Calculating Moles and Mass in Chemical Reactions Using Mole Ratios (stoichoimetric ratios) Chemistry Tutorial

Key Concepts

• A balanced chemical equation can tell us:

  ⚛ The ratio of the number of molecules of each type reacting and produced.

  ⚛ The ratio of the moles of each reactant and product.

• The ratio of moles of each reactant and product in a reaction is known as the mole ratio (or stoichiometric ratio)
• The mole ratio (stoichiometric ratio) can be used to calculate the mass of reactants and products in a chemical reaction.

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Mole Ratio (stoichiometric ratio)

The mole ratio is the stoichiometric ratio of reactants and products and is the ratio of the stoichiometric coefficients for reactants and products found in the balanced chemical equation.

Examples of Mole Ratios (stoichiometric ratios)

1. in the reaction	2Mg(s)	+	O2(g)	→	2MgO(s)
   the mole ratio of	Mg	:	O2	:	MgO
   is	2	:	1	:	2

   That is, the complete reaction requires twice as many moles of magnesium as there are moles of oxygen.

   n moles of oxygen gas will react with (2 × n) moles of magnesium to produce (2 × n) moles of magnesium oxide.

2. in the reaction	2Al(OH)3	+	3H2SO4	→	Al2(SO4)3	+	6H2O
   the mole ratio of	Al(OH)3	:	H2SO4	:	Al2(SO4)3	:	H2O
   is	2	:	3	:	1	:	6

   For each mole of Al₂(SO₄)₃ produced, twice as many moles of Al(OH)₃ are required to react with three times as many moles of H₂SO₄.

   n moles of Al₂(SO₄)₃ are produced when (2 × n) moles of Al(OH)₃ react with (3 × n) moles of H₂SO₄. (6 × n) moles of H₂O will also be produced.

Chemical Reactions and Moles of Reactants and Products

For the balanced chemical reaction shown below:

2Mg_(s) + O_2(g) → 2MgO_(s)

the mole ratio of Mg : O₂ : MgO is 2:1:2

That is, it requires 2 moles of magnesium and 1 mole of oxygen to produce 2 moles of magnesium oxide.

If only 1 mole of magnesium was present, it would require 1 ÷ 2 = ½ mole of oxygen gas to produce 2 ÷ 2 = 1 mole magnesium oxide.

If 10 moles of magnesium were present, it would require (1 ÷ 2) × 10 = 5 moles of oxygen gas to produce (2 ÷ 2) × 10 = 10 moles of magnesium oxide.

For n moles of magnesium :

• (1 ÷ 2) × n = ½n moles of oxygen gas are required
• (2 ÷ 2) × n = n moles of magnesium oxide are produced

The table below shows the moles of MgO produced when various amounts of Mg in moles react with the stoichiometric ratio of O₂:

Chemical Reactions and Masses of Reactants and Products

It is possible to calculate the mass of each reactant and product using the mole ratio (stoichiometric ratio) from the balanced chemical equation and the mathematical equation moles = mass ÷ molar mass

For the balanced chemical equation shown below:

2Mg_(s) + O_2(g) → 2MgO_(s)

Given a mass of m grams of magnesium:

• mass O₂ = moles(O₂) × molar mass(O₂)

  (a) Calculate moles Mg = mass(Mg) ÷ molar mass(Mg)

  moles(Mg) = m ÷ 24.31

  (b) Use the balanced chemical equation to determine the mole ratio O₂:Mg

  moles(O₂) : moles(Mg)   is   1 : 2

  (c) Use the mole ratio to calculate moles O₂

  moles(O₂) = (1 ÷ 2) × moles(Mg)

  substitute value for moles(Mg)

  moles(O₂) = ½ × (m ÷ 24.31)

  (d) Calculate mass of O₂

  mass(O₂) = moles(O₂) × molar mass(O₂)

  = [½ × (m ÷ 24.31)] × [2 × 16.00]

  = [½ × (m ÷ 24.31)] × [32.00]

• mass MgO = moles(MgO) × molar mass(MgO)

  (a) Calculate moles Mg = mass(Mg) ÷ molar mass(Mg)

  moles(Mg) = m ÷ 24.31

  (b) Use the balanced equation to determine the mole ratio MgO:Mg

  moles(MgO) : moles(Mg)   is   2:2   which is the same as   1:1

  (c) Use the mole ratio to calculate moles MgO

  moles(MgO) = 1 × moles(Mg)

  substitute in the value for moles(Mg)

  moles(MgO) = 1 × (m ÷ 24.31)

  (d) Calculate mass MgO

  mass(MgO) = moles(MgO) × molar mass(MgO)

  = [1 × (m ÷ 24.31)] × [24.31 + 16.00]

  = [1 × m ÷ 24.31] × 40.31

Worked Example of Using Mole Ratio to Calculate Mass of Reactant or Product

The Question: 12.2 g of magnesium metal (Mg_(s)) reacts completely with oxygen gas (O_2(g)) to produce magnesium oxide (MgO_(s)).

Calculate the mass of oxygen consumed during the reaction and the mass of magnesium oxide produced.

How to Answer the Question:

(1) Write the balanced chemical equation for the chemical reaction:

2Mg_(s) + O_2(g) → 2MgO_(s)

(2) Determine the mole ratio (stoichiometric ratio) from the equation, Mg : O₂ : MgO

moles(Mg) : moles(O₂) : moles(MgO)   is   2:1:2

(3) Use the mole ratios to calculate the mass of O₂ consumed and MgO produced as shown below:

• mass O₂ = moles(O₂) × molar mass(O₂)

  (a) Calculate moles(Mg) = mass(Mg) ÷ molar mass(Mg)

  moles(Mg) = 12.2 ÷ 24.31 = 0.50 mol

  (b) Use the balanced chemical equation to determine the mole ratio O₂:Mg

  moles(O₂) : moles(Mg)   is   1:2

  (c) Use the mole ratio to calculate moles O₂

  moles(O₂) = (1 ÷ 2) × moles(Mg)

  substitute in the value for moles of Mg

  moles(O₂) = ½ × 0.50 = 0.25 mol

  (d) Calculate mass O₂

  mass(O₂) = moles(O₂) × molar mass(O₂)

  mass(O₂) = 0.25 × (2 × 16.00) = 0.25 × 32.00

  mass(O₂) = 8.03 g

• mass MgO = moles(MgO) × molar mass(MgO)

  (a) Calculate moles Mg

  moles(Mg) = mass(Mg) ÷ molar mass(Mg)

  moles(Mg) = 12.2 ÷ 24.31 = 0.50 mol

  (b) Use the balanced equation to determine the mole ratio MgO:Mg

  moles(MgO) : moles(Mg)   is   2:2   which is the same as   1:1

  (c) Use the mole ratio to calculate moles MgO

  moles(MgO) = 1 × moles(Mg)

  substitute in the value for moles of Mg

  moles(MgO) = 1 × 0.50 = 0.50 mol

  (d) Calculate mass MgO

  mass(MgO) = moles(MgO) × molar mass(MgO)

  mass(MgO) = (1 × 0.50) × (24.31 + 16.00) = (1 × 0.50) × 40.31

  mass(MgO) = 20.16 g