Q & A: Lowering of Melting Point

Q:
Why does salt stop water from freezing?
- Rachel (age 14)
Kincumber, NSW, Australia
A:

Looking over our old answer (below), I realized that we said many interesting things but did not actually answer the question "why". Maybe whoever wrote the first draft didn't know the answer, and we just patched it to remove errors.  Anyway, here's why.

Say you have a cup of pure water and a cup of somewhat salty water. As you lower the temperature some of the pure water starts to form ice crystals. The reason is that although the frozen water molecules, lined up into a crystal,  have fewer ways to move around (lower "entropy") than the liquid molecules, they release heat when they freeze and that raises the entropy of the surroundings even more. So the net entropy goes up as the water freezes, as it always does on the way to any equilibrium state.

What about in the salty water? There's one extra term in the entropy change. The salt doesn't fit into the ice crystals. So as they form, the remaining salt is left with less room to roam around in, and thus less entropy. So you have to get the salt water even colder before you get a net entropy gain from freezing it.

It sounds like that explanation isn't special to salt- it should work for any molecules or ions dissolved in the water. And so it does.

Now for the old discussion:

If you live in a place that has lots of snow and ice in the winter, then you have probably seen the highway department spreading salt on the road to melt the ice. You may have also used salt on ice when making home-made ice cream. Salt lowers the freezing/melting point of water, so in both cases the idea is to take advantage of the lower melting point.

Ice forms when the temperature of water reaches 32 degrees Fahrenheit (0 degrees Celsius). When you add salt, that temperature drops: A 10-percent salt solution freezes at 20 °F (-6 °C), and a 20-percent solution freezes at 2 °F (-16 °C). On a roadway, this means that if you sprinkle salt on the ice, you can melt it. One way you can think about this is that the salt is so dry, so hungry for liquid water, that it actually pulls liquid water out of the ice. You can see that salt is hungrier for water than a drop of pure water would be, because salt certainly gets wet and dissolves when it's put near water. That's shows it's better at attracting liquid water than water itself is, and so it can pull water out of ice at a lower temperature than pure water can.

If you ever watch salt melting ice, you can see the dissolving process happen -- the ice immediately around the grain of salt melts, and the melting spreads out from that point. Those melted spots are actually very salty. Once the salt crystals are used up, they start to get diluted, more like ordinary liquid water, and their freezing point goes back up. If the temperature of the roadway is lower than 15 °F or so, then the salt can only melt a small amount of the ice. (If it gets below about 0 °F, it can't melt ANY of the ice.) In that case, spreading sand over the top of the ice to provide traction is a better option.

When you are making ice cream, the temperature around the ice cream mixture needs to be lower than 32 °F if you want the mixture to freeze. If you tried using pure ice around the bucket, it would warm up to 32 °F before it started to melt. It wouldn't absorb much heat in the process, so you wouldn't get ice cream. If there's a lot of salt around, the ice will melt at around 0 °F, which is cold enough. As the ice melts, it pulls a lot of heat from its surroundings, enough to cool down the ice cream. That's a key point- just warming up the ice or warming up the liquid doesn't soak up a whole lot of heat. Providing the energy to break molecules away from the ice into the liquid does soak up a lot of heat. So you want that melting process to occur cold enough to freeze the ice cream, not up at a temperature where the ice cream is still liquid.

By the way, you may wonder why you have to get the ice cream colder than 32 °F to freeze it. Just like salt water, it has molecules dissolved in the water (sugar,salts, proteins, ...) that lower its freezing point below that of pure water.

(published on 10/22/2007)

Follow-Up #1: freezing saltwater

Q:
If salt lowers the freezing point of water, does that mean that salt water will only freeze at colder temps than pure water?
- Elliot Frie (age 12)
Stevens Point, Wisconsin, U.S.A
A:
Yes, exactly.

Mike W.
Lee H

(published on 10/22/2007)

Follow-Up #2: Ice can be colder than 0 degrees Celsius

Q:
given it is so cold at north and south pole, is the ice there colder than0 degrees celcius?
- Nicola Carr
A:
Yes it can be considerably colder, just like the ice in your home refrigerator freezer compartment. If the ice is floating in water, like an iceberg in the North Sea or an ice cube in your favorite drink, the ice will probably be very close to the water temperature.  This may be lower than 0 degrees Celsius depending on the salt content.

LeeH

(published on 10/31/2007)

Follow-Up #3: saltwater freezing

Q:
on follow up question 2 does that mean salt water will freeze slower then normal pure water?
- Tai
Japan
A:
Salt water certainly starts to freeze at lower temperature than pure water. And it completes freezing at even lower temperature than that. So under normal conditions it will freeze more slowly if the temperature is gradually lowered.

Mike W.

(published on 12/14/2007)

Follow-Up #4: melting point of ice

Q:
what is the melting point of Pure Ice.? I have been asked this and can only think its 0 degrees Celsius !!! What is meant by Pure Ice?....is it because there are no other substances like salt present?
- daniel (age 14)
england
A:
You're right on all counts.

Mike W.

.

(published on 09/07/2008)

Follow-Up #5: entropy and freezing point depression

Q:
Hi, I am a middle school teacher, teaching general science. My students asked me the same question on why salt lowers the melting point of ice. I have read your explanation. However I have some lingering questions:[1] Can you elaborate about the part on "entropy"?[2] I look up "entropy". It seems so complicated as it is under the topic of thermodynamics. Any recommendation on a good website that introduces thermodynamic entropy conceptual. The complex equations are giving me a headache.[3] Is this possible to relate this to the kinetic model of matter?
- Jerry (age 35)
Singapore
A:

I'm not sure where to find a good website to introduce entropy, but Reif's book in the Berkeley series is very good: http://www.amazon.com/Statistical-Physics-Berkeley-Course-Vol/dp/0070048622. (The Wikipedia entropy article is currently (6/15) hopelessly complex and confusing for somebody first learning the topic.)

The basic idea is this. Take some set of gross fixed conditions, e.g.
{number of molecules, temperature of environment, pressure}. How likely are you to find the molecules in some type of arrangement (liquid, solid)? Nature turns out to be extremely indifferent to which state things are in. In equilibrium the probability of finding something (e.g. liquid) is just proportional to the number of quantum states that look like that. Will the water be liquid or solid? It just depends on which type is consistent with more quantum states. The total number of quantum states that look like the liquid is the product of the number of states of the water that are liquid times the number of states of the environment that go along with the liquid. It's a product for the same reason that if you roll two dice there are 6*6=36 possible results. The same goes for the solid. The number of environment states depends on whether the water is liquid or solid, because the solid has lower energy, so that leaves more energy (and thus more states reachable) for the environment.

So finding the most likely form means finding the form with the biggest product of system state number times environment state number. It's a nuisance to maximize a product. So we convert it to a sum by taking the logarithm. The most likely form has the biggest log of the total number of states, meaning the biggest sum of the  log of the number of states of the system plus the log of the number of states of the environment.

These words are getting awkward. Let's make up a new one for "natural log of number of states". The word is "entropy".  So the most likely result is the one that maximizes total entropy.

You can  see why whether the water ends up liquid or solid depends on how much the environment's entropy goes up when it gets the energy released by conversion to solid. It would be nice to have a name for that too. We call the energy required to increase the entropy by one unit the "temperature". At high temperature the environment entropy doesn't change much so the water find the form that gives itself a lot of entropy: liquid. At low temperature, the environment entropy is very sensitive to an energy it can pick up, so the water takes the form that releases the most energy: solid.

Now you can also see why solutes in water favor the liquid state. If some of the water freezes to ice, the solutes (left in the liquid) have less room to run around and thus have lower entropy. That means you have to lower the environment temperature a little more to make the solid the form that maximizes total entropy.

Unfortunately some of this argument is obscured by traditional definitions of entropy, which use weird historical units and don't bring out the relation to number of states. To get more precise, there are some subtle adjustments when some of the quantum states are more likely than others, but you don't need that for starters.

Yes, it is possible to relate all this to the classical kinetic model, especially for something simple like a gas. For example, on another question (https://van.physics.illinois.edu/qa/listing.php?id=14736) we derive pV=NkT for an ideal gas from this picture, which you can connect to the common derivation from a classical kinetic picture.

Mike W.

p.s. Googling around turned up this  good discussion:   http://www.science20.com/hammock_physicist/what_entropy-89730.

(published on 06/16/2015)

Follow-Up #6: ice, salt, heat of solvation

Q:
We heard on NPR that the effect of salt on ice is not so much freezing point depression but heat of solvation. So for sodium chloride, the temperature lowers when it dissolves but for calcium chloride it warms. So one uses NaCl to make ice cream but CaCl2 to melt ice on roads. Is this the whole story? If you predissolved CaCl2 then added to ice you could still make ice cream, right?
- Linda (age >50)
Palo Alto CA US
A:

The heat of solvation is not really the main effect. In fact, roads are usually de-iced with ordinary NaCl, which is very cheap. CaCl2 has the advantage of releasing heat as it dissolves, but that's not important enough to get most places to use it.

As you say, you could use pre-dissolved CaCl2 for the ice-cream maker. There's no real reason to, however, since NaCl works well.

Mike W.

(published on 07/01/2015)