Limiting Reactants - the Idea

When we burn a log in a fireplace, we know that the amount of heat and ash produced depends on the size of the log we are burning. We never think about the fact that it also depends on the amount of oxygen available in the house. Obviously, that’s because there is so much more oxygen in the house than needed for the log to burn.

The issue is much more obvious when we think about baking. The number of chocolate cookies you can bake depends on the amount of flour you have, but also on the amount of sugar, eggs, butter and the number of bags of chocolate chips you own. Having a 30 pound sack of flour isn’t helpful if you only have a teaspoon of sugar.

The same idea comes into play in chemistry. When you drop a piece of magnesium into a solution of phosphoric acid the amount of hydrogen gas produced depends on the amount of magnesium, but also on the volume and molarity of the acid. Chemists call this idea Limiting Reactants (or Limiting Reagents).

How Chemists think about limiting reactants

If we need to know the amount of product we can expect, we need to look at all of the reactants. For each reactant, we need to determine the amount of product that can be produced. Then, the smallest of those potential answers is the correct one.

If that’s not obvious (and I wouldn’t expect it to be), let’s look at an example. Here is the traditional Toll House Cookie recipe from Nestle.

Let’s assume for the moment that I have plenty of butter, salt, brown sugar, vanilla, chocolate chips, and baking soda, but I have only 8 cups of flour, 4 cups of granulated sugar and 8 eggs. How many batches of cookies can I make?

We can do some simple math. We'll start looking at the granulated sugar and the eggs.

We have enough granulated sugar to make more than 5 batches of cookies, but only enough eggs to make 4 batches. That means if we tried to make a fifth batch, we would not have any eggs to use. Eggs LIMIT our ability to make more cookies.

If we do the same math with the flour 

we discover that the flour limits us even more. So if we tried to use all of our eggs by making 4 batches of cookies, we would not have enough flour for that 4th batch.  In “chemistry speech” we would say that the flour is the limiting reactant.

Important things to notice

We should notice that the amount of product (in this case batches of cookies) is the smallest answer to our separate calculations. We have enough sugar to make more than 5 batches, but we will have to stop after 3 batches (actually 3.56 batches if that’s possible) because we will have run out of flour at that point.

It is also important to realize that the limiting reactant here is actually the ingredient I had the MOST of. I had far more flour than granulated sugar, but because they are not used in the same amounts (based on the recipe) we can’t compare the original amounts. You cannot expect the limiting reactant to be the one of which you have the least or the most. You must look at the amount of product that each can make and compare those values.