Making ice cream...
When you make homemade ice cream, you put (relatively warm) ice cream mixture in a vessel and you put that vessel into ice. Then, you churn the ice cream mixture as it freezes. The churning-while-freezing is essential: it makes sure the ice cream freezes into a soft mixture of evenly-sized ice crystals rather than a big hard block. It also whips some air into it, further softening the ice cream.
Trouble is, as the ice removes heat from the ice cream, it melts into water. Pure water cannot go colder than freezing (0°C). But since the ice cream mixture contains sugar and other stuff dissolved in water, it needs to go below 0°C to freeze.
To make this work, then, you need to add salt. (To the ice. Not to the ice cream mix!) When salt dissolves in water, it bonds with the water, making it harder to freeze into ice, thus lowering its freezing point. This allows the mixture to go below 0°C.
In the 1984 edition of his excellent book On Food and Cooking, Harold McGee explains what happens like this:
I think this is generally correct, bu I've begun to doubt that this explains all that the salt does. I think there are two more significant effects that contribute to the making of ice cream.
The first effect has to do with what happens when salt dissolves in water. Salt is NaCl, and when it dissolves it goes from being a solid to being an aqueous solution:
The second effect is a bit trickier. We should be able to understand it by comparing it with a related phenomena: wind chill. If you get out of a swimming pool and a breeze is blowing, you feel cold, even if the breeze is warmer than your body temperature. This is because of evaporative cooling, the same effect which is responsible for soup cooling down when you blow on it.
How does evaporative cooling work? The model, as I understand it, is something like this. Not all molecules of liquid water are moving with the same energy. Some have more energy and are moving faster, while others have less energy and move slower. At any point in time, you'll find molecules of water that are moving fast enough to fly off the liquid, turning into water vapor. When this happens, the liquid loses a bit of energy and drops in temperature. Eventually you get a little cloud of vapor that just next to the liquid. That cloud will get saturated enough so that molecules of water from the vapor will re-enter the liquid, heating it up again. If the vapor and the liquid are in equilibrium, so that just as many molecules leave as return, then no more temperature change will occur.
But if you blow on the water, even with air at the same temperature as the water, that will clear out the water vapor layer. The liquid continues to lose energy as it loses molecules of water, but it doesn't gain any back since the vapor cloud is gone. Do this enough and you'll begin to see a noticable drop in temperature of the water.
So how does this relate to salt and ice? Basically, we have a similar thing going on: molecules of water are breaking free of the ice, and taking heat away. But at the same time, molecules of water from the liquid are attaching themselves to the ice, adding heat back in. In equilibrium, both will happen at the same rate, and there is no temperature change.
But add enough salt to the water, and you decrease the concentration of water in the liquid phase. Also, some of the water molecules in the liquid are bonding with the Na+ and Cl- ions of the dissolved salt, so they are prevented from returning to the ice. This means there will be more molecules of water breaking off the ice and fewer molecules attaching back on. This ought to lower the temperature.
So while McGee cites freezing point depression, the low temperature of the starting ice, and melting ice as the three factors which contribute to making home-made ice cream, there are actually two more cooling effects. One comes from the heat of solution of salt and the other comes from the "forced melting" which occurs when pure ice is put into a salt solution.
The question now is: how significant are these two effects? I would count these effects as fairly significant if it is possible to make ice cream starting with "warm" ice: ice just at 0°C. Since such ice is only just at freezing, not below freezing, it is unable to freeze ice cream by itself. But mix salt in, and if my discussion above are right, the temperatures should decrease. Will it decrease enough to make ice cream?
It should be fairly easy to calculate the theoretical limit of the magnitude of the first effect (heat of solution), assuming you have the molar heat of solution for NaCl. Unfortunately, I don't have that information handy.
I can, however, take a stab at estimating the second quantity, the "heat of fusion" effect. I guess that you get the maximum temperature drop possible with salt added to ice when you add just enough salt and ice so the two would form a saturated solution when the ice completely melts. If this is right, the temperature drop is given by:
Constants (found on the web)
Heat of fusion of ice: 334 J/g
Solubility of NaCl at 0 C: 35.7 g in 100 mL of water
Heat capacity of water: 4.18 j/g-C
So, if we add 35.7 g of salt to 100 g of water and all of it is forced to dissolve, we get: 100 grams of water * 334 joules per gram / 4.18 joules per gram-C / 135.7 grams = 58.9 degrees
The only thing I can think of that would stop this process is the freezing point of salt water. So my guess so far: adding salt to ice should produce brine that may be well below the initial temperature of the constituents. In particular, you should be able to reach the freezing point of salt water (-21 C) by adding an appropriate amount of zero degree salt to zero degree ice.
Anyone know if this is right?
Trouble is, as the ice removes heat from the ice cream, it melts into water. Pure water cannot go colder than freezing (0°C). But since the ice cream mixture contains sugar and other stuff dissolved in water, it needs to go below 0°C to freeze.
To make this work, then, you need to add salt. (To the ice. Not to the ice cream mix!) When salt dissolves in water, it bonds with the water, making it harder to freeze into ice, thus lowering its freezing point. This allows the mixture to go below 0°C.
In the 1984 edition of his excellent book On Food and Cooking, Harold McGee explains what happens like this:
Ice from the freezer is generally around 10°F (-12°C), or plenty cold enough to freeze the mix if it weren't for the combination of friction, warm mix, and warm air melting some of it into ice water with a much higher temperature. Since this is inevitable, salt is added to lower the freezing point of the water, and so the temperatures at which it can remain liquid (for the same reason, salt is used to turn icy roads into merely wet ones). The brine then absorbs heat from the mix, the colder ice melts and keeps the brine cold, and salt crystals dissolve to keep the brine from being diluted. (p. 29)The updated 2005 edition cuts all this out, saying only "If salts are added to the ice, the salts dissolve in the slush, lower its freezing point, and allow it to get cold enough to freeze the sugared cream" (p. 39).
I think this is generally correct, bu I've begun to doubt that this explains all that the salt does. I think there are two more significant effects that contribute to the making of ice cream.
The first effect has to do with what happens when salt dissolves in water. Salt is NaCl, and when it dissolves it goes from being a solid to being an aqueous solution:
NaCl → Na+ (aq) + Cl- (aq)
For this reaction to occur, the salt must first dissociate into a sodium ion and a chlorine ion: this requires energy, which absorbs heat from the system. Then, the Na+ and Cl- ions bond with water, releasing heat into the system. The first amount of energy is greater than the second amount of energy, so this reaction can lower the temperature of the system. So as salt dissolves in water, the temperature of the two should go down. The molar heat of solution for salt is the amount of heat absorbed when 6.02x1023 salt molecules dissolve in water.The second effect is a bit trickier. We should be able to understand it by comparing it with a related phenomena: wind chill. If you get out of a swimming pool and a breeze is blowing, you feel cold, even if the breeze is warmer than your body temperature. This is because of evaporative cooling, the same effect which is responsible for soup cooling down when you blow on it.
How does evaporative cooling work? The model, as I understand it, is something like this. Not all molecules of liquid water are moving with the same energy. Some have more energy and are moving faster, while others have less energy and move slower. At any point in time, you'll find molecules of water that are moving fast enough to fly off the liquid, turning into water vapor. When this happens, the liquid loses a bit of energy and drops in temperature. Eventually you get a little cloud of vapor that just next to the liquid. That cloud will get saturated enough so that molecules of water from the vapor will re-enter the liquid, heating it up again. If the vapor and the liquid are in equilibrium, so that just as many molecules leave as return, then no more temperature change will occur.
But if you blow on the water, even with air at the same temperature as the water, that will clear out the water vapor layer. The liquid continues to lose energy as it loses molecules of water, but it doesn't gain any back since the vapor cloud is gone. Do this enough and you'll begin to see a noticable drop in temperature of the water.
So how does this relate to salt and ice? Basically, we have a similar thing going on: molecules of water are breaking free of the ice, and taking heat away. But at the same time, molecules of water from the liquid are attaching themselves to the ice, adding heat back in. In equilibrium, both will happen at the same rate, and there is no temperature change.
But add enough salt to the water, and you decrease the concentration of water in the liquid phase. Also, some of the water molecules in the liquid are bonding with the Na+ and Cl- ions of the dissolved salt, so they are prevented from returning to the ice. This means there will be more molecules of water breaking off the ice and fewer molecules attaching back on. This ought to lower the temperature.
So while McGee cites freezing point depression, the low temperature of the starting ice, and melting ice as the three factors which contribute to making home-made ice cream, there are actually two more cooling effects. One comes from the heat of solution of salt and the other comes from the "forced melting" which occurs when pure ice is put into a salt solution.
The question now is: how significant are these two effects? I would count these effects as fairly significant if it is possible to make ice cream starting with "warm" ice: ice just at 0°C. Since such ice is only just at freezing, not below freezing, it is unable to freeze ice cream by itself. But mix salt in, and if my discussion above are right, the temperatures should decrease. Will it decrease enough to make ice cream?
It should be fairly easy to calculate the theoretical limit of the magnitude of the first effect (heat of solution), assuming you have the molar heat of solution for NaCl. Unfortunately, I don't have that information handy.
I can, however, take a stab at estimating the second quantity, the "heat of fusion" effect. I guess that you get the maximum temperature drop possible with salt added to ice when you add just enough salt and ice so the two would form a saturated solution when the ice completely melts. If this is right, the temperature drop is given by:
Constants (found on the web)
Heat of fusion of ice: 334 J/g
Solubility of NaCl at 0 C: 35.7 g in 100 mL of water
Heat capacity of water: 4.18 j/g-C
So, if we add 35.7 g of salt to 100 g of water and all of it is forced to dissolve, we get: 100 grams of water * 334 joules per gram / 4.18 joules per gram-C / 135.7 grams = 58.9 degrees
The only thing I can think of that would stop this process is the freezing point of salt water. So my guess so far: adding salt to ice should produce brine that may be well below the initial temperature of the constituents. In particular, you should be able to reach the freezing point of salt water (-21 C) by adding an appropriate amount of zero degree salt to zero degree ice.
Anyone know if this is right?
posted by Ang at 8:50 PM
2 Comments:
Yeah, that sounds right. I do seem to remember some curve with a bump in it from Chemistry...
You've got most of it right. Sorry my chemical engineering is demanding that I put in my two cents. It's less of a chemical problem, and more of a standard heat transfer/thermodynamics problem.
Although evaporative cooling has got less to do with it. Water is one of those things that's more dense as a liquid than a solid. If it were a normal solid, this might be so, but since water does have this unique and rare property, expanding when it freezes, thus on the whole it takes energy to freeze it, and it gives off energy (in the form of heat) when it melts.
And I think the molar heat of solution, for salt in water, is probably negligable.
Thus most of the cooling effect comes from moving the ice, which is at -10 C, back to water, which is at 0C. Ice is a notoriously bad conductor of heat, so the ice won't actually give off any heat, unless there's somthing to transport the heat away. That being the water which is melting to the bottom.
Should I get out my engineering pad and CRC, and make some caluclations.
-J
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