Why is an ice cube rock solid whereas a scoop of Italian gelato is almost liquid like? Even a ‘simple’ popsicle isn’t as hard as a pure water ice cube. Instead you can bite some off quite easily. Isn’t that interesting?
We’ve made quite a lot of ice creams already, quite complex ice creams involving custards, a super simple ice cream with only two ingredients or an Italian style semifreddo. In all cases we’ve kind of taken it for granted that the ice cream didn’t turn out rock solid. Part of that is due to the introduction of air. The ice cream was either made airy by incorporating whipped cream or thanks to the continuous stirring of the ice cream machine. But just introducing air doesn’t do the trick. Freezing pure whipped cream will still give quite a solid icy structure.
In comes the importance of sugar (or alcohol) and a phenomenon called the freezing point depression!
What is freezing point depression?
The freezing point depression says that the freezing point of a mixture of two components is lower than that of individual components. It involves a solvent (e.g. water) and a solute which you’ll mix with the solvent.
A very common example of this phenomenon in everyday life is salting of the roads in water. Pure water freezes at 0°C. However, by mixing in salt the freezing point of this mixture of water and salt will drop well below zero. This is why salt is used to keep roads free from ice. Even at temperatures below zero there won’t be sheets of ice on the road.
So why is the freezing point of the solvent changed by dissolving something else in it? Well, if you only have pure water (or any other solvent) these water molecules can organize themselves nice and tight. When the temperature lowers and the water freezes they can form a nice crystal amongst themselves (read more about phase transitions). However, by mixing in a solute (e.g. salt or sugar) this nicely ordered structure is disturbed. Instead, they might only form these crystals at a lower temperature. This is what happens because of the freezing point depression.
The freezing point depression in ice cream
In ice cream the freezing point of the water in the ice cream is modified. Water is the main components of most ice cream since it makes up most of the milk or cream you might be using. The freezing point is mostly lowered through the addition of sugar. Sugar dissolves in the water and this ways interferes with the crystal formation.
You might also expect the fat in ice cream to impact the freezing point. However, that is not the case. Water and oil do not mix instead little bubbles of oil float around in the ice cream, but they never interfere in the same way as sugar does.
Alcohol and ice cream
In various recipes alcohol is used for making ice cream. Apart from the flavour and alcohol it contributes to the ice cream it is also used for lowering the freezing point of water! Theoretically you could make ice cream without sugar and just alcohol, however, not sure whether that would taste as good…
Calculating the freezing point depression
You can calculate the change in freezing point of water in ice cream quite easily. The freezing point depression is a so called colligative property. This means that the temperature drop, so how much the freezing point lowers, does not depend on the type of component added, the solute. Instead, it only depends on the number of particles added as well as the original properties of the solvent to which they are added.
In other words, if we would add 10.000 sugar molecules, this would have the same effect on the freezing point as 10.000 salt particles. Only when the amount of solute becomes very high the type of solute becomes important.
Because of this simple relationship the freezing point depression can be calculated with a simple formula:
ΔTF = – KF · m · i
- ΔTF = The change in the freezing temperature in °C
- KF = the cryoscopic constant, this value depends on the solvent you’re looking at, for water it’s 1,853 °C·kg/mol
- m = the molality of the solute, in other words, the number of particles per kg of solvent, in mol/kg
- i = the van ‘t Hoff constant if your particles splits in 2 or 3 parts after it’s been added to the solvent you have to take that into account, this is most common for salts. For sugars and the like which don’t break apart, this constant is one, for sodium chloride (salt) it’s two.
Calculating the change in freezing point for ice cream
Vanilla ice cream
Let’s have a look at the change in freezing point for a basic vanilla ice cream. This ice cream contains approximately 600g (rough assumption: 300 + 0.65* 300 + 4 * 25) of water and 75g of sugar.
- If sugar dissolves in water it will not split so i in the formula above is 1 and we also know the value for the cryoscopic constant of water (1,853 °C·kg/mol).
- We then need to know how many sugar crystals we have. From literature we found that 1 mole of sugar molecules weighs 342,3g. Therefore 75g of sugar is 75 / 342,3 = 0,22 mol. Since we have 600g of water, the molality of the sugar is: 0,22 / 0,60 = 0,37 mol/kg.
Now it’s a matter of filling in the formula:
ΔTF = – KF · m · i = -1,853 · 0,37 · 1 = -0,68°C
The freezing point dropped less than 1 degree. This is actually really little, so this ice cream can be made lot softer by adding more sugar.
Soft two-ingredient ice cream
Let’s do another example to practice these calculations, now looking at a super simple 2-ingredient ice cream. This ice cream contains 245g water (0,7 * 230 + 0,55 * 150) and 70g sugar (0,45 * 150), for simplicity we’ve rounded of the numbers.
You can use a lot of the same numbers as in the previous calculation, but you’ll need to calculate the molality of sugar for this new ice cream recipe. Using the same method we find it is: 70 / 342,3 = 0,20 mol and 0,02 / 0,245 = 0,83 mol/kg,
Let’s fill in the formula again:
ΔTF = -KF · m · i = -1,853 · 0,83 · 1 = -1,55°C
Just this change of freezing point doesn’t tell the complete ice cream story yet, it’s only the start. Instead, once you’ve got these new temperatures you should have a look at a phase diagram. In a phase diagram you can see exactly how much ice and liquid will be present at each different temperature. This is a bit too much in-depth for this post, but luckily there’s a separate post on the topic of phase diagrams for you.
A note on frozen fruits
Ever noticed that frozen fruits often aren’t rock solid? Apart from the impact of the fruit’s texture this is also due to the freezing point depression. The fruits contain quite a lot of sugar which prevent all the water from freezing!
A video for more explanation
A more fundamental explanation can be found in this great video from the Khan Academy.
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