The mole ratio describes the fixed proportions between reactants and products in a chemical reaction. It is important in stoichiometry, particularly when used as a conversion factor in mole to gram conversions. Here is the mole ratio definition, with examples showing how to find the ratio and use it.

### Mole Ratio Definition

The mole ratio is the ratio between any two substances in a chemical reaction. It is the ratio between two coefficients in a balanced chemical equation. The mole ratio is also known as the molar ratio or mole-to-mole ratio.

### Finding the Mole Ratio in a Balanced Equation

Find the mole ratio between any two components of a chemical reaction using the coefficients of the chemical formulas. The coefficients are the numbers in front of the formula.

For example, in the equation for the reaction between hydrogen and oxygen to make water:

2 H_{2}(g) + O_{2}(g) → 2 H_{2}O(g)

The coefficient for hydrogen is 2. For oxygen, there isn’t a coefficient, which stands for 1. The coefficient for water is 2.

The mole ratio between hydrogen and oxygen is 2:1. The mole ratio between oxygen and water is 1:2. The mole ratio between hydrogen and water is 2:2, but you can reduce this to 1:1.

### Finding the Mole Ratio in an Unbalanced Equation

To write a mole ratio, you need a balanced equation. If you are given an unbalanced equation, balancing it is your first step.

For example, consider the reaction that converts ozone into oxygen:

O_{3} → O_{2}

This chemical equation is unbalanced. How do you know? A balanced equation has the same number and type of atoms on both sides of the reaction arrow. In the given equation, there are 3 oxygen atoms on the left side of the arrow and two oxygen atoms on the right side of the arrow. Balance the equation by adding coefficients in front of the reactants and products until the number of atoms is the same on both sides.

The balanced equation is:

2O_{3} → 3O_{2}

Now, get the mole ratio using the coefficients. The ratio is 2 ozone molecules to 3 oxygen molecules or 2:3.

### Example Problem Using the Mole Ratio

A ratio is just a way of showing a relationship between two things. In chemistry, its importance is that you can use the ratio to solve stoichiometry problems.

For example, let’s say you’re asked to find out how many moles of oxygen you get by reacting 4 moles of ozone. One way to solve this is to set up the ratio like equivalent fractions:

4 moles ozone / x moles oxygen = 2 moles ozone / 3 moles oxygen

Solving for “x”:

x moles oxygen = (4 moles ozone)*(3 moles oxygen)/2 moles ozone

x moles oxygen = 6

Note the “units” for moles of ozone cancels out, leaving moles of oxygen. Double-check your work! The most common mistake students make in this calculation is setting the fractions up so that the units don’t cancel out.

Usually, you’ll get a value in grams and be asked for an answer in grams. The mole ratio does not work with mass units, like grams. So, you get to do algebra and the gram-to-mole and mole-to-gram conversion. Combining all these skills takes practice.

For example, find how many grams of oxygen you get from reacting 0.2 grams of ozone.

- First, get a balanced equation for the reaction that makes oxygen from ozone. From this, write the mole ratio.
- Next, find the number of moles in 0.2 g of ozone. To do the mole to gram conversion, look up the atomic mass of oxygen on the periodic table. There are 16.00 grams of oxygen per mole of oxygen.
- Solve the conversion problem:

x moles = 0.2 grams * (1 mole/16.00 grams) = 0.0125 moles - Use the mole ratio to find how many moles of oxygen form from 0.125 moles of ozone.

moles of oxygen = 0.125 moles ozone * (3 moles oxygen/2 moles ozone)

moles of oxygen = 0.01875 moles oxygen gas - Now, convert the moles of oxygen gas into grams of oxygen gas to get the final answer:

grams of oxygen gas = 0.01875 moles * 16.00 grams/mole

grams of oxygen gas = 0.3 grams

In this case, you actually could have saved yourself some math because only one type of atom (oxygen) occurred on both sides of the chemical equation. But, it’s good practice to follow all the steps. Also, remember to report your answer using the correct number of significant figures.

Finally, recognize you could be given any reactant or product and can use the same technique to find the amount of any other reactant or product. Sometimes you’ll have two quantities and use the mole ratio to find the limiting reactant.

### Mole Ratio as a Unit of Concentration

In stoichiometry, the mole ratio is the ratio between moles of species in a balanced chemical equation, but the mole ratio is also a unit of concentration in some disciplines. For example, in atmospheric chemistry, the mole ratio is the value obtained by dividing the moles of the constituent of interest by the total number of moles of a substance:

r_{i} = n_{i} / n_{tot}

Here, r_{i} is the mole ratio of *i*, n_{i} is the number of moles of *i*, and n_{tot} is the total number of moles. To avoid confusion, the concentration unit may be known as the mole fraction rather than the mole ratio.

### Reference

- IUPAC (1997)
*Compendium of Chemical Terminology*(the “Gold Book”). (2nd ed.). Blackwell Scientific Publications. ISBN 0-9678550-9-8.