Formulae

1. Overview

Chemical formulae and equations are the universal language of chemistry. This topic focuses on how we represent individual atoms, molecules, and ions, and how we use these symbols to describe chemical reactions precisely through balanced equations.

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Key Definitions

• Molecular Formula: The actual number and type of different atoms present in one molecule of a compound.
• Empirical Formula: The simplest whole-number ratio of the different atoms or ions present in a compound.
• Word Equation: A chemical reaction described using the full names of the reactants and products.
• Symbol Equation: A chemical reaction represented using chemical formulae, showing the ratio of substances and their physical states.
• State Symbols: Notations used in equations to show the physical state of a substance: (s) solid, (l) liquid, (g) gas, (aq) aqueous solution.

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Core Content

Common Formulae to Know

You are expected to recognize and use the formulae for common elements and compounds:

• Elements: $H_2$, $O_2$, $N_2$, $Cl_2$, $Br_2$, $I_2$ (Diatomic molecules)
• Compounds: $H_2O$ (Water), $CO_2$ (Carbon dioxide), $CO$ (Carbon monoxide), $CH_4$ (Methane), $NH_3$ (Ammonia), $HCl$ (Hydrochloric acid), $H_2SO_4$ (Sulfuric acid).

Deducing Formulae from Models

If given a diagram of a molecule, count the number of each type of atom to determine the formula.

• Example: A molecule containing 1 Carbon atom and 4 Hydrogen atoms has the formula $CH_4$.
• 📊A central black sphere (Carbon) bonded to four smaller white spheres (Hydrogen) arranged in a tetrahedron shape.

Constructing Equations

Chemical equations show the transformation of reactants (left side) into products (right side).

Step 1: Word Equation Methane + Oxygen → Carbon dioxide + Water

Step 2: Symbol Equation (Balanced with State Symbols) $CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(l)$

State Symbols

• (s): Solids (e.g., metals, precipitates like $AgCl$)
• (l): Pure liquids (e.g., $H_2O$, $Hg$)
• (g): Gases (e.g., $H_2$, $CO_2$)
• (aq): Aqueous (substances dissolved in water, e.g., $NaCl$ solution)

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Extended Content (Extended Curriculum Only)

Empirical Formula

The empirical formula is the simplest ratio.

• Example: The molecular formula of Glucose is $C_6H_{12}O_6$. The ratio 6:12:6 can be simplified to 1:2:1. Therefore, the empirical formula is $CH_2O$.

Deducing Ionic Formulae

To write the formula of an ionic compound, the total positive charge must equal the total negative charge (net charge = 0).

• Example 1: Magnesium ($Mg^{2+}$) and Chloride ($Cl^-$). To balance charges, we need two $Cl^-$ ions for every one $Mg^{2+}$ ion. Formula: $MgCl_2(s)$.
• Example 2: Aluminium ($Al^{3+}$) and Oxide ($O^{2-}$). The lowest common multiple of 3 and 2 is 6. We need two $Al^{3+}$ and three $O^{2-}$. Formula: $Al_2O_3(s)$.

Ionic Equations

Ionic equations focus only on the particles that take part in the reaction, removing "spectator ions" (ions that remain unchanged in solution).

Full Equation: $AgNO_3(aq) + NaCl(aq) \rightarrow AgCl(s) + NaNO_3(aq)$

Ionic Equation: $Ag^+(aq) + Cl^-(aq) \rightarrow AgCl(s)$

Deducing Equations from Information

You may be asked to turn a description into a symbol equation.

• Task: "Solid copper(II) carbonate reacts with dilute sulfuric acid to form aqueous copper(II) sulfate, carbon dioxide gas, and liquid water."
• Deduction: $CuCO_3(s) + H_2SO_4(aq) \rightarrow CuSO_4(aq) + CO_2(g) + H_2O(l)$

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Key Equations

While "Formulae" is a conceptual topic, the balancing of equations follows the Law of Conservation of Mass: $$\text{Total Mass of Reactants} = \text{Total Mass of Products}$$

Example Calculation Table:

Component	Reactant Side ($CH_4 + 2O_2$)	Product Side ($CO_2 + 2H_2O$)
Carbon (C)	1	1
Hydrogen (H)	4	4
Oxygen (O)	4	4

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Common Mistakes to Avoid

• ❌ Wrong: Writing $H2O$ or H2O.
• ✓ Right: Using subscripts: $H_2O$.
• ❌ Wrong: Changing the formula to balance an equation (e.g., changing $H_2O$ to $H_2O_2$).
• ✓ Right: Only change the coefficients (the numbers in front, e.g., $2H_2O$).
• ❌ Wrong: Using (aq) for pure water.
• ✓ Right: Water is a pure liquid (l); (aq) is only for substances dissolved in water.
• ❌ Wrong: Forgetting diatomic elements (writing $O$ instead of $O_2$).

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Exam Tips

• Command Word "Deduce": This means you don't need to memorize the answer; look at the charges or the diagram provided in the question to figure it out.
• Command Word "State": Give a brief answer without explanation (e.g., "State the formula of ammonia" → $NH_3$).
• Real-world Contexts: Be prepared for "Thermal" contexts (thermal decomposition of carbonates) and "Chemical" contexts (neutralization between acids and bases).
• State Symbols: In Paper 4 (Extended), you often lose 1 mark per equation if state symbols are missing or incorrect. Always double-check them.
• Calculations: Typical values like 98.0 ($H_2SO_4$) or 58.5 ($NaCl$) often appear in formula-based calculations. Practice calculating Relative Formula Mass ($M_r$) to assist with deducing formulae.

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Exam-Style Questions

Practice these original exam-style questions to test your understanding. Each question mirrors the style, structure, and mark allocation of real Cambridge 0620 Theory papers.

Exam-Style Question 1 — Short Answer [6 marks]

Question:

Ethanol can be produced by the fermentation of glucose.

(a) Give the molecular formula of glucose. [1]

(b) Write a word equation for the fermentation of glucose. [2]

(c) Write a balanced symbol equation for the fermentation of glucose, including state symbols. [3]

Worked Solution:

(a)

1. $C_6H_{12}O_6$ The molecular formula of glucose is given.

How to earn full marks:

• Correct formula with subscripts.

(b)

1. glucose → ethanol + carbon dioxide The reactants and products of fermentation are stated.

How to earn full marks:

• State "glucose" as a reactant
• State "ethanol" and "carbon dioxide" as products

(c)

1. $C_6H_{12}O_6(aq) \rightarrow 2C_2H_5OH(aq) + 2CO_2(g)$ The correct chemical formulas are used, with the correct balancing and state symbols.

How to earn full marks:

• Correct chemical formulas for all substances (1 mark)
• Correct balancing of the equation (1 mark)
• Correct state symbols for all substances (1 mark)

Common Pitfall: Make sure your state symbols are correct. Remember that aqueous (aq) means dissolved in water, and that carbon dioxide is a gas. Also, double-check that your equation is properly balanced – count the number of each type of atom on both sides.

Exam-Style Question 2 — Short Answer [5 marks]

Question:

An ionic compound contains the metal ion $M^{2+}$ and the non-metal ion $X^-$.

(a) State the number of electrons lost by each atom of element $M$ when it forms the ion $M^{2+}$. [1]

(b) State the number of electrons gained by each atom of element $X$ when it forms the ion $X^{-}$. [1]

(c) Deduce the formula of the ionic compound formed between $M^{2+}$ and $X^{-}$. [2]

(d) Name a compound with a similar ionic structure to the one you deduced in (c). [1]

Worked Solution:

(a)

1. 2 The charge of the ion indicates the number of electrons lost.

How to earn full marks:

• State "2" only

(b)

1. 1 The charge of the ion indicates the number of electrons gained.

How to earn full marks:

• State "1" only

(c)

1. $MX_2$ Two $X^-$ ions are needed to balance the +2 charge of the $M^{2+}$ ion.

How to earn full marks:

• Correct elements, $M$ and $X$ (1 mark)
• Correct subscript of 2 for $X$ (1 mark)

(d)

1. Magnesium chloride / Calcium chloride / Copper(II) chloride Any common metal chloride with a 2:1 ratio of chloride ions to metal ions.

How to earn full marks:

• Correct chemical name.

Common Pitfall: Remember that the overall charge of an ionic compound must be zero. The subscripts in the formula indicate the ratio of ions needed to achieve this balance. Also, be careful with Roman numerals in naming compounds – they indicate the charge of the metal ion.

Exam-Style Question 3 — Extended Response [8 marks]

Question:

A student investigates the reaction between hydrochloric acid and calcium carbonate. The equation for the reaction is:

$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$

The student uses $2.0 \text{ g}$ of calcium carbonate, $CaCO_3$.

(a) Define the term relative molecular mass, $M_r$. [2]

(b) Calculate the relative molecular mass, $M_r$, of calcium carbonate, $CaCO_3$. [A_r values: Ca = 40, C = 12, O = 16] [2]

(c) Calculate the number of moles of calcium carbonate used in the experiment. [2]

(d) The student collects the carbon dioxide gas produced. Assuming the reaction goes to completion, calculate the volume of carbon dioxide gas produced at room temperature and pressure (rtp). [Molar volume of gas at rtp = 24 dm³/mol] [2]

Worked Solution:

(a)

1. The sum of the relative atomic masses of all the atoms in a molecule. The definition of relative molecular mass is stated.

How to earn full marks:

• Mention "sum of" (1 mark)
• Mention "relative atomic masses" and "atoms in a molecule" (1 mark)

(b)

1. $M_r (CaCO_3) = 40 + 12 + (3 \times 16)$ The relative atomic masses of each element are added, accounting for the number of atoms.
2. $M_r (CaCO_3) = \boxed{100}$ The correct relative molecular mass is calculated.

How to earn full marks:

• Correct calculation (1 mark)
• Correct final answer (1 mark)

(c)

1. moles = mass / $M_r$ The formula relating moles, mass and relative molecular mass is stated.
2. moles of $CaCO_3 = 2.0 \text{ g} / 100 \text{ g/mol} = \boxed{0.02 \text{ mol}}$ The number of moles of calcium carbonate is calculated.

How to earn full marks:

• Correct calculation (1 mark)
• Correct final answer with unit (1 mark)

(d)

1. moles of $CO_2$ = moles of $CaCO_3$ = 0.02 mol The stoichiometry of the equation is used to determine the moles of carbon dioxide produced.
2. Volume of $CO_2$ = moles $\times$ molar volume = $0.02 \text{ mol} \times 24 \text{ dm}^3\text{/mol} = \boxed{0.48 \text{ dm}^3}$ The volume of carbon dioxide is calculated.

How to earn full marks:

• Moles of $CO_2$ = moles of $CaCO_3$ (1 mark)
• Correct final answer with unit (1 mark)

Common Pitfall: Always include units in your calculations and final answers. Also, pay close attention to the stoichiometry of the balanced equation to determine the mole ratios between reactants and products.

Exam-Style Question 4 — Extended Response [9 marks]

Question:

A student investigates the cracking of decane ($C_{10}H_{22}$). Decane is passed over a hot catalyst, producing a mixture of smaller alkanes and alkenes. One possible reaction is:

$C_{10}H_{22} \rightarrow C_6H_{14} + C_4H_8$

(a) Define the term empirical formula. [2]

(b) Determine the empirical formula of decane ($C_{10}H_{22}$). [1]

(c) The $C_4H_8$ product is an alkene. Draw the displayed formula of two different isomers of $C_4H_8$. [4]

(d) Describe a chemical test to distinguish between decane ($C_{10}H_{22}$) and the alkene $C_4H_8$. Include the observation for each compound. [2]

Worked Solution:

(a)

1. The simplest whole number ratio of atoms of each element in a compound. The definition of empirical formula is stated.

How to earn full marks:

• Mention "simplest ratio" (1 mark)
• Mention "atoms of each element" (1 mark)

(b)

1. $C_5H_{11}$ Divide the subscripts in the molecular formula by the highest common factor (2).

How to earn full marks:

• Correct formula with subscripts.

(c)

1. 📊But-1-ene: a straight chain of 4 carbons, with a double bond between carbons 1 and 2, and sufficient hydrogens to give each carbon 4 bonds. All bonds must be displayed.
   *The displayed formula of but-1-ene is drawn.*
2. 📊But-2-ene: a straight chain of 4 carbons, with a double bond between carbons 2 and 3, and sufficient hydrogens to give each carbon 4 bonds. All bonds must be displayed.
   *The displayed formula of but-2-ene is drawn.*

How to earn full marks:

• Correct displayed formula for the first isomer (2 marks)
• Correct displayed formula for the second isomer (2 marks)

(d)

1. Add bromine water. The reagent is stated.
2. Decane: bromine water remains orange/brown. The observation for decane is stated.
3. $C_4H_8$: bromine water decolourises. The observation for $C_4H_8$ is stated.

How to earn full marks:

• Mention "bromine water" (1 mark)
• Correct observation for both decane and $C_4H_8$ (1 mark)

Common Pitfall: When drawing displayed formulas, make sure you show all the bonds between atoms. Also, remember that alkenes have a carbon-carbon double bond, which is key to their reactivity with bromine water.