Limiting And Excess Reactants In Chemistry

But first, pancakes.

I bet at some point when you were first being taught about moles, to help you get your head around the idea, your teacher said “the mole is just a number of things, the same way a dozen is twelve of something”.

Everyday analogies can help understand some of the weird, abstract ideas you meet in chemistry. Here’s a situation that you might encounter in the kitchen.

Suppose it’s pancake day and you’re having friends over, so you look up the following recipe on the internet:

5 pancakes aren’t really a lot though you think – what is everyone else going to eat?!

You need to make more than 5, so you check what ingredients you have in the cupboard, and find you have:

The question is, how many pancakes can you make with this lot?

If 3 eggs make 5 pancakes, then with 12 eggs we can make 12/3 x 5 = 20 pancakes. So, we can make four batches, right?

Well that’s true in theory, but there’s a caveat: we can only make four times as many if we have enough of the other ingredients.

How do we check if that’s the case? Easy, just scale up the quantities for the other ingredients by the same factor to see how much of each we’d need, then compare with what we have. Here, the factor we’re scaling up by is 4.

First let’s check if we have enough milk. We needed 250 mL for the recipe with 3 eggs, so if we’re going to use all 12 eggs, we’ll need 12/3 x 250 mL = 1,000 mL of milk. That’s one litre of milk, which is what we have.

Now the flour. The recipe needs 125 g to make one batch, but we’re scaling everything up by a factor of 4. We therefore would need 4 x 125 g = 500 g but uh-oh, we only have 375 g!

There isn’t enough flour to use up all our eggs and milk, so we can’t make 20 pancakes after all.

To work out how many pancakes we could make, we take the total amount of flour we have and divide it by the amount needed to make one batch. 375 / 125 = 3, which tells us we can only make 3 batches, or 15 pancakes. Sad day 🙁

So, what does this tell us?

To make these 15 pancakes, we scaled up the original recipe by a factor of 3 and used 3 x 3 = 9 eggs (leaving 3 leftover) and 3 x 250 = 750 mL of milk (leaving 250 mL leftover).

You could describe the flour in this scenario as the limiting ingredient and the eggs and milk as the excess ingredients.

Some important things to note here:

1. The limiting ingredient limits the total amount of pancakes we can make
2. The limiting ingredient is the one used to calculate how many pancakes we can make
3. The limiting ingredient is also the one used to calculate how many ingredients we’ll have leftover

Why is limiting reactants a thing in chemistry?

Recipes require specific quantities and ratios, but we buy ingredients in all sorts of package sizes. It’s no surprise to find that for some recipes, we’ll have too few of some ingredients and too many of others.

A chemical equation is also really a recipe where the quantities are in moles. It says X moles of this react with Y moles of that to give Z moles of this. We follow the recipe, calculate masses and volumes required, and mix the reactants together.

Why would we need to worry about one reactant limiting the amount of product? Is this just a concept dreamed up to torture chemistry students?

Actually, no. There are several reasons why we’d deliberately not mix reactants in the proportions suggested by the chemical equation. These include:

• To ensure the reaction goes to completion (meaning that the reaction has finished because the reactants are used up). Let’s say we wanted to work out how much calcium carbonate is present in eggshell. We can react the eggshell with excess acid, then titrate the acid remaining with an alkali to work out how much acid was used. Using an excess of acid guarantees all the calcium carbonate in the eggshell reacts. If we don’t ensure this, our analysis will be inaccurate
• The reaction may reach equilibrium and we want to use excess reactants to maximise the amount of product formed
• One of the reactants may be impure, so we use extra to compensate for impurities and ensure we have enough to fully react
• One of the reactants may be unstable, so we use an additional amount of it to compensate for any that might decompose during the reaction

The Golden Rule

If you find limiting reactant calculations confusing and your head is just a fog of numbers when working through them, remember the golden rule:

“The limiting reactant is the one used to calculate how much product and leftover reactants will be present at the end of the reaction”

Once you’ve found the limiting reactant, just focus on it because in 99% of questions you’ll use it as the basis for calculating everything you need to know.

The Methods

There is no ‘official’ way of doing limiting reactant calculations, so think of these methods as training methods to help you structure the calculations until you get used to them. At that point you’ll be able to take shortcuts to arrive at the solutions must faster.

The method I usually teach first is a step-by-step approach where you use the chemical equation to generate ‘rules’ that state how much of each reactant is theoretically needed based on actual amounts. This method is lengthy but methodical, so it’s helpful if you’re just getting used to the concept of limiting reactants.

The second method will be familiar to students who have studied chemical equilibria and carried out calculations using ICE tables. This method is useful because numbers are organised into a table. This method also makes it easy to quickly calculate the amounts of all substances at the end of the reaction.

Finally, there is a variation of the ICE table method that is applicable for gaseous reactions. This can be useful in multiple choice questions on limiting reactants where you need to find the answer quickly without too much calculation.