You will be using a balanced equation and mole ratios to solve. what is this process called?

Updated November 05, 2018

By Chris Deziel

In stoichiometry, or the study of relative amounts of substances in reactions, you'll come across two situations that call for the calculation of mole ratio. In one, you're analyzing a mystery substance to determine its empirical formula, and in the other, you're calculating relative amounts of reactants and products in a reaction. In the first case, you usually have to weigh the individual components of a compound and calculate the number of moles of each. In the second case, you can usually find the mole ratio by balancing the equation for the reaction.

The typical procedure to determine the empirical formula of a mystery compound is to analyze it for its component elements. If you obtain the weight of each element in the compound, you can determine the number of moles of each compound by dividing the actual weight in grams by the atomic weight of that element. To do this, you have to look up the atomic weights in the periodic table or, to make things easier on yourself, you can use an online mole calculator that automatically converts between weight in grams and number of moles.

Once you know the number of moles of each component of the compound, you divide each by the one with the lowest number and round to the nearest integer. The numbers are the mole ratios, and they appear as subscripts in the empirical formula.

Example: You analyze a compound and find that it contains 0.675 g of hydrogen (H), 10.8 g of oxygen (O) and 13.5 g of calcium (Ca). What is the empirical formula?

The molar mass of hydrogen is 1 g (rounding to one decimal place), so the number of moles present in the compound is 0.675/1 = 0.675. The molar mass of oxygen is 16 g, and the molar mass of calcium is 40.1 g. Performing the same operation for these elements, you find that the number of moles of each element are:

• H – 0.675
  
• O – 0.675
  
• Ca – 0.337 
  

Calcium is the element with the lowest number of moles, which is 0.337. Divide this number into the others to obtain the mole ratio. In this case, it's H – 2, O – 2 and Ca – 1. In other words, for every calcium atom in the compound, there are two hydrogens and two oxygens.

The numbers derived as the mole ratio of the elements appear in the empirical formula as subscripts. The empirical formula for the compound is CaO2H2, which is usually written Ca (OH)2.

If you know the reactants and products of a reaction, you can write an unbalanced equation for the reaction by putting the reactants on one side and the products on the other. The law of conservation of mass requires that both sides of the equation must have the same number of atoms of each element, and this provides the clue on how to find the mole ratio. Multiply each side of the equation by a factor that balances the equation. The multiplication factors appear as coefficients, and these coefficients tell you the mole ratios of each of the compounds in the reaction.

For example, hydrogen and oxygen combine to form water. The unbalanced equation is H2 + O2 –> H2O. However, this equation isn't balanced because there are more oxygen atoms on one side than the other. The balanced equation is 2H2 + O2 –> 2 H2O. It takes two hydrogen atoms for every oxygen atom to produce this reaction, so the mole ratio between hydrogen and oxygen is 2:1. The reaction produces two water molecules, so the mole ratio between oxygen and water is 1:2, but the mole ratio between water and hydrogen is 2:2.

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.

• 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.

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 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 O2 to 1 mole of H2 is 3:1 or 3 mol O2: 1 mol H2.

For the reaction:
2 H2(g) + O2(g) → 2 H2O(g)

The mole ratio between O2 and H2O is 1:2. For every 1 mole of O2 used, 2 moles of H2O are formed.

The mole ratio between H2 and H2O is 1:1. For every 2 moles of H2 used, 2 moles of H2O are formed. If 4 moles of hydrogen were used, then 4 moles of water would be produced.

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

O3 → O2

By inspection, you can see this equation is not balanced because mass is not conserved. There are more oxygen atoms in ozone (O3) than there are in oxygen gas (O2). You cannot calculate mole ratio for an unbalanced equation. Balancing this equation yields:

2O3 → 3O2

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.

1. 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.)
2. 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.
3. 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.

4. 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.

5. 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.

• Himmelblau, David (1996). 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.