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Infinitely scaling sherbet recipe

By David Shaw, 6 March 2020

Sherbet is great fun! It’s sweet and tangy and has a fantastic fizz.

Here’s a fizzy treat for your mouth! But this sherbet recipe has a mathematical trick. You can use it to make as much or as little as you like. Keeping the ingredients in proportion in this way is known as scaling.

Safety: Use clean hands and clean equipment when preparing food.

You will need

• Icing sugar
• Citric acid
• Bicarb soda
• Jelly crystals (optional)
• Measuring equipment
• Large bowl
• Mixing spoon

What to do

1. This recipe will make 12 units of sherbet, but you need to choose what those units are. So, before you start, think about how much sherbet you need. Then try to estimate it – is it 12 teaspoons? 12 tablespoons? 12 litres?

   Hint: When calculating the amount of sherbet you’d like to make, consider the number of people you want to feed, or the number of days you’d like the sherbet to last. Sherbet is best enjoyed in small amounts. We suggest one tablespoon per person per day. If you eat too much, you might feel a bit yuck!

2. If you want to be precise, you can start with the final volume you want, and then divide by 12 to find the volume of your units. For example, if you want 60 mL of sherbet, calculate 60 ÷ 12 = 5 mL. In this case, one unit is 5 mL.
3. In a large bowl, measure one unit of citric acid and one unit of bicarb soda.
4. Add five units of icing sugar.
5. Add five units of jelly crystals. (Or, you can use more icing sugar.)
6. Mix thoroughly.
7. To test your sherbet, pour half a teaspoon onto your hand and eat it from there. That way you won’t accidentally put a wet teaspoon from your mouth back into the sherbet!

What’s happening?

Chemistry chitchat

Sherbet is great fun! It’s sweet and tangy and has a fantastic fizz. And all that comes from chemistry.
The two most important ingredients in this sherbet recipe are bicarb soda and citric acid. They are pretty stable as solid powders, but dissolve them in water – or in your saliva – and they react! This reaction produces carbon dioxide gas and gives sherbet its fizz.

The reaction can be represented as a chemical equation:
citric acid + bicarb soda → carbon dioxide + water + sodium citrate

Citric acid and bicarb soda also have quite strong tastes. Citric acid is very sour, and bicarb tastes salty. That’s where the other ingredients come in. Sugar and jelly crystals are both very sweet, and there’s lots in this recipe. So your sherbet tastes sweet, with a bit of sourness and saltiness to round out the flavour.

Mathematical musings

Recipes like this one, that don’t tell you what measurements to use, might seem strange. But they’re quite common when you’re working. If you worked in a lolly factory, you might need different amounts of sherbet on different days. This recipe gives you a way to make the right amount for each day.

Bakers also use recipes without units, but they write them down differently. A bread dough recipe can be based on flour, adding 70% water, 2% salt and 1% yeast. To use this recipe, weigh the flour you want to use and then multiply that weight by each percentage. If you used 1000 g of flour, you would need 700 g of water, 20 g of salt and 10 g of yeast.

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