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Formulae

Paper 1Paper 2Paper 3Paper 4Paper 6

This section is examined in Paper 1, Paper 2, Paper 3, Paper 4, and Paper 6.

Understanding Chemical Formulae
A chemical formula is a concise way of representing the composition of a substance. It tells us which elements are present and how many atoms or ions of each element are involved. We distinguish between two main types: molecular formulae for covalent compounds (made of discrete molecules) and empirical formulae for ionic compounds (made of giant lattices).
Building on the concept of atomic structure, we use the periodic table to determine the charge of ions. This is crucial because ionic compounds must be electrically neutral. Covalent molecules, however, are held together by shared pairs of electrons, and their formula reflects the actual number of atoms in one molecule.
Molecular Formula
The molecular formula of a compound is the actual number and type of different atoms present in one molecule of that compound. For example, the molecular formula of glucose is C_6H_{12}O_6, meaning one molecule contains 6 carbon atoms, 12 hydrogen atoms, and 6 oxygen atoms.
Empirical Formula
The empirical formula of a compound is the simplest whole-number ratio of the different atoms or ions in a compound. It does not necessarily represent the actual number of atoms in a molecule, but rather the ratio in which they combine. For example, the molecular formula C_6H_{12}O_6 has an empirical formula of CH_2O (ratio 6:12:6 simplifies to 1:2:1).
Deducing Formulae from Models and Charges

For Ionic Compounds (Supplement): You may be asked to deduce the formula from a diagrammatic representation of a lattice or from ion charges.

  1. From Charges: Identify the charge of each ion (e.g., Na^+, Cl^-). The compound must be neutral. Therefore, one +1 ion balances one -1 ion. Formula: NaCl. For Mg^{2+} and Cl^-, you need two chloride ions to balance one magnesium ion. Formula: MgCl_2.

  2. From Diagrams (Unit Cells): In a crystal lattice diagram, ions are often shared between adjacent unit cells. You must count the contribution of each ion based on its position:

    • Corner: Counts as 1/8 (shared by 8 cells).
    • Edge: Counts as 1/4 (shared by 4 cells).
    • Face: Counts as 1/2 (shared by 2 cells).
    • Inside: Counts as 1 (belongs entirely to that cell).

    Example: If a unit cell has ions of type A at all 8 corners and an ion of type B in the very center:

    • Number of A = 8 \times \frac{1}{8} = 1
    • Number of B = 1 \times 1 = 1
    • Ratio A:B is 1:1. Formula is AB.
Deducing Formula from a Lattice Diagram

Question: A diagram shows a cubic unit cell of an ionic compound. Ion X is located at all 8 corners, and ion Y is located at the center of each of the 6 faces. Deduce the formula.

Solution:

  1. Count Ion X (corners): 8 \text{ corners} \times \frac{1}{8} = 1 atom of X.
  2. Count Ion Y (faces): 6 \text{ faces} \times \frac{1}{2} = 3 atoms of Y.
  3. The ratio of X to Y is 1:3.
  4. Formula: XY_3.
⚠︎ Confusing Molecular and Empirical Formulae
Error: Students often write the molecular formula when asked for the empirical formula, or vice versa. For example, writing C_6H_{12}O_6 as the empirical formula of glucose.

Correct Understanding: Always simplify the ratio for the empirical formula. If the question asks for the molecular formula, give the actual count. If it asks for the empirical formula, divide all subscripts by their greatest common divisor until they are whole numbers with no common factor.

⚠︎ Incorrect Formulae for Elements
Error: Writing diatomic formulae for all elements (e.g., writing C_2 for carbon or Fe_2 for iron).

Correct Understanding: Only specific non-metal elements exist as diatomic molecules in their standard state: Hydrogen (H_2), Nitrogen (N_2), Oxygen (O_2), Fluorine (F_2), Chlorine (Cl_2), Bromine (Br_2), and Iodine (I_2). Remember the mnemonic HOFBrINC. Metals (like Fe, Cu, Na) and noble gases (like He, Ne) are written as single atoms in formulae.

Writing Balanced Symbol Equations with State Symbols

Context: When asked to construct a symbol equation, especially in Paper 4 or Paper 6.

Why Examiners Accept This: The markscheme requires both correct balancing (conservation of mass) and correct state symbols. A balanced equation with wrong states loses marks because it fails to describe the physical conditions of the reaction accurately.

Correct Usage: Always check:

  1. Balancing: Count atoms on both sides. For example, for 'Magnesium + Oxygen -> Magnesium Oxide', start with Mg + O_2 \rightarrow MgO. Oxygen is unbalanced (2 vs 1). Add a 2 to MgO: Mg + O_2 \rightarrow 2MgO. Now Mg is unbalanced (1 vs 2). Add a 2 to Mg: 2Mg + O_2 \rightarrow 2MgO. Balanced.
  2. States: Use (s) for solids, (l) for liquids, (g) for gases, and (aq) for aqueous solutions (dissolved in water). If the question says 'dilute sulfuric acid', use (aq). If it says 'heated magnesium ribbon', use (s).
Deducing Equations from Relevant Information
Context: When given partial information, such as a word equation or experimental data (e.g., 'X grams of metal reacts with Y liters of gas').

Why Examiners Accept This: You must translate the chemical names into correct symbols first. A common error is using incorrect charges for transition metals (e.g., writing FeCl instead of FeCl_3 for iron(III) chloride).

Correct Usage: If given 'Iron(III) chloride reacts with sodium hydroxide', identify ions: Fe^{3+}, Cl^-, Na^+, OH^-. Products are usually a salt and water/hydroxide precipitate. FeCl_3 + NaOH \rightarrow Fe(OH)_3 + NaCl. Balance it: FeCl_3 + 3NaOH \rightarrow Fe(OH)_3 + 3NaCl. Add states: FeCl_3(aq) + 3NaOH(aq) \rightarrow Fe(OH)_3(s) + 3NaCl(aq).

Practice Questions
Q:
Q1: Define the term molecular formula.
A:
A1: The actual number and type of atoms in one molecule of a compound.
Q:
Q2: Deduce the empirical formula of a compound with molecular formula C_4H_{10}.
A:
A2: Divide subscripts by 2. Empirical formula is C_2H_5.
Q:
Q3: Write a balanced symbol equation, including state symbols, for the reaction between solid calcium carbonate and dilute hydrochloric acid.
A:
A3: CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)
Q:
Q4: A unit cell has atoms of element X at the 8 corners and atoms of element Y at the body center. What is the formula?
A:
A4: X contributes 8 \times 1/8 = 1. Y contributes 1 \times 1 = 1. Formula is XY.
Q:
Q5: Identify the mistake in this equation: Na + Cl_2 \rightarrow NaCl_2.
A:
A5: Two mistakes. 1) Sodium forms Na^+, Chlorine forms Cl^-, so formula is NaCl, not NaCl_2. 2) It is unbalanced. Correct: 2Na + Cl_2 \rightarrow 2NaCl.
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