# Creating hot ice

We created hot ice from scratch, a solution that remains liquid even below its freezing point!

Ice Lolly, Flickr user adriana serra, licence CC BY-NC-SA 2.0.

This summer we decided to create some hot ice, a substance that is just as exciting as it sounds. Hot ice has a really cool property: it can be easily supersaturated. If you don’t know what it means, don’t worry! Simply keep on reading and everything will be explained to you, but essentially it means that with hot ice you can create a solution that contains more dissolved material than it could have under usual circumstances. As a result of this, once the solution is disturbed (a fancy way of saying that you need to add solid crystals of hot ice, or poke it with your finger!) then the liquid slowly transform into beautiful crystals of hot ice, creating a quite remarkable spectacle.

## Why is it called hot ice?

Once the solution is perturbed, the crystals of hot ice start forming and this process releases a lot of energy in the form of heat. As a result, the substance actually gets quite hot. Therefore, be careful when handling the hot ice, you might get burned (just like we did…)! In industry, this substance (sodium acetate trihydrate) is actually used to keep tortillas warm inside a container or to heat gloves during the winter. You get to control when you want the tortillas hot, so it’s a neat (and crucially, non-toxic) way to keep food and freezing fingers warm.

ice cream cone, Flickr user sussexcareers, licence CC 0 1.0 Universal (CC0 1.0)

## How to create hot ice?

To create it, first, you simply need to mix distilled vinegar with baking soda, let it react and what results from this is sodium acetate (CH$_3$OONa), a colourless, non-toxic water soluble salt with incredible chemical properties. This product will be useful to obtain sodium acetate trihydrate, the so-called hot ice (CH$_3$OONa$\cdot 3$H$_2$O), which is just basically the same substance but now surrounded by three molecules of water.

Make sure that the baking soda is fully dissolved in the vinegar because any nondissolved particles of baking soda might start the crystallisation process prematurely. Then you need to simmer the solution on medium heat until most of the water (from vinegar) has evaporated. When a tiny crust starts forming on the surface of the solution, remove the solution from heat immediately. Finally, you need to cool it down again to room temperature (approximately 20°C). This last step will allow the formation of sodium acetate trihydrate. Now you have everything you need for the formation of hot ice crystals.

Hot ice crystals forming on the container. Image: Chalkdust.

There are three ways to obtain it: the first one, simply add one sodium acetate crystal to the centre of a plate and pour the solution onto the top of the crystal, and you will observe that more crystals begin forming. If you continue pouring, the liquid will form a solid as soon as it touches the dish with the ground crystals. The product is the hot ice, and the impressive thing is that although the solid looks like water ice, it is actually hot.

The second option is to drop a tiny crystal of sodium acetate onto the solution. You will observe that a solid begin to crystallise in a similar way to the phenomenon observed in the formation of snowflakes. A pinch of baking soda should do the trick as well if you don’t have a crystal of sodium acetate at hand.

The third one is just simply by introducing your hand onto the solution: the same will happen, but this time your hand will be surrounded by hot ice (and you could actually feel that it is getting hotter).

Some pictures from our summer experiment creating hot ice 🙂

## The science behind hot ice

#### Estimation of sodium acetate obtained

In a recipient, we added 565 mL of vinegar (that contains 5 $\%$ of acetic acid, CH$_3$COOH) and approximately 48 g of sodium bicarbonate (NaHCO$_3$). The production of sodium acetate is given by the following chemical reaction:

CH$_3$COOH + NaHCO$_3$ $\longrightarrow$ CH$_3$OONa + H$_2$O + CO$_2$

We deduced the following equation to estimate the quantity of sodium acetate (SA) obtained from this chemical reaction:

$$SA = \frac{V \rho_{v} C_{ac} M_{SA}}{M_{ac}}$$,

where $V$ is the quantity in mL of vinegar used (in our case, $V=565$ mL, $\rho_{v}$ stands for the vinegar density (assumed to be $1$ g/mL, $C_{ac}$ is the concentration of acid acetic in the vinegar (this varies depending what kind of vinegar you used, but ours was 5 $\%$),  $M_{SA}=84.007$ g/mol and $M_{ac}=60.05$ g/mol are the molecular weights for the sodium acetate and the acetic acid, respectively. The quantity of sodium acetate that we obtained was $SA=38.79$ g, and this will give us an approximation of how much hot ice we would expect to obtain (notice that the equation shown above considers that the efficiency of the reaction is 100 $\%$ and is just valid for our case, as according to our calculations, there are fewer molecules of acetic acid than sodium bicarbonate).

#### Supersaturation

In order to understand how the hot ice is formed, we need to understand a simple concept, supersaturation. And to understand it, let’s propose the following hypothetical scenario: imagine that you want to prepare a solution of water and table salt. You have a glass that contains 100 mL of water at room temperature (say 20°C) and you start adding first 10 g of salt. With the help of a spoon, you mix both substances and eventually, you would observe that the water dissolves the salt without any inconvenient. You can add another 20 grams of salt and again the water would manage to dissolve it. But now if you want to add another 6 grams of table salt, no matter how hard you try, it is impossible to make the water fully dissolve all the salt present on the glass at room temperature. There is an excess of salt in the solution.

How do we know that this would happen? did we just make up all of this? The answer is no. We just used the concept of solubility of a substance $X$ ($S_X$), which is defined as:

$$S_X = \frac{X}{100 g H_2O}.$$

In this case, $X$ is the quantity, in grams, of salt, and it is reported that the solubility of table salt at room temperature (20°C) has a value of 35.89 g per 100 g of water. That means that 100 mL of water would just manage to dissolve 35.89 g of salt, having a temperature of 20°C. That is it is impossible to fully dissolve 36 g of salt in 100 mL of water.

But then, is there any way of dissolving more than 36 grams of salt in just 100 mL of water? The answer is yes, by increasing the temperature. If the solution is heated, at least 10°C more, the water would fully dissolve the remaining salt. If we want to keep adding salt (as if we have not added enough already!), we will face the same problem than before. The key factor is to keep increasing the temperature. Below you can find the values of solubility of the salt in water, and you can see that to dissolve more salt, higher temperatures are required.

Image: Chalkdust. Data source: Etacude

The situation described above is what we faced on the first step of producing hot ice, the only difference is that instead of table salt, we had another kind of salt (sodium acetate), the product obtained by mixing vinegar and baking soda. At first, it is noticed that the water didn’t dissolve completely the sodium acetate, so we heated the solution up to 75°C, or in other words, we increase the solubility of sodium acetate in water.

Taking again the hypothetical case described above, what would happen that instead of heating up the solution, we do the opposite case (cooling down)? Would this affect in some way? The answer is yes and no. Yes because it would reduce the solubility of the salt: let’s say that initially, you have 36.5 grams of salt dissolved in 100 mL of water at 50°C (from the diagram above, you can see this is true). if you reduce the temperature of the solution to 20°C, you are reducing the holding capacity of the water. This means that although the solubility decreases, you would have an excess of table salt dissolved in water. But how is this possible if we mention that it is impossible to dissolve 36 grams of salt in 100 mL of water at 20°C?. This phenomenon is known as a supersaturated solution and occurs when you cool down a solution. This phenomenon is also present in the formation of clouds and helps to understand why does it rain water (instead of solubility, the term humidity is used).

In our experiment, we had around 38.79 grams of sodium acetate dissolved in approximately 20-25 mL of water at 75°C. Then we cooled it down without disturbing it (we just introduced the recipient with our solution into an ice water bath) until it reached a temperature of 20°C. At that temperature, we had our supersaturated solution of sodium acetate.

#### Crystallisation

As we described above, supersaturated solutions have more dissolved solute (in our case, sodium acetate) than would normally contain under regular conditions. It is usually said that the state of our solution is in a meta-stable state. This means that our solution would stay in its current condition as long as nothing perturb it. However, the slightest perturbation would cause the solution to restore itself to the most stable case. But what case would this be? if the supersaturated solutions contained an excess of solute, the only way it can become more stable is by precipitating this excess of salt out of the solution. This phenomenon is known as crystallisation.

By either introducing our hand into the solution, adding a crystal or pouring the liquid onto a dish, we trigger the process of crystallisation, ie, the precipitation of tiny solids/crystals that come out of the solution. But something really interesting is happening here: it turns out to be that these solids are not sodium acetate, they actually are crystals of sodium acetate trihydrate, which is our hot ice. But how it is possible? The sodium acetate (CH$_3$OONa) has the amazing property of absorbing water into its crystal lattice, giving as result, sodium acetate trihydrate (CH$_3$OONa$\cdot 3$H$_2$O). The plot below helps us clarify this:

Image: Chalkdust. Data source: ChemPieceOfScience

We initially had a solution of sodium acetate anhydrious (this means, with no water molecules in its structure) at 75°C. We then cooled it down, but notice that at around 60°C, the formation of sodium acetate trihydrate is possible, as the curves of solubility of both substances had a matching point.

#### Why does the hot ice get hot? (Exothermic process)

When a solid dissolves in water, the process always has an energy change associated with it. When we heated our solution, we provided energy in form of heat to our solution. The system absorbed this energy and caused a breaking of the molecules of the sodium acetate into ions [Na]$_{ac}^{+}$ and  [CH$_3$OO]$_{ac}^{-}$ that interact with water. This process is known as an endothermic process.

The reverse process is known as an exothermic process, in which instead of absorbing energy, it releases heat to its environment. When we triggered our supersaturated solution, solid came out of the solution, causing an increase in temperature, explaining why the sodium acetate crystals are warm even though the supersaturated solution was initially cold. The transformation of ions dissolved in water (ac) into crystals (s) is described by the following reaction:

[Na]$_{(ac)}^{+}$ + [CH$_3$OO]$_{(ac)}^{-}$ + $3$H$_2$O $\longrightarrow$ CH$_3$OONa$\cdot 3$H$_2$O $\, (s)$

It can be proved mathematically and experimentally, that the formation of hot ice (precipitation of crystals) releases $0.1445$ kJ/g, (J stands for the unit of energy Joule). This information can also be used to calculate how much energy is required to dissolve sodium acetate trihydrate in water.

In our experiment, we obtained $44$ g of hot ice, and we calculated approximately the heat $H_{SAT}$ released by it:

$$H_{SAT} = (44 \, g) (0.1445 \, kJ/g ) = 6.358 kJ$$

Image: Chalkdust

## Try the experiment yourself

You can try to form hot ice by doing what we described above. All the substances used are non-toxic. If you want to avoid using vinegar, you can buy the sodium acetate trihydrate in any store.

If you wish to calculate an approximate of the maximum quantity in grams of either sodium acetate anhydrious (SA) or sodium acetate trhihydrate (SAT) that can be dissolved in a determined quantity of water $V$ as a function of the temperature, you can use the following equations we obtained from the data of the plot:

$$SA = V (0.0053 T^2 -3.0385 T + 557.72)$$

$$SAT = V (0.0102 T^2 -5.2693 T + 710.14),$$

where the units of $V$ are in mL and $T$ is in Kelvin degrees ($T(K)=T(°C) +273.15$).

Antigoni is a PhD student at UCL working on Boundary Element Methods for electromagnetic scattering.

Atheeta is a PhD student at UCL in the area of mathematical ecology. He also has interests in evolutionary game theory and social dynamics.

Belgin is a data scientist having got her PhD in population genetics. When not working, you can usually find Belgin either playing the piano or playing Math Blaster. She is pictured here standing next to her copy of Zeeman’s catastrophe machine.

Hugo is a chemical engineer doing a PhD in Mathematics at University College London. He is currently working on non-Newtonian fluid dynamics. He is also interested in transport phenomena and rheology (the science of deformation).

Niki is a PhD student at UCL, working in analytic number theory.

Rafael Prieto Curiel is doing a PhD in mathematics and crime. He is interested in mathematical modelling of any social issues, such as road accidents, migration, crime, fear and gossip.

Rudolf Kohulák is a PhD student at UCL working on the modelling of freeze-drying processes.

Sean is a PhD student researching geophysical fluid dynamics at UCL. He studies coastal outflows, but so far has been unable to persuade the department to send him on a research trip to the beach.

I’m a 3rd year undergraduate maths student at UCL.

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