Counting by weighing

Jenny is measuring sweets for herself and for Michael. Michael prefers the grey sweets. Jenny likes the yellow ones. Now, they both have the same amount in weight, but Michael isn’t happy about that. Jenny has more in number.

How can that happen? Well, each grey sweet weighs more than a yellow one. Therefore, you don’t as many grey ones to reach the same number of grams. However, Michael thinks they should both get the same number of sweets instead. You could count out one sweet at a time, but Michael has another idea.

He starts by weighing one of each colour. One grey sweet weighs 4 grams while a yellow sweet weighs 3 grams. Jenny’s pile of yellow sweets weighs 300 grams. What should be the total weight of Michael’s grey sweets for them to be equal in number? You can think of it like this.

The mass of one grey sweet is four-thirds of the mass of a yellow one. Then, the pile of grey sweets should weigh four-thirds as much as the pile of yellow sweets. The ratio between the mass of the piles needs to be the same as the ratio between the mass of the individual sweets. That way, there will be the same number in both piles. We don’t have to count the sweets to compare their number.

We can do that by weighing them. 400 grams of the grey sweets is the same number as 300 grams of the yellow ones. There are some things that are impossible to count one by one, like atoms. Here are two elements: Iron and Sulphur. How much of each should you weigh out if you want to have the same number of both types of atom.

Just like with the sweets, you need to know how much one atom weighs. The mass of an atom is usually measured in the atomic mass unit ‘u’. Iron atoms weigh about 56 atomic mass units or 56 u. The atomic mass of sulphur is about 32 u. If we have the same number of grams of both substances, we’ll have fewer iron atoms since they are heavier.

If we want the same number of the iron atoms as sulphur atoms, we need more grams of iron on the scales. How much iron do we need? Remember how we solved it with the sweets. Each iron atom weighs 56 over 32 times more than a sulphur atom. This means that we need 56 over 32 times more iron than sulphur on the scales.

If we have 10 grams of sulphur, we are going to need 17.5 grams of iron to get the same number of atoms. In chemical reactions, it’s the number of atoms we are concerned with. We don’t have to count each atom because we can compare their numbers by weighing them. When the masses of the substances have the same ratio as the atomic masses, they both contain the same number of atoms. But when you’re measuring out sweets, maybe it is more fair if you both get the same weight.