Formulae, Equations and Amount of Substance

Edexcel International A-Level Chemistry· 1.1-1.12 (2018 Specification)· 45 min read

1. Key Terms and Formula Fundamentals★★☆☆☆⏱ 8 min

📘 Definition

Empirical vs Molecular Formula

Empirical formula = simplest whole number ratio of atoms of each element in a compound. Molecular formula = actual number of atoms of each element in one molecule of the compound, which is a whole-number multiple of the empirical formula.

Example:

Ethane: empirical formula = CH₃, molecular formula = C₂H₆

Foundational terms for this topic include: atom (smallest unit of an element), element (substance made of only one type of atom), ion (charged particle from gain/loss of electrons), molecule (neutral particle of covalently bonded atoms), compound (substance made of two or more elements chemically bonded). The mole is the standard unit for amount of substance, with 1 mole containing 6.02×10²³ particles (Avogadro constant).

📐 Worked Example

A compound contains 40.0% carbon, 6.7% hydrogen and 53.3% oxygen by mass. Calculate its empirical formula.

1
Assume a 100g sample, so masses: C = 40.0g, H = 6.7g, O = 53.3g
2
Calculate moles of each element: $n (C) = 40.0/12.0 \approx 3.33$ , $n (H) = 6.7/1.0 = 6.7$ , $n (O) = 53.3/16.0 \approx 3.33$
3
Divide all mole values by the smallest value (3.33): C = 1, H = 2, O = 1
4
Final empirical formula: CH₂O

Exam tip:

Always round mole ratios to the nearest whole number, and confirm no common factors remain in your final empirical formula.

2. Balanced Full and Ionic Equations★★☆☆☆⏱ 10 min

📘 Definition

Ionic Equations

Equations that show only reacting ions in a reaction, omitting spectator ions that do not take part. They must be balanced for both mass and total charge, and include state symbols for all species (s/l/g/aq).

To write an ionic equation: first write a balanced full equation with state symbols, split all aqueous ionic compounds into their constituent ions, cancel spectator ions that appear on both sides, then check balance of mass and charge.

📐 Worked Example

Write the ionic equation for the reaction between aqueous silver nitrate and aqueous sodium chloride, forming solid silver chloride and aqueous sodium nitrate.

1
Full balanced equation: $A g N O_{3} (a q) + N a C l (a q) \to A g C l (s) + N a N O_{3} (a q)$
2
Split aqueous species into ions: $A g^{+} (a q) + N O_{3}^{-} (a q) + N a^{+} (a q) + C l^{-} (a q) \to A g C l (s) + N a^{+} (a q) + N O_{3}^{-} (a q)$
3
Cancel spectator ions (Na⁺ and NO₃⁻) from both sides
4
Final balanced ionic equation: $A g^{+} (a q) + C l^{-} (a q) \to A g C l (s)$

Exam tip:

Never split solids, pure liquids, or gases into ions, only aqueous ionic compounds. Always check total charge on both sides of ionic equations matches.

3. Mole Calculations: Mass, Concentration and ppm★★★☆☆⏱ 12 min

📘 Definition

Molar Quantities

Molar mass ( $M$ ) = mass of 1 mole of substance, units g mol⁻¹, equal to the Ar/Mr of the substance. Concentration can be measured in mol dm⁻³ (moles of solute per dm³ of solution) or g dm⁻³ (mass of solute per dm³ of solution). ppm (parts per million) is used for trace concentrations.

$n = \frac{m}{M}$ where $n$ = moles, $m$ = mass (g), $M$ = molar mass (g mol⁻¹)
Concentration (mol dm⁻³) = $\frac{n}{V}$ where $V$ = volume (dm³, divide cm³ by 1000 to convert)
ppm = $\frac{mass of component}{total mass of mixture} \times 1 0^{6}$

📐 Worked Example

Calculate the concentration in g dm⁻³ of a 0.200 mol dm⁻³ solution of NaOH.

1
Calculate Mr of NaOH: $23.0 + 16.0 + 1.0 = 40.0$ g mol⁻¹
2
Multiply molar concentration by Mr: $0.200 \times 40.0 = 8.00$ g dm⁻³

Exam tip:

Round final calculation answers to the same number of significant figures as the least precise data given in the question.

4. Gas Volume Calculations and pV=nRT★★★☆☆⏱ 10 min

📘 Definition

Ideal Gas Equation

At room temperature and pressure (RTP = 298 K, 101 kPa), 1 mole of any gas occupies 24.0 dm³. For non-RTP conditions, use the ideal gas equation $p V = n R T$ , where $p$ = pressure (Pa), $V$ = volume (m³), $n$ = moles, $R$ = 8.31 J K⁻¹ mol⁻¹, $T$ = temperature (K).

📐 Worked Example

Calculate the volume occupied by 0.0200 mol of carbon dioxide gas at RTP.

1
Use the molar volume relationship: $V = n \times V_{m}$
2
Substitute values: $V = 0.0200 \times 24.0 = 0.480$ dm³ (or 480 cm³)

📐 Worked Example

Calculate the number of moles of gas in a 500 cm³ container at 27°C and 100 kPa pressure.

1
Convert units: $V = 500 \times 1 0^{- 6} = 5 \times 1 0^{- 4}$ m³, $T = 27 + 273 = 300$ K, $p = 100 \times 1 0^{3} = 1 \times 1 0^{5}$ Pa
2
Rearrange $p V = n R T$ to $n = \frac{p V}{R T}$
3
Calculate: $n = \frac{1 \times 1 0 ^{5} \times 5 \times 1 0 ^{- 4}}{8.31 \times 300} \approx 0.0201$ mol

Exam tip:

Always convert all units to SI before using pV=nRT to avoid order of magnitude errors.

5. % Yield, Atom Economy and Core Practical 1★★★☆☆⏱ 10 min

📘 Definition

Yield and Atom Economy

% yield measures the efficiency of product formation: $% y i e l d = \frac{actual yield}{theoretical maximum yield} \times 100$ . % atom economy measures the sustainability of a reaction: $% a t o m eco n o m y = \frac{M r of desired product}{sum of Mr of all reactants} \times 100$ .

📐 Worked Example

Calculate the atom economy for the production of ethanol from ethene and water: $C_{2} H_{4} + H_{2} O \to C_{2} H_{5} O H$ .

1
Calculate Mr of desired product (ethanol): $(2 \times 12) + (6 \times 1) + 16 = 46$
2
Sum of Mr of reactants: $C_{2} H_{4} = 28$ , $H_{2} O = 18$ , total = 46
3
Atom economy = $\frac{46}{46} \times 100 = 100%$ (no waste products for this addition reaction)

Core Practical 1: Molar volume of gas method: React a known mass of magnesium ribbon with excess hydrochloric acid, collect the hydrogen gas produced over water, measure its volume at RTP. Calculate moles of Mg (and thus moles of H₂ from the 1:1 reaction ratio), then $V_{m} = \frac{volume of H₂}{moles of H₂}$ . Expected result = ~24 dm³ mol⁻¹ at RTP.

Exam tip:

Common sources of error for Core Practical 1 include gas escaping during collection, measuring gas volume before it cools to room temperature, and inaccurate mass measurement of magnesium.

6. Common Pitfalls

Wrong move:

Forgetting to add state symbols to equations

Why:

Exam questions explicitly require state symbols for full marks, you will lose 1 mark per equation missing them

Correct move:

Always add (s)/(l)/(g)/(aq) to every species in all equations you write

Wrong move:

Using cm³ directly in pV=nRT without converting to m³

Why:

pV=nRT requires SI units for volume, using cm³ will give an answer 1 million times too large

Correct move:

Convert cm³ to m³ by multiplying by 10⁻⁶, or dm³ to m³ by multiplying by 10⁻³

Wrong move:

Balancing ionic equations only for mass, not charge

Why:

Ionic equations require equal total charge on both sides to be chemically correct, unbalanced charge will lose marks

Correct move:

After balancing mass, check total charge on left equals total charge on right, adjust coefficients if needed

Wrong move:

Using total Mr of all products for the atom economy denominator

Why:

Atom economy uses total mass of reactants, not products, so using products gives an incorrect value

Correct move:

Use the sum of Mr of all reactants in the denominator of the atom economy formula

Wrong move:

Leaving empirical formula ratios not fully simplified

Why:

Empirical formula is defined as the simplest whole number ratio, non-simplified ratios are invalid

Correct move:

Divide all mole ratios by the smallest mole value, then confirm no common factors remain between all numbers

7. Quick Reference Cheatsheet

Formula	Units/Notes	Use Case
$n = \frac{m}{M}$	n: mol, m: g, M: g mol⁻¹	Calculate moles from mass of substance
$C o n c (m o l d m^{- 3}) = \frac{n}{V}$	V: dm³ (divide cm³ by 1000)	Calculate concentration or moles in solution
ppm = $\frac{component mass}{total mass} \times 1 0^{6}$	No units	Calculate trace concentration values
$V = n \times 24.0$ dm³	At RTP (298 K, 101 kPa)	Calculate gas volume at room temperature
$p V = n R T$	p: Pa, V: m³, T: K, R=8.31 J K⁻¹ mol⁻¹	Calculate gas quantities at non-RTP conditions
% Yield = $\frac{actual}{theoretical} \times 100$	% value	Calculate efficiency of product formation
% Atom Economy = $\frac{Mr(desired)}{sum Mr(reactants)} \times 100$	% value	Calculate sustainability of a reaction

8. Frequently Asked

Do I need to memorize the Avogadro constant or gas constant?

No, both values are provided in the exam data booklet, but you must know how to apply them correctly in calculations.

What units do I use for the ideal gas equation pV=nRT?

Always use SI units: pressure in Pa, volume in m³, temperature in Kelvin (°C + 273), and R=8.31 J K⁻¹ mol⁻¹ to get correct values.

Do I have to include state symbols in all equations?

Yes, every exam equation requires state symbols (s/l/g/aq) to be awarded full marks. You will lose 1 mark per equation missing state symbols.

Going deeper

official documentEdexcel IAL Chemistry 2018 SpecificationRefer to section 1.1-1.12 for official topic guidance
practical guideCore Practical 1: Molar Volume of GasStep-by-step method and error analysis for required practical

What's Next

This foundational stoichiometry content is the building block for all quantitative chemistry in both AS and A2 Edexcel IAL Chemistry, so practice plenty of calculation questions to build confidence. You will use these mole calculation skills extensively in future topics including energetics, equilibrium, kinetics, and organic chemistry. Mastery of this topic will help you avoid common calculation errors across all units, and make more advanced content much easier to grasp.