Lec III

   Chem 1200

Angel C. de Dios

Solutions III

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We need to keep in mind that the thermodynamic quantities, Gibbs' free energy, enthalpy and entropy are all extensive quantitites. What we usually find in thermodynamic tables are for standard conditions, gases are at 1 atm pressure and solutions are at 1 M concentration. Changing these conditions can change the spontaneity of the reaction. An example is shown below. A 1 M solution of oxygen gas in aqueous solution is not going to be favored against 1 atm of oxygen gas. The volume is simply too confining in solution and a decrease in volume leads to a decrease in entropy. However, against a dilute solution, the situation has dramatically changed. We expect now that the more dilute solution is favored over the gas on top of it. We will learn more about this when we examine equilibrium in greater detail.

Both molality and mole fraction are directly proportional to the amount of solute per solvent in molecular or particle terms. Mole fraction obviously is directly related to the ratio of the number of solute particle to the number of solvent molecules. Molality is likewise since this is the number of moles of solute per kilogram of solvent, and kilogram of solvent, of course, is directly proportional to the number of moles of solvent. Both molality and mole fraction are also independent of temperature, which is an important consideration if one is trying to measure changes in freezing and boiling points.

The following is a specific example. In order to determine the molality, one needs the mass of the solvent, the mass of the solute, and the formula weight of the solute.

Here is another example:

The following are some useful relationships:

Those who have laboratory meetings on Tuesday would have seen a colligative experiment before this lecture. In a way, it may help to see this topic in action before the lecture. For those who have not done this experiment. here is my son sharing his experiment.

Since concentration plays a very important role in colligative properties, we need to review various measures of concentration and conversions between them.

Here are some example of conversions between different measures of concentration. The following is mole fraction to molality.

The following is from molarity to molality. Since molarity is expressed in terms of amount of solute per volume of solution. One needs to convert volume to mass and for this, we need the density of the solution. In addition, molality requires moles of solute and mass of solvent, thus, we need to remove the mass of the solute from the mass of the solution to get the mass of the solvent.

Now that we have covered what molality is, we then proceed to discussing the various colligative properties quantitatively.

Where does the solution lie on the entropy scale, with respect to the three phases?

The following is for a pure solvent, like water. Keep in mind, entropy is a measure of the number of ways or options.

In the presence of a solute, solvent molecules now have additional options: to be adjacent to another solvent molecule, or to be adjacent to a solute particle. These additional options do not exist in the solid and vapor phases, where only solvent molecules are present.

The solution therefore lies somewhere between the pure liquid and the vapor phase on the entropy scale.

The solution therefore lies closer to the vapor phase than the pure liquid is to the vapor phase. Remember that vaporization is driven by the increase in entropy when a molecule goes from the liquid phase to the vapor phase. In terms of the entropy difference, the following is true: S(vapor)-S(liquid) is greater than S(vapor)-S(solution). This is due to the fact that S(solution) > S(liquid). Therefore, there is now less incentive for molecules to go into the vapor phase. This obviously manifests in a reduction of the vapor pressure above a solution:

Last semester, you have seen a phase diagram of a substance such as the one shown below. We can add the solution to this diagram, keeping in mind, that at every liquid-vapor equilibrium, the pressure is lower:

The solution-vapor equilibrium curve therefore is shifted lower, and it now meets the solid-vapor curve at a lower temperature where the triple point lies. The solid-liquid curve starts from the triple point so the solid-liquid curve is shifted to lower temperatures. The solid-liquid curve now intersects the pressure line of 1 atm at a lower temperature, thus, a freezing point depression. This should not be surprising since we expect this from the change in entropy between a pure liquid and a solution. For melting the change in entropy is S(liquid)-S(solid) for the pure solvent. For the solution, it is S(solution)-S(solid). Since S(solution) > S(liquid), the increase in entropy upon melting is higher with the solution than it is with the pure solvent. Therefore, there is a greater incentive for melting, so it now occurs at a lower temperature.

On the other side of the phase diagram, the solution-vapor curve will now intersect the 1 atm pressure line at a higher temperature, thus, a boiling point elevation.

Since both freezing point depression and boiling point elevation are due to the change in entropy from pure solvent to solution. And this change in entropy is dependent on the number of solute particles, we can then assume that both freezing point depression and boiling point elevation will be directly proportional to the amount of solute. For the amount of solute, the convenient measure is the molality of the solution (since this measure is proportional to moles, and is independent of temperature).

Both constants for boiling point elevation and freezing point depression are properties of the solvent. As one could imagine, both constants would be inversely proportional to the molecular weight of the solvent since molality is given per kilogram of solvent. As the molecular weight of the solvent increases, the number of moles of solvent in one kilogram of solvent decreases. Thus, 1 m solution with benzene as solvent, for instance, has less moles of solvent than a 1 m solution with water as solvent. 1 kilogram of benzene has less moles than 1 kg of water. 

Here are sample calculations:

Some substances dissociate when dissolved in water. In these cases, the number of solute particles is greater than the number of units in one formula.

The above van't Hoff factors are ideal. In real solutions, there is some ion-pairing that occurs, especially at high concentrations:

We expect ion-pairing to be dependent on the concentration. This is much more likely to occur when there are a lot of ions present. Thus, the van't Hoff factor will be less than ideal as the concentration is increased.

Sucrose, table sugar, is a non-electrolyte - so it stays intact upon dissolution and does not form ions. Therefore, its van't Hoff factor remains at one at all concentrations.