olive oil ice cream, super smooth

The Science of Ice Cream – Freezing Point Depression

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 = 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

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.

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21 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: https://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

  2. What’s the cyroscopic comstant of milk

    • Hi Paing,

      Thank you for coming by! In order to calculate the freezing point of milk you should use the cryoscopic constant for water and then use the formula to calculate the new freezing point. However, this isn’t straight forward since there are both salts and sugars in milk. You would have to know the concentrations of all solutes in your milk and this varies per breed type and the diet of the cow.
      That said, there is quite a lot of published data on the freezing point of milk. Generally, the freezing point depression of milk is a little more than 0,5C (so the new freezing point is -0.5c). Milk is mostly water with only some salts and sugar, so the lowering of the freezing point is not that much. This article might help you further.

      • Thanks you and please answer what’s tha van ‘hof constant for milk? Is that 1 or something else. and you should mentioned this formual result of freezing point depression should be in minus,i’m totally confused with the 0.62 degree celsius of freezing point depression of water added with sugar while original water freezing point is 0 degree celsius.should be Tfi – Tfs = Kf*m*i

        • Hi Paing,

          I added some clarification in the post that will hopefully help you. Adding sugar to water lowers the freezing point by 0.62C. So the new freezing point is -0.62C.

          There exist no van ‘t Hoff constant for milk. Instead, see milk as water with solutes such as sugar and salts dispersed throughout. Use the cryoscopic constant for water and then find the molality and Van ‘t Hoff constant for the solutes that are present in the milk.

          Hope that helps!

  3. Hello,

    I am assuming sucrose, but not milk fat, lowers the freezing point of ice cream (about minus 20 degrees C) .

    What percentage of sucrose (or dextrose?) would need to be added to otherwise plain milk to prevent it freezing at minus 22 degrees C.
    Are there other food grade additives which have a similar effect?

    • Hi Pete,

      Sucrose indeed lowers the freezing point, however, it does not lower the freezing point of all the water to below -22C in the quantities that you’d use in ice cream. Part of the water will still freeze, just not all of it (so the freezing point of that remaining portion is indeed very low). I would not know the exact concentration of sugar required to prevent any of the milk from freezing, generally, at this point the mixture becomes very viscous and other components in milk (such as the lactose) also influence freezing so it’s not an easy calculation. I would say you’d need >60w% of sugar (so of 100g of ice cream, more than 60% should be sugar), chances are your ice cream won’t taste good anymore and you might start having issues dissolving all the sugar in your ice cream mix.
      Propylene glycol (which is also used in antifreeze, for the same reason) is also a strong freezing point depressor and is allowed to use in ice cream, though it depends by location how much, definitely at far lower concentrations then sugar.

      I think our course on ice cream, especially the section on freezing point depression might help you out as well, it contains a few more details than discussed in this post.

      Hope that helps!
      Alcohol also lowers the freezing point, again, it won’t prevent all freezing, only part of it.

      • Thanks kindly for the response. I am mostly interested in storing milk (or sweetened milk if needs be) at minus 22 C. Such that it remains both palatable and liquid. [There is no standard refrigeration (+4 degrees C) available].
        However, 60% w/w sucrose is likely to be more thick syrup rather than liquid. Probably attempting to do the impossible.

        • Hi Pete,

          Is there any reason why you wouldn’t want the milk to freeze? I don’t think milk will damage much when frozen, it’s just very bulky and impractical to freeze, but I don’t see why you couldn’t?

  4. This is so interesting. How do you manage to come up with the water content in each. For example, in the vanilla. I would have just assumed it was 300mL x 2 from the milk and the cream. Where did the extra 50g come from and how can I calculate this for my own batches?

    Thanks very much! Gonna be nerding out on your site for the longest time.

    • Hi Tiffany,

      Great question (and I did notice there was a slight error which I adjusted)! The water in the vanilla ice cream recipe comes from three sources: milk (which we’re assuming is 100% water here), cream (65% water) and egg yolks (we’re assuming 25g water each). Do notice that whether you use 600g of water of 650g the difference in freezing point is pretty small.

      If you’re interested in digging deeper, I’d suggest you have a look at our free ice cream course as well where we explain this in even more detail!

      • Thanks for your reply and clarification. I actually am enrolled in the course. I did want to double check however. If I get one question wrong on the quiz it usually doesn’t let me move on and it seems as though I have to redo the whole thing until I can get to the next section.

        I’m not sure if this is the case or if I’m just having trouble navigating.

        Another question though to clarify. Is it true that most ice creams have around 20% sucrose and some sort of glucose syrup and thus the freezing point depression of commercial items are usually -18 deg C? Does this mean that up until -18 deg C the icecream will not freeze rock hard like water?

        Thanks again!

        • Hi Tiffany,

          Thanks for flagging your quiz issue! It shouldn’t do that and allow you to progress even if you didn’t get everything correct. We’ve updated some settings and it should now work fine.

          For your second question, good question and one that requires a long answer!:
          The freezing point of your ice cream mix will generally not be -18C. For it to be so low, you’d have to add way too much sugar. What happens though is that once you freeze ice cream, some of the water in the mix will freeze and turn into ice. As a results you’re left with ice + sugar solution (aka water + sugar). Since there’s less water in the solution now, the concentration of sugar has increased. As a result, the freezing point will be lower. Again, some water will freeze into ice and you’re left with an even more concentrated sugar solution with an even lower freezing point.
          In reality, this doesn’t go in steps but is a smooth transition. It means that at the end you’ve got ice crystals + sugar solution. The sugar solution makes sure the ice cream is still soft. The ice cream harden the ice cream. Balancing the concentration of sugar will ensure you’ve got your ideal texture at the end and remember that this can be influenced by other ingredients in the ice cream as well (e.g. alcohol or salt).

          Hope that clarifies!

          • Ahh thank you so much for your quick reply. I’ll take a look at the rest of the course. It’s been great!

            That makes sense! I thought that would be a bit crazy too. I just kept seeing -18 deg everywhere. Maybe that’s the temperature alot of icecream ends up being stored at. I’m just trying to think of scoopability, but I’m figuring it’s way more complicated!

            So am I correct in saying then that the goal starting Freezing point depression is usually around -3 deg C when you’re making the sugar solution, and once you put in the freezer, all the above that you mentioned happens, that’s where the super concentrated sugar solution can still remain in ‘liquid state’ at pretty low temps?

          • Hi Tiffany,

            Yes, you’re right!

            With regards to the -18C (which is 0F): most conventional freezers are set at this temperature (industrial ones may go a little lower). Thus most ice creams will be stored at this temperature which is why you might come across this temperature often. At -18C most foods tend to be stable enough to be stored for months, if not years.
            If you’re wondering why -18C and not -16 or -20, I was wondering the same. It seems to have been an arbitrary number though, it might have originated from the US, where manufacturers pleaded for the nice round 0F (link). Colder is better for shelf life, but it also costs more energy, -18C somehow was found to be a good balance and has become pretty much the standard since!

  5. Awesome sharing of Ideas,i learned something for my ice cream process

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