Equations & Calculations
Balancing equations, conservation of mass, Mr, moles, and calculating masses
Conservation of Mass
This is because during a chemical reaction, the atoms are simply rearranged into new substances. The same atoms are present before and after the reaction – just in different combinations.
Explaining Mass Changes in Experiments
Sometimes in experiments, the measured mass appears to change. This doesn't mean mass has been created or destroyed – it means a gas has escaped or been absorbed.
Mass Appears to Decrease
When a metal reacts with acid in an open container:
- Hydrogen gas is produced and escapes into the air
- The mass of the container and contents decreases
- The “lost” mass is the mass of the hydrogen gas that escaped
Similarly, when a carbonate decomposes:
CO2 gas escapes, so the mass of the solid remaining is less than the mass of the starting material.
Mass Appears to Increase
When a metal burns in air (e.g. magnesium):
- The metal reacts with oxygen from the air
- The oxygen adds to the metal, forming a metal oxide
- The mass of the product is greater than the mass of the starting metal
- The “extra” mass comes from the oxygen in the air
Mass of MgO > mass of Mg because oxygen atoms have been added.
Why Chemical Equations Must Be Balanced
Chemical equations must be balanced because of the law of conservation of mass. Atoms cannot be created or destroyed in a chemical reaction, so:
- The number of atoms of each element on the left side (reactants) must equal the number on the right side (products)
- We balance equations by putting numbers in front of formulae (coefficients), never by changing the formulae themselves
How to Balance an Equation
Example: Balance the equation for magnesium reacting with hydrochloric acid.
Step 1: Write the unbalanced equation:
Step 2: Count atoms on each side:
| Element | Left | Right | Balanced? |
|---|---|---|---|
| Mg | 1 | 1 | Yes |
| H | 1 | 2 | No |
| Cl | 1 | 2 | No |
Step 3: Put a 2 in front of HCl:
Step 4: Re-check:
| Element | Left | Right | Balanced? |
|---|---|---|---|
| Mg | 1 | 1 | Yes |
| H | 2 | 2 | Yes |
| Cl | 2 | 2 | Yes |
The equation is now balanced.
Interpreting Equations in Terms of Mole Ratios H
Example:
This tells us:
- 2 moles of magnesium react with 1 mole of oxygen to produce 2 moles of magnesium oxide
- The mole ratio is 2 : 1 : 2
More Examples
| Equation | Mole Ratio |
|---|---|
| Mg + 2HCl → MgCl2 + H2 | 1 : 2 : 1 : 1 |
| 2Na + 2H2O → 2NaOH + H2 | 2 : 2 : 2 : 1 |
| 2Fe2O3 + 3C → 4Fe + 3CO2 | 2 : 3 : 4 : 3 |
Relative Formula Mass (Mr)
You can find relative atomic masses on the periodic table. Some key values to know:
| Element | Symbol | Ar |
|---|---|---|
| Hydrogen | H | 1 |
| Carbon | C | 12 |
| Nitrogen | N | 14 |
| Oxygen | O | 16 |
| Sodium | Na | 23 |
| Magnesium | Mg | 24 |
| Sulfur | S | 32 |
| Chlorine | Cl | 35.5 |
| Calcium | Ca | 40 |
| Iron | Fe | 56 |
| Copper | Cu | 64 |
| Zinc | Zn | 65 |
Worked Examples
Example 1: Calculate the Mr of water (H2O):
Example 2: Calculate the Mr of magnesium oxide (MgO):
Example 3: Calculate the Mr of calcium carbonate (CaCO3):
Example 4: Calculate the Mr of iron(III) oxide (Fe2O3):
The Mole and Moles Calculations H
The mass of one mole of a substance (in grams) is equal to its relative formula mass. For example:
- 1 mole of carbon (Ar = 12) has a mass of 12 g
- 1 mole of water (Mr = 18) has a mass of 18 g
- 1 mole of CaCO3 (Mr = 100) has a mass of 100 g
The Moles Formula
This can be rearranged:
- mass = moles × Mr
- Mr = mass ÷ moles
Worked Examples
Example 1: How many moles are in 48 g of magnesium (Ar = 24)?
Example 2: What is the mass of 0.5 moles of calcium carbonate (Mr = 100)?
Example 3: How many moles are in 11.2 g of iron (Ar = 56)?
Calculating Masses from Balanced Equations H
You can use a balanced equation and mole calculations to work out the mass of a product formed or a reactant needed.
Step-by-Step Method
- Write the balanced equation
- Calculate the moles of the substance you know (using moles = mass ÷ Mr)
- Use the mole ratio from the equation to find moles of the substance you want
- Calculate the mass (using mass = moles × Mr)
Worked Example 1
Question: What mass of magnesium oxide is produced when 6 g of magnesium burns in excess oxygen?
Step 1: Balanced equation:
Step 2: Calculate moles of Mg (Ar = 24):
Step 3: Use mole ratio – from the equation, 2 mol Mg produces 2 mol MgO, so the ratio is 1 : 1:
Step 4: Calculate mass of MgO (Mr = 24 + 16 = 40):
Worked Example 2
Question: What mass of iron can be extracted from 320 g of iron(III) oxide using excess carbon?
Step 1: Balanced equation:
Step 2: Calculate moles of Fe2O3 (Mr = (2 × 56) + (3 × 16) = 160):
Step 3: Use mole ratio – from the equation, 2 mol Fe2O3 produces 4 mol Fe:
Step 4: Calculate mass of Fe (Ar = 56):
Practice Questions
When magnesium burns in air, the mass of the product (magnesium oxide) is greater than the mass of the magnesium. Why?
Magnesium reacts with oxygen from the air. The oxygen atoms add to the magnesium, so the product (MgO) has a greater mass than the magnesium alone. Mass is conserved – the “extra” mass came from the oxygen in the air.
A student reacts zinc with hydrochloric acid in an open beaker. They notice the mass of the beaker and contents decreases during the reaction. Explain why.
Hydrogen gas is produced during the reaction [1 mark]. The hydrogen gas escapes from the open beaker into the air, so the total mass of the beaker and contents decreases [1 mark]. (The total mass of all products, including the escaped gas, still equals the mass of the reactants – conservation of mass.)
What is the coefficient needed in front of HCl to balance this equation?
Zn + ?HCl → ZnCl2 + H2
ZnCl2 has 2 chlorine atoms on the right, and H2 has 2 hydrogen atoms. So we need 2HCl on the left to provide 2 H atoms and 2 Cl atoms. The balanced equation is: Zn + 2HCl → ZnCl2 + H2
Balance the following equations:
- Na + H2O → NaOH + H2
- Fe + O2 → Fe2O3
(a)
[1 mark]
(b)
[1 mark]
In the equation: 2Mg + O2 → 2MgO, what is the mole ratio of magnesium to oxygen to magnesium oxide?
The coefficients tell us the mole ratio: 2 moles of Mg react with 1 mole of O2 to form 2 moles of MgO. The ratio is 2 : 1 : 2.
State the law of conservation of mass and explain why chemical equations must be balanced.
The law of conservation of mass states that no atoms are created or destroyed in a chemical reaction [1 mark]. Chemical equations must be balanced so that the number of atoms of each element is the same on both sides of the equation, reflecting the fact that atoms are only rearranged, not created or destroyed [1 mark].
For the reaction: Fe2O3 + 3CO → 2Fe + 3CO2
- How many moles of CO are needed to react with 1 mole of Fe2O3? [1 mark]
- How many moles of Fe are produced from 2 moles of Fe2O3? [1 mark]
(a) 3 moles of CO [1 mark] – from the coefficients, the ratio of Fe2O3 : CO is 1 : 3.
(b) 4 moles of Fe [1 mark] – from the coefficients, the ratio of Fe2O3 : Fe is 1 : 2, so 2 moles of Fe2O3 produces 2 × 2 = 4 moles of Fe.
What is the relative formula mass (Mr) of calcium hydroxide, Ca(OH)2?
(Ar: Ca = 40, O = 16, H = 1)
Ca(OH)2: Ca = 40, plus 2 × (O + H) = 2 × (16 + 1) = 34. Total Mr = 40 + 34 = 74.
Calculate the relative formula mass of magnesium sulfate, MgSO4.
(Ar: Mg = 24, S = 32, O = 16)
Mr = 24 + 32 + (4 × 16) [1 mark]
Mr = 24 + 32 + 64 = 120 [1 mark]
Calculate the number of moles in 5.6 g of iron. (Ar of Fe = 56)
moles = mass ÷ Mr [1 mark]
moles = 5.6 ÷ 56 = 0.1 mol [1 mark]
Zinc reacts with hydrochloric acid:
Zn + 2HCl → ZnCl2 + H2
Calculate the mass of zinc chloride produced when 13 g of zinc reacts with excess hydrochloric acid.
(Ar: Zn = 65, Cl = 35.5)
Step 1: Moles of Zn = 13 ÷ 65 = 0.2 mol [1 mark]
Step 2: From the equation, 1 mol Zn produces 1 mol ZnCl2, so moles of ZnCl2 = 0.2 mol [1 mark]
Step 3: Mr of ZnCl2 = 65 + (2 × 35.5) = 136 [1 mark]
Step 4: Mass = 0.2 × 136 = 27.2 g [1 mark]
What is the mass of 0.25 moles of copper oxide (CuO)?
(Ar: Cu = 64, O = 16)
Mr of CuO = 64 + 16 = 80. Mass = moles × Mr = 0.25 × 80 = 20 g.