This is not quite as "household" as some of the other posts in this series, but does involve some chemicals that we handle often. Since it is so cold, it might be appropriate to investigate the science behind deicing chemicals. We use them all of the time, from salt on the roads to solutions pumped on aeroplanes. This is also how we can make ice cream using salt and ice as the freezing mixture.
It is a fact that, with very few exceptions, mixtures of materials have lower freezing points than pure ones. One of purity determinations in the old practice of organic chemistry was to take a melting point, and it it fell very close to the accepted value, and was sharp, the identity of the material was confirmed, if other data were in line with it.
In chemical physics, there is a set of properties called the colligative properties of matter. One of the properties in this set has to do with the depression of freezing point when substances are dissolved in a solvent. First, a few terms need to be defined:
Molality: the number of moles of a material dissolved in one kilogram of solvent. For example, salt, with a molecular mass (actually, this is a bit of a misnomer, since salt consists of a lattice of ions rather then discrete molecules, so this is the formula mass in this instance) is 58.5 grams per formula mass. For sugar, sucrose, the molecular mass is 342 grams per molecular mass. Remember that molality, expressed as m, is moles per kilogram of solvent, not moles per liter of solution, called molarity, expressed as M.
Freezing point constant (Kf): this is a constant, expressed in (degrees K)(kg) / mol. This constant is unique (except by coincidence) for every solvent. For water, the value is 1.86 K kg / mol. (Degrees Celsius are the same, since a Kelvin and a degree Celsius are the same size, as we discussed last Thursday).
The van't Hoff factor (i): the van't Hoff factor is determined by the degree of dissociation of a material when dissolved in a given solvent. For salt, this factor is exactly 2 because 100% of the salt ions are dissociated from each other when dissolved in water, and salt contains two types of particles. For sugar, the factor is exactly 1 because none of the sugar molecules are dissociated in water solution. IT is possible to have van't Hoff factors greater than two, if a material dissociates into more than two species, like sulfuric acid in extreme dilution in water.
ΔTf: this is the change in the freezing point resulting from dissolved materials. The formula is
ΔTf = (m)(Kf)(i).
FP total: FP total = FP solvent - ΔTf. This is the final freezing point of a solvent, taking into account the dissolved materials.
This expression has traditionally been used to calculate the van't Hoff factor for unknown materials. In a few systems, materials become more associated in solution, and in these cases, i is less than one. These are rare. A more common situation is for materials to disassociate partially in solution, in then the factor is greater than one but less than two. Once the van't Hoff factor is known, the degree of dissociation in a given solvent for a given concentration can be found. This has some important theoretical and practical applications.
One note about these equations: they hold rigorously only at very low (less than 0.1 m) concentrations, so with higher concentrations nonlinearity is a threat. We shall see that shortly.
So, why does salt melt ice? When you put salt on ice, even if the ice is firmly frozen and the salt is cold, there is some diffusion of salt into the water and vice versa. Now, we have a solution of salt in frozen water, but the salt in the water causes the freezing point of the solution to become depressed, so the ice melts, drawing energy from the environment (the latent heat of fusion for water has to come from some where).
This is also why you can make ice cream using ice and salt. Adding the salt to the ice depresses the freezing point, and the system reacts by melting, but energy (heat) is required for melting, and that heat comes from the bucket of ice and salt (and the ice cream mixture in the metal can). This reinforces the difference between heat and temperature as we discussed in the irregular installment Thursday past.
Thus, anything that will dissolve in water and does not become more associated will lower the freezing point. In aircraft, salt is not a very good idea because of corrosion to metal, so noncorrosive materials are used, generally glycol solutions in water that are heated and sprayed on the icy aircraft surfaces. The traditional deicing solutions were based on ethylene glycol (the same thing as in the green automotive antifreeze, for the same reason), but in the developed world propylene glycol is generally used since ethylene glycol is highly toxic and propylene glycol is not. Ethylene glycol is more efficient since it has a lower molecular mass, but its toxicity to most animal life makes it undesirable. Since the glycols do not dissociate in water, the van't Hoff factor is one for both of them.
You might ask, well, why not use something with a higher van't Hoff factor? Good thinking, but almost any material that dissociated in water is ionic, and ions conduct electricity (they are electrolytes), and electrical conduction leads to corrosion, so they would all act like salt. We are limited to nonionic materials in environments were corrosion is a concern.
There is a limitation as to what salt will do in melting ice. Actually, there are two limitations. The practical one is that if the ice is extremely heavy, it takes a lot of salt to melt it. This is because the concentration of the salt has to be high enough to bring the freezing point of the mixture to below whatever the ambient temperature happens to be. (This is the "m" factor in the ΔTf equation). However, with enough salt you could melt any given amount of ice if you could afford it.
The other limitation is related. The solubility of salt in water is fairly constant with temperature. Many other substances have solubilities strongly dependent on temperature, generally decreasing as temperature decreases. Assuming that the solubility of salt is the same in water at any temperature (a fairly good assumption for sodium chloride), the lowest temperature that salt will melt ice can be estimated if the solubility of salt in water is known. That comes to 360 grams per kg of water. Since salt has a formula mass of 58.5 grams per unit, that amounts to a 6.2 molal solution. Substituting into the equations shown earlier, and remembering that the van't Hoff factor for salt is 2, we have:
ΔTf = (6.1 m)(1.86 degrees C kg/mol)(2), which comes to
23 degrees C.
Putting this figure into the FP total expression, we have
FP total = FP solvent - ΔTf, or 0 degrees C - 23 degrees C, or negative 23 degrees C. Converting this to degrees F, we have negative 9.4 degrees F. Actually, salt is not quite as soluble in very low temperature solutions as it is at room temperature, so the actual figure is not as low. In addition, in saturated solutions the van't Hoff factor may not be exactly 2, since the ions are crowed together, reducing the dissociation somewhat. Experimentally it is known that the freezing point of the most concentrated brine is around negative 6 degrees F, which is still in pretty good agreement with theory.
A much more effective road deicer is calcium chloride, CaCl2. We note right away that the van't Hoff factor is 3, since three ions result when it dissolves in water. That is good. The formula mass for this material is 111 g/unit, higher than that for salt, and the molality is about 6.7 for a saturated solution at room temperature. Plugging in these values, we get a ΔTf of 37 degrees C, or a freezing point of negative 37 degrees C, which equates to negative 35 degrees F. Actually, it is a little colder than that, experimentally determined to be as low as negative 62 degrees F. I believe the error comes both from nonlinear behavior at high concentrations and uncertainty in the molality of the solution at low temperatures on my part. Another advantage is that calcium chloride releases heat when is dissolves in water, thus raising the temperature of the roadway, at least a bit.
There are problems with calcium chloride, though. It is considerably more expensive than salt, and it is also hygroscopic, meaning that it absorbs moisture from the air. There are severe problems with it caking during storage, and it can also become a corrosive puddle since it hangs onto that water strongly. As a matter of fact, it is sometimes put on dirt roads in the summertime as a dust suppressant due to it being hygroscopic.
The bottom line is, salt is fine on the roads if the temperature is not much below zero degrees F, but ineffective at lower temperatures. It still does a good job freezing ice cream.
As always, comments, suggestions, questions, and criticisms, as well as any other science or technology topic are welcome in the comments. I always learn more than I teach writing this series.
UPDATE: Well, folks, the results are in for the poll. Chocolate ice cream wins by a trickle, followed by "other". I voted Black Walnut, but also think that vanilla is more versatile. If I can find some decent pictures, I will post a new installment of A Primer in US Coins tomorrow or Tuesday. I have been having difficulty getting quality pictures of the new Lincoln cent series that just started. If anyone has good jpgs or other picture files, please attach them in the comments. I am gone at 9:30 PM Eastern, but will check for comments made after that tomorrow. Thanks to everyone for speaking out and asking questions. I always learn more that I teach in this series.
Warmest regards,
Doc