using english to calculate

What do cookies and chemistry have in common? Many things, it turns out! A balanced chemical equation is the recipe for a reaction: it contains a list of all the reactants (the ingredients) and products (the cookies) as well as their relative proportions.

Using a balanced chemical equation to calculate amounts of reactants and products is called stoichiometry. It is a super technical-sounding word that simply means using ratios from the balanced equation. In this article, we will discuss how to use mole ratios to calculate the amount of reactants needed for a reaction.

Balanced reactions and mole ratios

The stoichiometric coefficients are the numbers we use to make sure our equation is balanced. We can make ratios using the stoichiometric coefficients, and the ratios will tell us about the relative proportions of the chemicals in our reaction. You might see this ratio called the mole ratio, the stoichiometric factor, or the stoichiometric ratio. The mole ratio can be used as a conversion factor between different quantities.

Problem solving tip: The first and most important step for all stoichiometry problems is the same no matter what you are solving for—make sure your equation is balanced! If the equation is not balanced, the mole ratios will be wrong, and the answers will not be correct.

For example, the stoichiometric coefficients for the following balanced equation tell us that 1 mole of Fe₂O₃ wiil react with 2 moles of Al to yield 2 moles of Fe and 1 moles of AL₂O₃.

            Fe₂O₃(s) + 2Al (s)               2Fe(l) + Al₂O₃

If we have a known mass of the reactant Fe₂O₃, we can calculate how many moles of Al we need to fully react with the Fe₂O₃ using the ratio of their coefficients:

Mole ratio between Al and Fe₂O₃ = 2mole Al/1mole Fe₂O₃

Example: Using mole ratios to calculate mass of a reactant

For the following unbalanced reaction, how many grams of NaOH will be required to fully react with 3.10 grams of H₂SO₄ ?

NaOH(aq)+H₂SO₄(aq)→H₂O+Na₂SO₄(aq)       Not balanced!

For this reaction, we have 1 Na and 3 H on the reactant side and 2 Na and 2 H on the product side. We can balance our equation by multiplying NaOH by two—so that there are 2 Na on each side—and multiplying H₂O on both sides. That gives the following balanced reaction:

2NaOH(aq)+H2SO4(aq)→2H2O+Na2SO4(aq)    Balanced!

Once we have the balanced equation, we can ask ourselves the following questions:

• For which reactant(s) do we already know the amount of the chemical?
• What are we trying to calculate?

In this example, we know the amount of H₂SO₄ is 3.10 grams, and we would like to calculate the mass of NaOH. Armed with the balanced equation and a clear sense of purpose—hopefully—we can use the following strategy to tackle this stoichiometry problem:

Step 1: Convert known reactant amount to moles.

The known quantity in this problem is the mass of H₂SO₄. We can convert the mass of H₂SO₄ to moles using the molecular weight. Given that the molecular weight of H₂SO₄ is 98.09 g/mol, we can find the moles of H₂SO₄

Step 2: Use mole ratio to find moles of other reactant.

We are interested in calculating the amount of NaOH so we can use the mole ratio between NaOH and H₂SO₄. Based on our balanced chemical equation, we need 2 moles of NaOH for every 1 mole of H₂SO₄, which gives the following ratio:

Mole ratio between NaOH and H₂SO₄=2mol NaOH/1mol H₂SO₄ or 1mol H₂SO₄/2mol NaOH

Each format gives a different answer! However, only one ratio will allow the units of H₂SO₄ to cancel out properly.

Step 3: Convert moles to mass.

We can convert the moles of NaOH from Step 2 to mass in grams using the molecular weight of NaOH:

We will need 2.53 grams of NaOH to fully react with 3.10 grams of H₂SO₄ in this reaction.

Shortcut: We could also combine all three steps into a single calculation, with the caveat that we should pay extra close attention to our units. In order to convert the mass of H₂SO₄ to mass of NaOH, we could solve the following expression:

If we look carefully at the expression, we can break it down into steps 1 to 3 above. The only difference is that instead of doing each conversion separately, we did them all at once.

Summary

The coefficients from the balanced chemical reaction tell us the proportions of the reactants and products. We can use ratios of the coefficients to convert between amounts of reactants and products in our reaction.