Freezing point depression in ice cream

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…

2 ingredient vanilla ice cream - top view
Ice cream with plenty of sugar

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

Where:

  • ΔT= 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 = 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, this is called the van ‘t Hoff constant

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 650g 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 650g of water, the molality of the sugar is: 0,22 / 0,65 = 0,34 mol/kg.

Now it’s a matter of filling in the formula:

ΔTF = KF · m · i = 1,853 · 0,34 · 1 = 0,62°C

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

Phase diagrams

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!

 

Coffee chocolate caramel ice cream - discussing how best to add chocolate chips or chunks to your ice cream without breaking your teeth upon eating! Ice cream inclusion science | foodcrumbles.com

A video for more explanation

A more fundamental explanation can be found in this great video from the Khan Academy.

Resources

A more detailed explanation of the thermodynamics behind the freezing point depression can be found on the websites of: UC Davis Bristol University.

Semifreddo - The secret of ice cream & the freezing point depression

4 Comments

  1. Great post.

    You say “If you like you can even calculate how much ice crystals have formed and you can calculate what the new freezing temperature of your sugar solution is. If you like you can even calculate how much ice crystals have formed and you can calculate what the new freezing temperature of your sugar solution is.” Please tell me more. I guess, I could simply measure the temperature of some frozen ice cream to determine the freezing point.

    For context, I ‘m making home low-calorie ice cream, frozen yogurts, and sorbets. Over the months the batches are improving, but I am bedeviled by ice crystals, had texture after freezing, and excess coldness on the tongue. Pure erythritol was great for calories and taste, but yielded hard and cold product. Presently, I am using a mixture of erythritol and sucrose (50% each). It’s better, but still too hard and not creamy. I plan to try another fruit alcohol with more freezing point depression next.

    • Hello Mark,

      Thank you for this fascinating comment and question. It took me some time to come up with an appropriate answer, but here it is, I hope it’s useful.

      To start with your first question, calculating the concentrations of ice crystals versus sugar solution. This question requires an answer longer than just a comment so I decided to finish a blog post I had been working on which talks about this exact topic. Using so-called phase diagrams can tell you more about how to calculate these values: http://foodcrumbles.com/phase-diagrams.
      There is also a way to calculate the freezing point depression of a pure solution. It uses the molality of the sugar (or sugar substitute) to calculate the freezing point depression. This molality describes the number of molecules in a certain mass. Therefore the more molecules there are and thus the smaller they are, the more effective they are. Again, it’s a little bit too much for just a comment.

      Then there’s your issue using erythritol for ice cream. I must say that I have never used erythritol but I did some digging on the internet. Erythirtrol is a so called sugar alcohol as you might know. One of the characteristics of erythritol is that it crystallizes more easily than regular sugar, which might be one of the causes of your hard ice cream. This doesn’t necessarily have anything to do with the freezing point depression. At the same time, erythritrol does have completely different freezing point depression then regular sugar due to the different size of the molecule. Maybe this pdf file can help you: http://www.jungbunzlauer.com/fileadmin/content/_PDF/JBL_AR_Erythritol_makes_a_difference_2015-104.pdf.

      Hope that helps and thanks for the questions!

      • Thank you very much. I look forward to reading your fascinating post and learning. It may be a bit of a challenge as I didn’t pay enough attention in high school chemistry and was tossed out after I set off a potassium permanganate and sugar bomb. I guess I can always forget my pride and ask my high school kids.

        Nonetheless, I grew to be an epidemiologist and one day was confronted by a hospital where the water system was contaminated with ethylene glycol antifreeze due to a cross connection in the pipes. the contamination had happened at night and we needed to decide quickly if the water was safe to drink and for the hemodialysis machines (one patient had died during the night as the molecules of ethylene glycol passed the semipermeable membrane.

        My team went to the chemistry laboratory where we learned they were unable to measure levels of ethylene glycol. the head tech had an idea. He filled a beaker with distilled water and another with ethylene glycol. He put both in an ice bath and we watched in fascination as the water began to ice over and he inserted a thermometer and it showed 0 C. Soon afterword, the contaminated tap water froze well below 0. Hence, we didn’t allow people to drink the water.

        the hospital toxicologist told us that he air conditioning fluid was marked with uridene green so people would know if there was contamination. Alas, he explained that uridene green is a relatively large molecule so it didn’t pass the dialysis semipermeable membrane so nobody thought the fluid was contaminated until the patient slipped off into a deep sleep and died.

        This was in New York City, where the city lab could test for anything and they provided us with hourly tests as we flushed out the building, which took about 12 hours.

        Forgive an old man for his stories. Based on the article you attached I have followed its recommendation to use 1/3 erythritol to 2 parts sucrose. Erythritol is great stuff. It is absorbed into the body, so it doesn’t cause osmotic diarrhea like other sugar alcohols. Also, is cannot be metabolized by the body, so it is excreted unchanged in the urine and contributes 0 calories to the body. Also, it can’t be metabolized by oral bacteria, so it is not associated with dental caries.

        Since my goal is produce the lowest possible calorie ice cream, erythritol seems good for the job.

        If I may, I’ll let you know how my freezing point determinations on commercial products works out and use this as a target for my home brew ice cream. If I can figure out how to use the formula in your posting, I’ll compare this with my experimental results.

        Best Wishes,
        Mark

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