Erin- we always like follow-up questions. It shows somebody actually read an answer.
I went on Google, searching for 'molecular elevation of boiling point', a name I got from looking in the CRC Handbook of Chemistry and Physics. There were a number of hits, including:http://en.wikipedia.org/wiki/Boiling-point_elevation
Perhaps I should explain why there's a simple relation between the number of dissolved molecules or ions per unit volume and the boiling point elevation. This explanation may be more technical than you or many other readers want, but I can't resist trying to show that there's a logic to these rules, not just a set of sayings to remember. The description below is somewhat general, but the solvent could often be water, and the solute could be salt or sugar.
A liquid boils when it's heated to a temperature for which the net free energy doesn't change when some molecules leave the liquid and join the gas (at the particular pressure used). The free energy change involves the change in both energy and entropy (see below) of the liquid and the gas. It takes a lot of energy to pull a molecule out of the liquid, but it gains a lot of entropy by having a lot of space to run around in in the gas. (Entropy is defined as the natural logarithm of the number of states available.) The relative importance of the entropy and the energy is determined by the temperature. So there's a particular temperature (the boiling point) where the two effects balance, and both the liquid and the gas are stable.
For each solvent, those effects can be pretty hard to figure out, but fortunately all we care about here is the change when a little solute is added, because that's what changes the boiling point. Let's think of what happens when you add just a little solute, not enough for there to be much interaction between the solute molecules or ions. The solute may change the entropy and energy of the solvent, but that effect isn't sensitive to changes in the number of solvent molecules because each solute molecule is completely surrounded by solvent anyway. The key change is this: when a solvent molecule evaporates, it leaves less room for the solute molecules to rattle around in. There are fewer states available to them. Another way to say that is that they have lost some entropy. If, say, 1% of the solvent boiled away each solute molecule would have only 99% as many states available to it, so it would lose about 0.01 of entropy, in natural entropy units. The entropy loss per solute molecule doesn't depend on its molecular properties, so neither does the effect on the boiling point!
This simple everyday question has some interesting physics in it, and I've re-thought the answer a few times. The question is whether for small non-volatile solute concentrations the boiling point elevation (or equivalently, the vapor pressure reduction) depends only on the concentration of solute molecules, not on any of their properties. I'm sure the argument is in physical chemistry textbooks, but these days it's easy to get lazy and try to get all info from the Web or by thinking.
At first I wrote yes, then altered the answer to say sort-of. After some thought, the answer is yes for any non-ionic solute. I'll post an update when I'm more sure about ionic solutes.
Anyway, here's the argument for non-ionic solutes. These have no long-range interactions with each other or the solvent. So you can break up the free energy into four parts:
1. from pure solvent regions.
2. from little balls of solvent each containing one solute molecule
3. from solute-solute interactions.
4. the part from the entropy of where the solute molecules are
Term 4 is the one that gives the effect we discussed above.
Term 3 is negligibly small for dilute solutions.
Term 2 doesn't change when a solvent molecule evaporates, because the number of solute molecules doesn't change.
Term 1 is the same as for pure solvent.
So the free-energy change when a solvent molecule leaves to go to the vapor (or the solid) is the same as for the pure solvent plus the term we calculated which depends only on the solvent and the density of solute molecules.
This is the sort of argument which must seem boring to most people, but some of us get a big thrill when some exact rigorous result like that pops out of the murk of complications that are important for most problems.
As I said, things get a little more complicated if there are long-range electrostatic interactions, so an update will follow.
mike w, again
p.s. A preliminary calculation of what happens with salts (ions) indicate that they only have the same effect on the boiling point as other solutes when their concentration is significantly lower than the background ionic concentration in the solvent. In water that's 10-7
M each of H+
. So for the sorts of salt concentration which have a major effect, electrostatic interactions make the effect per ion different from the result per molecule for non-ionic solutes.
(published on 10/22/2007)