Welcome to the World of Formulae and Equations!
Hello IGCSE Chemists! This chapter, Formulae, is absolutely critical. Think of chemical reactions like baking a cake—you need a precise recipe, and that recipe is the chemical formula and the balanced equation.
Mastering this topic ensures you know exactly what goes into a reaction and how much, which is the foundation of the whole Stoichiometry section.
What is a Chemical Formula?
A chemical formula is a shorthand way to represent a substance using the symbols of the elements it contains. It also tells us the ratio of the atoms present.
1. Molecular Formula vs. Empirical Formula
Don't worry if these terms sound similar. The difference is simple: one tells you the full story, the other tells you the simplest story.
Molecular Formula (Core Concept)
The molecular formula shows the actual number and type of different atoms combined in a single molecule of a compound.
- Example: The molecular formula for water is \(H_2O\). This means one molecule contains exactly two hydrogen atoms and one oxygen atom.
- Example: Glucose (sugar) has the molecular formula \(C_6H_{12}O_6\).
Empirical Formula (Extended Concept)
The empirical formula shows the simplest whole number ratio of the different atoms or ions in a compound.
This is often used for giant structures, like ionic compounds or giant covalent structures, where there are no individual molecules.
- Example: Take glucose (\(C_6H_{12}O_6\)). The simplest ratio of C:H:O is 6:12:6. Dividing by the greatest common factor (6) gives the ratio 1:2:1.
- The empirical formula for glucose is \(CH_2O\).
Quick Review Box:
Molecular Formula: Shows the actual count. (e.g., \(C_6H_{12}O_6\))
Empirical Formula: Shows the simplest ratio. (e.g., \(CH_2O\))
Key Takeaway: Formulae are chemical shorthand. Molecular formulae are for actual molecules; Empirical formulae are the simplest ratios, often used for ionic compounds or for calculations.
2. Writing Formulae for Elements and Simple Molecules
Formulae of Elements (Core Concept)
Elements can exist in two main forms in their uncombined state:
- Monatomic: Most elements, especially metals (e.g., Sodium, Na; Iron, Fe; Argon, Ar). They exist as single atoms.
- Diatomic: Some non-metals exist naturally as molecules containing two atoms bonded together.
Memory Aid: Remember the seven elements that are always diatomic. They form a '7' on the periodic table (N, O, F, Cl, Br, I) plus Hydrogen.
- Hydrogen: \(H_2\)
- Oxygen: \(O_2\)
- Chlorine: \(Cl_2\)
- Nitrogen: \(N_2\)
- Bromine: \(Br_2\) (a liquid)
- Iodine: \(I_2\) (a solid)
- Fluorine: \(F_2\)
Deducing Formulae from Models (Core Concept)
If you are shown a model or diagram of a simple compound, all you need to do is count the different atoms.
Step-by-Step Deduction Example:
Imagine a model where there is one large Black sphere and four small White spheres.
1. Identify the atoms: 1 Black (let's say Carbon, C), 4 White (let's say Hydrogen, H).
2. Write the symbols and subscripts: \(CH_4\) (Methane).
Key Takeaway: Know the difference between monatomic and diatomic elements, and practice counting atoms in models to quickly determine simple formulae.
3. Writing Ionic Formulae: The "Swap and Drop" Method (Extended Concept)
Ionic compounds are held together by the strong electrostatic attraction between positive ions (cations) and negative ions (anions). Since the overall compound must be neutral (no charge), the charges on the ions must balance out.
Syllabus Requirement: Deduce the formula from the charges on the ions.
To write the formula of an ionic compound, you need to know the charge (valency) of each ion.
Prerequisite Tip: Knowing Ion Charges
- Group I elements form ions with a \(+1\) charge (e.g., \(Na^+\)).
- Group II elements form ions with a \(+2\) charge (e.g., \(Mg^{2+}\)).
- Group III elements form ions with a \(+3\) charge (e.g., \(Al^{3+}\)).
- Group VII elements (Halogens) form ions with a \(-1\) charge (e.g., \(Cl^-\)).
- Group VI non-metals usually form ions with a \(-2\) charge (e.g., \(O^{2-}\)).
The "Swap and Drop" Rule:
This is a handy trick to help you balance the charges quickly:
- Write the symbols of the ions, including their charges.
- Swap the numerical values of the charges.
- Drop the positive/negative signs. These numbers become the subscripts in the final formula.
Example 1: Magnesium Oxide
- Ions: \(Mg^{2+}\) and \(O^{2-}\).
- Swap charges: The 2 from Mg goes to O, the 2 from O goes to Mg.
- Result: \(Mg_2O_2\).
- Simplify: Because the subscripts are in a 2:2 ratio, they simplify to 1:1. The formula is \(MgO\).
Example 2: Aluminium Sulfide
- Ions: \(Al^{3+}\) and \(S^{2-}\).
- Swap charges: The 3 from Al goes to S, the 2 from S goes to Al.
- Result: The formula is \(Al_2S_3\). (Cannot be simplified further).
Common Mistake to Avoid: Always simplify the subscripts to the empirical (simplest) ratio if possible (like in Example 1, \(Mg_2O_2\) becomes \(MgO\)).
Key Takeaway: Ionic compounds must be electrically neutral. Use ion charges and the "Swap and Drop" method to find the correct, balanced formula.
4. Chemical Equations
Chemical equations are the formal language used by chemists to describe a reaction. They show the reactants (starting materials) and the products (finished materials).
Word Equations (Core Concept)
These are the simplest way to represent a reaction.
Reactants \(\rightarrow\) Products
Example: Methane + Oxygen \(\rightarrow\) Carbon dioxide + Water
Symbol Equations and State Symbols (Core Concept)
A symbol equation uses chemical formulae instead of names. For an equation to be useful, it must be balanced (the number of atoms of each element must be the same on both sides).
Additionally, you must include state symbols (Syllabus 3.1 Core 4).
- (s): solid
- (l): liquid
- (g): gas
- (aq): aqueous (dissolved in water)
Example (Combustion of Methane):
\(CH_4 (g) + 2O_2 (g) \rightarrow CO_2 (g) + 2H_2O (l)\)
Step-by-Step: Balancing Equations
Balancing an equation is like ensuring all your baking ingredients are accounted for.
- Write the correct, unbalanced formulae for reactants and products. (Do NOT change these formulae!).
- List the number of atoms for each element on the left (LHS) and right (RHS).
- Adjust the numbers in front of the formulae (these are called coefficients) until the counts match on both sides.
- Balance elements that appear only once on each side first. Leave H and O until last.
Practice Example: Decomposition of Hydrogen Peroxide (\(H_2O_2 \rightarrow H_2O + O_2\))
Unbalanced:
LHS: H=2, O=2
RHS: H=2, O=3
To balance O, we need an even number of oxygen atoms on the RHS. Put 2 in front of \(H_2O\):
\(H_2O_2 \rightarrow 2H_2O + O_2\)
New counts:
LHS: H=2, O=2
RHS: H=4, O=4
Now balance the LHS by placing 2 in front of \(H_2O_2\):
\(2H_2O_2 (aq) \rightarrow 2H_2O (l) + O_2 (g)\) (Balanced!)
Ionic Equations (Extended Concept)
An ionic equation only shows the ions and molecules that are actually participating in the reaction. It is often used for precipitation or neutralization reactions.
Ions that do not change state or participate in the reaction are called spectator ions and are left out of the final ionic equation.
Step-by-Step: Writing an Ionic Equation (e.g., Silver Nitrate reacting with Sodium Chloride)
1. Write the full balanced symbol equation:
\(AgNO_3 (aq) + NaCl (aq) \rightarrow AgCl (s) + NaNO_3 (aq)\)
2. Split all aqueous ionic compounds into their ions. Leave solids, liquids, and gases as they are:
\(Ag^+ (aq) + NO_3^- (aq) + Na^+ (aq) + Cl^- (aq) \rightarrow AgCl (s) + Na^+ (aq) + NO_3^- (aq)\)
3. Identify and cancel the spectator ions (ions that appear identically on both sides): In this case, \(Na^+\) and \(NO_3^-\).
4. Write the final ionic equation:
\(Ag^+ (aq) + Cl^- (aq) \rightarrow AgCl (s)\)
Did you know? Ionic equations are so useful because they show that many different reactions (like mixing silver nitrate with potassium chloride, \(KCl\)) result in the exact same net change: the silver ion reacting with the chloride ion!
Key Takeaway: Symbol equations must be balanced and include state symbols. Ionic equations only show the species that react, ignoring spectator ions.