphere pressure. One can also apply external pressure with a piston or by putting the liquid in a tank and increasing the air pressure.

In osmotic pressure experiments we are trying to keep make the vapor pressure of a solution the same as the vapor pressure of the pure liquid (all without fooling around with the temperature). This is because we want the solution to be in equilibrium with the pure liquid. The pressure that must be applied to the solution is called the osmotic pressure and it is given the symbol, P (upper case pi).

For osmotic pressure it turns out that the natural unit of concentration of the solute is molarity rather than molality. The equation for osmotic pressure, P , is familiar equation,

If we recognize that the molarity, M, is the number of moles per unit volume, n/V, then we see that this equation is just like the ideal gas equation,
Example,
Calculate the osmotic pressure of blood plasma at the normal human body temperature, 37oC. Blood plasma has about the same osmotic pressure as 0.15 M NaCl (this is called an "isotonic solution"). As before, we must modify this equation for ionic solutions. That is we put in the van't Hoff factor which takes account of the fact that the number of particles is not the same as the number of moles in an ionic solution. So we write, for ionic solutions,
Since the van't Hoff factor, i, is approximately 2 for NaCl, this becomes,
7.6 atm is about 112 psi.