IMAT Chemistry · Free notes

Stoichiometry: Moles, Equations and Yield

Stoichiometry and Reactions has 22 past questions since 2011, and the ministry papers from 2023 on have asked 4 of them. Almost every question is a short calculation built on one chain: mass to moles, moles through the ratio in a balanced equation, then back to mass or to a number of particles. The ministry papers asked for a percentage yield, the reactant that runs out first, and the number of atoms in a small mass of gas. The difficulty is in the bookkeeping, not the chemistry: a two-atom molecule, a coefficient that is not 1, or a reactant left over at the end.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

IMAT home All formulas on one page

Subtopic notes

Formula & revision sheet

11 formulas · 3 reference tables · 15 gotchas across all subtopics — the exam-eve cheat-sheet

The Mole, Molar Mass and Avogadro's Number

Formulas (3)

Relative atomic mass, relative formula mass and molar mass · Relative formula mass $M_r = \sum (\text{number of atoms} \times A_r)$
Amount of substance: moles from a mass · Moles from mass $n = \frac{m}{M}$
Avogadro's number: counting molecules and atoms · Number of particles $N = n \times N_A = \frac{m}{M} \times N_A$

Watch out for (3)

A bracket multiplies everything inside it
→ Relative atomic mass, relative formula mass and molar mass
Kilograms must become grams before you divide
→ Amount of substance: moles from a mass
Nitrogen gas is made of two-atom molecules
→ Avogadro's number: counting molecules and atoms

Percentage Composition, Empirical and Molecular Formulas

Formulas (3)

Percentage by mass of an element in a compound · Percentage by mass $\%\,\text{element} = \frac{x \times A_r}{M_r} \times 100$
Empirical formula from masses or percentages · Mole ratio of elements $\text{ratio of atoms} = \frac{m_1}{A_{r,1}} : \frac{m_2}{A_{r,2}} : \dots$
Molecular formula from the empirical formula and molar mass · Molecular formula multiplier $n = \frac{M_r(\text{compound})}{M_r(\text{empirical formula})}$

Watch out for (3)

Share of atoms is not share of mass
→ Percentage by mass of an element in a compound
Do not round 1.5 or 1.33 to the nearest whole number
→ Empirical formula from masses or percentages
Different compounds can share one empirical formula
→ Molecular formula from the empirical formula and molar mass

Conservation of Mass, Balancing and Ionic Equations

Formulas (2)

Conservation of mass and balancing an equation · Conservation of mass $\sum m_{\text{reactants}} = \sum m_{\text{products}}$
Balancing the combustion of organic compounds · Complete combustion $\mathrm{C_xH_yO_z} + \left(x + \tfrac{y}{4} - \tfrac{z}{2}\right)\mathrm{O_2} \rightarrow x\,\mathrm{CO_2} + \tfrac{y}{2}\,\mathrm{H_2O}$

Watch out for (3)

Never balance by changing a subscript
→ Conservation of mass and balancing an equation
Count the oxygen already inside the fuel
→ Balancing the combustion of organic compounds
Simplest ionic equation means no spectators
→ Ionic equations and spectator ions

Types of Reaction, Displacement and Precipitates

Reference tables (3)

The main types of chemical reaction7 rows

Type	Pattern	Example	How to spot it
Synthesis	A + B → AB	$2\mathrm{Mg} + \mathrm{O_2} \rightarrow 2\mathrm{MgO}$	Several reactants, one product
Decomposition	AB → A + B	$\mathrm{CaCO_3} \rightarrow \mathrm{CaO} + \mathrm{CO_2}$ (heated)	One reactant, several products
Single displacement	A + BC → AC + B	$\mathrm{Fe} + \mathrm{CuSO_4} \rightarrow \mathrm{FeSO_4} + \mathrm{Cu}$	An element in, a different element out
Double displacement	AB + CD → AD + CB	$\mathrm{AgNO_3} + \mathrm{NaCl} \rightarrow \mathrm{AgCl} + \mathrm{NaNO_3}$	Two compounds swap ions
Precipitation	ions (aq) → insoluble solid	$\mathrm{Fe^{3+}} + 3\mathrm{OH^-} \rightarrow \mathrm{Fe(OH)_3(s)}$	A solid appears when two solutions mix
Neutralisation	acid + base → salt + water	$\mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{NaCl} + \mathrm{H_2O}$	Net change is $\mathrm{H^+} + \mathrm{OH^-} \rightarrow \mathrm{H_2O}$
Combustion	fuel + oxygen → oxides	$\mathrm{CH_4} + 2\mathrm{O_2} \rightarrow \mathrm{CO_2} + 2\mathrm{H_2O}$	Oxygen is a reactant; heat is given out

Displacement reactions and the reactivity series5 rows

Reaction	General result	Example
Group 1 metal or calcium + cold water	hydroxide + hydrogen	$2\mathrm{Na} + 2\mathrm{H_2O} \rightarrow 2\mathrm{NaOH} + \mathrm{H_2}$ Magnesium reacts the same way with cold water, but only very slowly.
Magnesium, zinc or iron + steam	oxide + hydrogen	$\mathrm{Mg} + \mathrm{H_2O(g)} \rightarrow \mathrm{MgO} + \mathrm{H_2}$
Metal above hydrogen + dilute acid	salt + hydrogen	$\mathrm{Zn} + 2\mathrm{HCl} \rightarrow \mathrm{ZnCl_2} + \mathrm{H_2}$
Metal + salt solution of a less reactive metal	the less reactive metal is deposited	$\mathrm{Fe} + \mathrm{CuSO_4} \rightarrow \mathrm{FeSO_4} + \mathrm{Cu}$
Halogen + salt of a less reactive halogen	the less reactive halogen is released	$\mathrm{Cl_2} + 2\mathrm{NaBr} \rightarrow 2\mathrm{NaCl} + \mathrm{Br_2}$

The formula of each product follows the ion charges:

\mathrm{Mg^{2+}}

with

\mathrm{OH^-}

gives

\mathrm{Mg(OH)_2}

, never MgOH.

Solubility rules for predicting a precipitate6 rows

Compounds of	Usually	Main exceptions
Sodium, potassium, ammonium	Soluble	None at this level
Nitrates	Soluble	None at this level
Chlorides, bromides, iodides	Soluble	Silver and lead(II) salts are insoluble
Sulfates	Soluble	Barium and lead(II) insoluble; calcium only slightly soluble
Carbonates	Insoluble	Sodium, potassium and ammonium carbonates dissolve
Hydroxides	Insoluble	Group 1 hydroxides dissolve; calcium hydroxide slightly

Watch out for (3)

A reaction can have more than one label
→ The main types of chemical reaction
Cold water gives a hydroxide, steam gives an oxide
→ Displacement reactions and the reactivity series
The precipitate never contains sodium, potassium or nitrate
→ Solubility rules for predicting a precipitate

Reacting Masses, Limiting Reagent and Percentage Yield

Formulas (3)

Reacting masses through the mole ratio · Mole ratio from the equation $\frac{n_B}{n_A} = \frac{b}{a}$
Limiting reagent and the reactant in excess · Finding the limiting reagent $\text{limiting} = \text{smallest of } \frac{n_A}{a},\ \frac{n_B}{b}$
Percentage yield · Percentage yield $\%\,\text{yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100$

Watch out for (3)

Coefficients are a ratio of moles, not of grams
→ Reacting masses through the mole ratio
The limiting reagent is not simply the smaller mass or the fewer moles
→ Limiting reagent and the reactant in excess
Compare product with product, not product with reactant
→ Percentage yield

PYQ weightage by concept

15 concepts · 0 PYQs — where the marks actually sit, so you know what to drill first

The Mole, Molar Mass and Avogadro's Number0 PYQs · 0%

Concept	PYQs	Share
Relative atomic mass, relative formula mass and molar massfoundation	—	—
Amount of substance: moles from a massfoundation	—	—
Avogadro's number: counting molecules and atomsfoundation	—	—

Percentage Composition, Empirical and Molecular Formulas0 PYQs · 0%

Concept	PYQs	Share
Percentage by mass of an element in a compoundfoundation	—	—
Empirical formula from masses or percentagesfoundation	—	—
Molecular formula from the empirical formula and molar massfoundation	—	—

Conservation of Mass, Balancing and Ionic Equations0 PYQs · 0%

Concept	PYQs	Share
Conservation of mass and balancing an equationfoundation	—	—
Balancing the combustion of organic compoundsfoundation	—	—
Ionic equations and spectator ionsfoundation	—	—

Types of Reaction, Displacement and Precipitates0 PYQs · 0%

Concept	PYQs	Share
The main types of chemical reactionfoundation	—	—
Displacement reactions and the reactivity seriesfoundation	—	—
Solubility rules for predicting a precipitatefoundation	—	—

Reacting Masses, Limiting Reagent and Percentage Yield0 PYQs · 0%

Concept	PYQs	Share
Reacting masses through the mole ratiofoundation	—	—
Limiting reagent and the reactant in excessfoundation	—	—
Percentage yieldfoundation	—	—