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Reaction Calculations: Mass and Moles

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 can be used to calculate the mass of reactants and products.

Mole Ratio

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

For the reaction aA + bB → cC + dD

mol ratio for A : B : C : D

is a : b : c : d

Examples of Mole Ratios

in the reaction	2Mg_(s)	+	O_2(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.

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.

Reactions and Moles

For the balanced chemical reaction:
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 x 10 = 5 moles of oxygen gas to produce 2 ÷ 2 x 10 = 10 moles of magnesium oxide.

For n moles of magnesium :

1 ÷ 2 x n = ½n moles of oxygen gas are required
2 ÷ 2 x n = n moles of magnesium oxide are produced

Mg
2 : O₂
1 : MgO
2

example 1 0.50 mol 0.25 mol 0.50 mol

example 2 1.00 mol 0.50 mol 1.00 mol

example 3 1.50 mol 0.75 mol 1.50 mol

example 4 2.00 mol 1.00 mol 2.00 mol

Reactions and Masses

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

For the balanced chemical equation:

2Mg_(s) + O_2(g) → 2MgO_(s)

Given a mass of m grams of magnesium:

mass O₂ = moles(O₂) x molar mass(O₂)
Calculate moles Mg = mass(Mg) ÷ molar mass(Mg) = m ÷ 24.31
Use the balanced chemical equation to determine the mole ratio O₂:Mg 1:2
Use the mole ratio to calculate moles O₂ = 1 ÷ 2 x moles(Mg)
Calculate moles of O₂ = ½ x m ÷ 24.31
mass O₂ = moles(O₂) x molar mass(O₂)
= ½ x m ÷ 24.31 x (2 x 16.00)
= ½ x m ÷ 24.31 x 32.00
mass MgO = moles(MgO) x molar mass(MgO)
Calculate moles Mg = mass(Mg) ÷ molar mass(Mg) = m ÷ 24.31
Use the balanced equation to determine the mole ratio MgO:Mg 2:2 = 1:1
Use the mole ratio to calculate moles MgO = 1 x moles(Mg)
Calculate moles of MgO = 1 x m ÷ 24.31
mass MgO = moles(MgO) x molar mass(MgO)
= 1x m ÷ 24.31 x (24.31 + 16.00)
= 1 x m ÷ 24.31 x 40.31

Example

12.2g of magnesium reacts completely with oxygen gas.
Calculate the mass of oxygen consumed during the reaction and the mass of magnesium oxide produced.

Wite the balanced chemical equation: 2Mg_(s) + O_2(g) → 2MgO_(s)
Determine the mole ratio from the equation, Mg : O₂ : MgO is 2:1:2
Use the mole ratios to calculate the mass of each reactant and product as shown below:

mass O₂ = moles(O₂) x molar mass(O₂)
Calculate moles Mg = mass(Mg) ÷ molar mass(Mg) = 12.2 ÷ 24.31 = 0.50mol
Use the balanced chemical equation to determine the mole ratio O₂:Mg 1:2
Use the mole ratio to calculate moles O₂ = 1 ÷ 2 x moles(Mg)
Calculate moles of O₂ = ½ x mol(Mg) = ½ x 0.50 = 0.25mol
mass O₂ = moles(O₂) x molar mass(O₂)
= 0.25 x (2 x 16.00)
= 0.25 x 32.00 = 8.03g
mass MgO = moles(MgO) x molar mass(MgO)
Calculate moles Mg = mass(Mg) ÷ molar mass(Mg) = 12.2 ÷ 24.31 = 0.50mol
Use the balanced equation to determine the mole ratio MgO:Mg 2:2 = 1:1
Use the mole ratio to calculate moles MgO = 1 x moles(Mg)
Calculate moles of MgO = 1 x mol(Mg) = 0.50mol
mass MgO = moles(MgO) x molar mass(MgO)
= 1x 0.50 x (24.31 + 16.00)
= 1 x 0.50 x 40.31 = 20.16g

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