Deducing Balanced Chemical Equations
This topic involves determining the stoichiometry of a chemical reaction by using experimental data, such as the masses of reactants or volumes of gases, to deduce the simplest whole-number mole ratio for the balanced equation.
Part of the ESAT Chemistry syllabus — revision for the Engineering and Science Admissions Test (ESAT), the UAT-UK admissions test for Cambridge, Imperial, Oxford and UCL.
Key points
- The core principle is that the stoichiometric coefficients in a balanced equation represent the simplest whole-number ratio of moles of reactants and products.
- To find this ratio from masses, first convert the mass of each substance into moles using the formula n = m / Mr.
- For gases at the same temperature and pressure, the ratio of their volumes is equal to the ratio of their moles. You can therefore use the volume ratio directly to find the stoichiometry.
- Once you have the mole ratio (e.g., 0.25: 0.5: 0.25), divide all numbers in the ratio by the smallest value to find the simplest integer relationship (e.g., 1: 2: 1).
- These integers are the stoichiometric coefficients used to construct the final balanced chemical equation.
Formulae
n = m / Mr To calculate the number of moles (n) from a given mass (m) of a substance with a known relative atomic or molecular mass (Mr).
Volume Ratio = Mole Ratio (for gases) To determine the mole ratio of gaseous reactants and products directly from their volumes, provided they are all measured at the same temperature and pressure.
Definitions
- Stoichiometric Ratio
- The ratio of the amounts (in moles) of reactants and products in a balanced chemical equation, as indicated by their coefficients.
Worked example
4.05 g of aluminium (Al) reacts completely with 3.60 g of water (H2O) to produce aluminium oxide (Al2O3) and hydrogen gas (H2). What is the balanced chemical equation for this reaction? [Ar: H = 1, O = 16, Al = 27]
- 1
Step 1:
Calculate the moles of the known reactants, aluminium and water.
Mr(H2O) = 2*1 + 16 = 18 - 2 Moles Al = mass / Ar = 4.05 g / 27 g/mol = 0.15 mol
- 3 Moles H2O = mass / Mr = 3.60 g / 18 g/mol = 0.20 mol
- 4
Step 2:
Find the simplest whole-number ratio of the moles of reactants.
Ratio Al :
H2O is 0.15 :
0.20.
- 5
Step 3:
Simplify the ratio.
Divide both sides by the smallest number, 0.05 (a common factor of 0.15 and 0.20).
This gives a ratio of 3 :
4.
- 6
Step 4:
Use these coefficients to start balancing the equation:
3Al + 4H2O → x Al2O3 + y H2.
- 7
Step 5:
Balance the products based on the reactants.
From 3Al on the left, we need 1.5 Al2O3.
From 4H2O, we need 4H2.
This gives 3Al + 4H2O → 1.5Al2O3 + 4H2.
- 8
Step 6:
Convert all coefficients to whole numbers by multiplying the entire equation by 2.
The final equation is 6Al + 8H2O → 3Al2O3 + 8H2.
Answer: 6Al + 8H2O → 3Al2O3 + 8H2
Common mistakes
- ×Forgetting to use the correct molecular mass (Mr) for diatomic elements like H2, N2, O2, Cl2. For example, using 14 for nitrogen gas instead of N2 (Mr = 28), which will make your mole calculation incorrect by a factor of 2.
- ×Making arithmetic errors when dividing masses by molar masses, especially with decimals. Double-check simple divisions like 3.6 / 18.
- ×Failing to simplify the mole ratio to the *smallest possible* whole numbers. A ratio of 2:4 must be simplified to 1:2 to find the correct coefficients.
- ×Assuming volume ratios equal mole ratios for substances that are not gases, or for gases at different temperatures and pressures.
No-calculator tips
- ✓Convert decimals to fractions or simple multiples before dividing to find moles. For example, to calculate 4.05 / 27, you can spot that 40.5 is 1.5 × 27, so 4.05 is 0.15 × 27.
- ✓When simplifying mole ratios like 0.15 : 0.20, multiply by 100 to get whole numbers (15:20) and then simplify by dividing by their highest common factor (5), which gives 3:4.
- ✓Before any calculation, quickly check the Mr values. Common ones like H2O=18, CO2=44, NH3=17 should be familiar and can save time.