In a chemical reaction, compounds react in a set ratio. If the ratio is unbalanced, there will be leftover reactant. To understand this, you need to be familiar with the molar ratio or mole ratio.

### Mole Ratio

- The mole ratio compares the number of moles in a balanced equation.
- This is the comparison between the coefficients in front of the chemical formulas.
- If a formula lacks a coefficient, it is the same as saying there is 1 mole of that species.
- Mole ratios are used to predict how much product a reaction forms or to determine how much reactant is needed to make a set amount of product.

## Mole Ratio Definition

A mole ratio is the ratio between the amounts in moles of any two compounds involved in a chemical reaction. Mole ratios are used as conversion factors between products and reactants in many chemistry problems. The mole ratio may be determined by examining the coefficients in front of formulas in a balanced chemical equation.

Also known as: The mole ratio is also called the **mole-to-mole ratio**.

## Mole Ratio Units

Mole ratio units are either mole:mole or else it is a dimensionless number because the units cancel out. For example, it's fine to say a ratio of 3 moles of O_{2} to 1 mole of H_{2} is 3:1 or 3 mol O_{2}: 1 mol H_{2}.

### Mole Ratio Example: Balanced Equation

For the reaction:

2 H_{2}(g) + O_{2}(g) → 2 H_{2}O(g)

The mole ratio between O_{2} and H_{2}O is 1:2. For every 1 mole of O_{2} used, 2 moles of H_{2}O are formed.

The mole ratio between H_{2} and H_{2}O is 1:1. For every 2 moles of H_{2} used, 2 moles of H_{2}O are formed. If 4 moles of hydrogen were used, then 4 moles of water would be produced.

## Unbalanced Equation Example

For another example, let's start with an unbalanced equation:

O_{3} → O_{2}

By inspection, you can see this equation is not balanced because mass is not conserved. There are more oxygen atoms in ozone (O_{3}) than there are in oxygen gas (O_{2}). **You cannot calculate mole ratio for an unbalanced equation.** Balancing this equation yields:

2O_{3} → 3O_{2}

Now you can use the coefficients in front of ozone and oxygen to find the mole ratio. The ratio is 2 ozone to 3 oxygen, or 2:3. How do you use this? Let's say you are asked to find how many grams of oxygen are produced when you react 0.2 grams of ozone.

- The first step is to find how many moles of ozone are in 0.2 grams. (Remember, it's a molar ratio, so in most equations, the ratio is not the same for grams.)
- To convert grams to moles, look up the atomic weight of oxygen on the periodic table. There are 16.00 grams of oxygen per mole.
- To find how many moles there are in 0.2 grams, solve for:

x moles = 0.2 grams * (1 mole/16.00 grams).

You get 0.0125 moles. - Use the mole ratio to find how many moles of oxygen are produced by 0.0125 moles of ozone:

moles of oxygen = 0.0125 moles ozone * (3 moles oxygen/2 moles ozone).

Solving for this, you get 0.01875 moles of oxygen gas. - Finally, convert the number of moles of oxygen gas into grams for the answer:

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

grams of oxygen gas = 0.3 grams

It should be fairly obvious that you could have plugged in the mole fraction right away in this particular example because only one type of atom was present on both sides of the equation. However, it's good to know the procedure for when you come across more complicated problems to solve.

## Sources

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*Basic Principles and Calculations in Chemical Engineering*(6th ed.). ISBN 978-0-13-305798-0. - International Bureau of Weights and Measures (2006).
*The International System of Units (SI)*(8th ed.). ISBN 92-822-2213-6. - Rickard, James N.; Spencer, George M.; Bodner, Lyman H. (2010).
*Chemistry: Structure and Dynamics*(5th ed.). Hoboken, N.J.: Wiley. ISBN 978-0-470-58711-9. - Whiteman, D.N. (2015).
*Encyclopedia of Atmospheric Sciences*(2nd ed.). Elsevier Ltd. ISBN 978-0-12-382225-3. - Zumdahl, Steven S. (2008).
*Chemistry*(8th ed.). Cengage Learning. ISBN 0-547-12532-1.