Chemical Formulae, Compounds, and Equations Study Guide

Chemical Formulae and Their Significance

• Definition of a Chemical Formula: A chemical formula is a useful shorthand method used to describe the atoms present in a compound, an element, or ions.
• Information Provided by a Formula:
  • Type of Element: The formula indicates the atomic structure of the element.
    • Monoatomic Elements: These contain only one atom. An example is Calcium ($Ca$). It is noted that all metals are represented as monoatomic elements.
    • Diatomic Elements: These are made up of two atoms of the same type that are chemically combined. Examples include Nitrogen ($N_2$), Oxygen ($O_2$), Chlorine ($Cl_2$), and all other Group 7 elements.
  • Elemental Composition: The formula identifies which specific elements are contained within a substance. For example, Iron(II) sulphate ($FeSO_4$) contains the elements iron, sulphur, and oxygen.
  • Quantitative Composition: The formula shows how many atoms of each kind are present in a single molecule. For example, Sulphuric acid ($H_2SO_4$) contains:
    • Two atoms of hydrogen ($H_2$).
    • One atom of sulphur ($S$).
    • Four atoms of oxygen ($O_4$).

Symbols of Common Simple Ions and Radicals

Simple Ions

• Magnesium ion: $Mg^{2+}$
• Calcium ion: $Ca^{2+}$
• Potassium ion: $K^{+}$
• Sodium ion: $Na^{+}$
• Silver ion: $Ag^{+}$
• Zinc: $Zn^{2+}$
• Cobalt: $Co^{2+}$
• Lead: $Pb^{2+}$ or $Pb^{4+}$
• Iron: $Fe^{2+}$ or $Fe^{3+}$
• Copper: $Cu^{+}$ or $Cu^{2+}$
• Manganese: $Mn^{2+}$ or $Mn^{4+}$
• Oxide ion: $O^{2-}$
• Nitride: $N^{3-}$
• Sulfide: $S^{2-}$

Radicals / Compound Ions

• Ammonium: $NH_4^{+}$
• Carbonate: $CO_3^{2-}$
• Sulphate: $SO_4^{2-}$
• Nitrate: $NO_3^{1-}$
• Hydroxide: $OH^{1-}$
• Hydrogen-carbonate: $HCO_3^{1-}$
• Phosphate: $PO_4^{3-}$
• Dichromate (vi): $Cr_2O_7^{2-}$
• Manganate (vii): $KMnO_4$ (Note: usually listed as the ion $MnO_4^{-}$ in other contexts, but transcript provides the full compound formula in the radical table).
• Sulphite: $SO_3^{2-}$
• Nitrite: $NO_2^{1-}$

Writing Correct Formulae of Compounds

• Valency: Defined as the combining power of elements and radicals. It is used to show the simplest ratio in which atoms combine together in a formula.
• Rules for Writing Formulae:
  1. Write down the symbols of the ions, elements, and radicals identified in the chemical name of the compound.
  2. Write the valency (or charge) of each element or radical directly under its corresponding symbol.
  3. Cancel out the charge signs to work only with the numerical valency.
  4. Identify common factors: if a common factor exists, the valencies must be simplified (divided by the common factor) before proceeding.
  5. Criss-cross the numbers: cross the valencies over to become the subscript for the opposite element or radical.
  6. Multiple Valencies: If an element has more than one possible valency, the specific valency to be used will be indicated in the compound's name (usually with Roman numerals).
  7. Usage of Brackets: A bracket must be placed around a radical if it is multiplied by 2 or more and is composed of more than one element.

Examples of Formula Writing

• Example A: Calcium chloride

  • Symbols: $Ca$ and $Cl$
  • Valency/Charge: $Ca = 2$, $Cl = 1$
  • Simplify: No common factor.
  • Criss-cross: The 2 goes to $Cl$ and the 1 goes to $Ca$.
  • Result: $CaCl_2$

• Example B: Copper (ii) oxide

  • Symbols: $Cu$ and $O$
  • Valency/Charge: $Cu = 2$, $O = 2$
  • Simplify: 2 is a common factor ($2/2 = 1$, $2/2 = 1$).
  • Criss-cross: 1 goes to $Cu$ and 1 goes to $O$.
  • Result: $CuO$

• Example C: Ammonium sulphate

  • Symbols: $(NH_4)$ and $(SO_4)$
  • Valency/Charge: $(NH_4) = 1$, $(SO_4) = 2$
  • Simplify: No common factor.
  • Criss-cross: The 2 goes to the ammonium radical and the 1 goes to the sulphate radical.
  • Brackets: Since the radical $NH_4$ is multiplied by 2, it requires brackets.
  • Result: $(NH_4)_2SO_4$

Formulae of Acids

• Definition of an Acid: A substance which dissociates in solution to give hydrogen ($H^+$) ions. It is described as an H donor.
• Common Acids and Their Formulae:
  • Hydrochloric acid: $HCl$
  • Sulphuric acid: $H_2SO_4$
  • Nitric acid: $HNO_3$
  • Carbonic acid: $H_2CO_3$
  • Phosphoric acid: $H_3PO_4$

Rules for Naming Compounds

1. Binary Compounds (Simple Ions): If there are only two elements present from simple ions, the name ends with -ide.

   • Example: $CaO$ is Calcium Oxide.
   • Example: $Na_2O$ is Sodium Oxide.
   • Example: $AlCl_3$ is Aluminium Chloride.
   • Hydroxides Exception: Compounds with an $-OH$ group also end with -ide (e.g., $NaOH$ is Sodium hydroxide).

2. Multiple Valencies: If elements have more than one valency, the specific valency used is shown in Roman numerals in brackets after the metal's name.

   • Example: $CuCl_2$ is copper (II) Chloride.
   • Example: $Fe(OH)_3$ is Iron (iii) hydroxide.

3. Non-Metal Compounds (Molecular): For compounds containing two or more non-metal atoms, the actual number of atoms of the element present is indicated using prefixes:

   • Mono-: One (1)
   • Di-: Two (2)
   • Tri-: Three (3)
   • Tetra-: Four (4)
   • Penta-: Five (5)
   • Examples:
     • $CO$: Carbon monoxide
     • $CO_2$: Carbon dioxide
     • $SO_2$: Sulphur dioxide
     • $SO_3$: Sulphur trioxide
     • $PCl_3$: Phosphorus trichloride
     • $PCl_5$: Phosphorus pentachloride
     • $CCl_4$: Carbon tetrachloride

Chemical Equations and Balancing

• Purpose: A chemical equation shows all substances that react together (reactants) as well as the resulting products in a chemical reaction.
• Word Equations: These use the full names of the substances involved.
  • Example: $hydrogen + oxygen \rightarrow water$
• Symbolic Equations: Use the chemical formulae and symbols of each substance.
  • Example: $H_2 + O_2 \rightarrow H_2O$

Balancing Equations

• The Law of Balancing: In a chemical equation, there must be the same number of atoms of the same type on the left-hand side (reactants) as on the right-hand side (products).
• Crucial Rule: NEVER change the formula (subscripts) of products or reactants when balancing. Only adjust the coefficients (the big number in front).
• Steps for Balancing:
  1. Count Atoms: Calculate the number of atoms on each side of the equation.
     • Example ($Mg + O_2 \rightarrow MgO$): Reactants have $Mg=1$, $O=2$. Products have $Mg=1$, $O=1$.
  2. Adjust Coefficients: Place a coefficient (big number) in front of the formula that contains unbalanced atoms.
  3. Iterate: Continue adjusting until both sides are equal.
     • Balanced example: $2Mg + O_2 \rightarrow 2MgO$
  4. Add State Symbols: If necessary, add sub-scripts to indicate physical states:
     • $(s)$: Solid
     • $(l)$: Liquid
     • $(g)$: Gas
     • $(aq)$: Aqueous (dissolved in water)

Balancing Tips

• Distributed Atoms: If an atom appears in several places on one side of the equation, always balance it last.
• Radical Ion Rule: If a radical ion (compound ion) appears unchanged on both sides (reactants and products), count it as a single unit rather than balancing individual atoms.
  • Example ($Ba(NO_3)_2 + Na_2SO_4 \rightarrow NaNO_3 + BaSO_4$): The $NO_3$ and $SO_4$ radicals remain unchanged.
• Fractional Balancing: Equations can be balanced using fractions (e.g., $1/2$, $3/2$, $5/2$).
  • Rule: Apply fractions ONLY to diatomic molecules. Afterward, multiply the entire equation by the smallest even number (usually 2) to remove the fraction.

Exercise: Practice Formulae and Balancing

Identify Formulae for These Compounds:

1. Sodium oxide: $Na_2O$
2. Magnesium chloride: $MgCl_2$
3. Calcium oxide: $CaO$
4. Silicon (iv) oxide: $SiO_2$
5. Iron (ii) hydroxide: $Fe(OH)_2$
6. Iron (iii) nitrate: $Fe(NO_3)_3$
7. Aluminium sulphate: $Al_2(SO_4)_3$
8. Ammonium phosphate: $(NH_4)_3PO_4$
9. Calcium carbonate: $CaCO_3$
10. Copper (ii) nitrate: $Cu(NO_3)_2$
11. Potassium sulphate: $K_2SO_4$
12. Ammonium chloride: $NH_4Cl$
13. Cobalt (ii) chloride: $CoCl_2$
14. Copper (ii) sulphate: $CuSO_4$
15. Aluminium oxide: $Al_2O_3$
16. Vanadium (v) oxide: $V_2O_5$
17. Manganese (iv) oxide: $MnO_2$
18. Sodium carbonate: $Na_2CO_3$
19. Magnesium sulphate: $MgSO_4$
20. Calcium hydroxide: $Ca(OH)_2$
21. Iron (iii) oxide: $Fe_2O_3$
22. Iron (ii) sulphate: $FeSO_4$
23. Aluminium nitrate: $Al(NO_3)_3$
24. Ammonium hydroxide: $NH_4OH$
25. Zinc carbonate: $ZnCO_3$
26. Copper (ii) carbonate: $CuCO_3$
27. Potassium hydrogen carbonate: $KHCO_3$
28. Ammonium nitrate: $NH_4NO_3$
29. Lithium chloride: $LiCl$

Balancing Practice Problems:

1. $H_2 + O_2 \rightarrow H_2O$
2. $BaCl_2 + NaOH \rightarrow Ba(OH)_2 + NaCl$
3. $H_2SO_4 + KOH \rightarrow K_2SO_4 + H_2O$
4. $K_2CO_3 + HCl \rightarrow KCl + H_2O + CO_2$
5. $CaCO_3 + HNO_3 \rightarrow Ca(NO_3)_2 + H_2O + CO_2$
6. $Ca + H_2O \rightarrow Ca(OH)_2 + H_2$
7. $Pb(NO_3)_2 + NaI \rightarrow PbI_2 + NaNO_3$
8. $Al_2(SO_4)_3 + NaOH \rightarrow Al(OH)_3 + Na_2SO_4$
9. $Al(OH)_3 + NaOH \rightarrow NaAlO_2 + H_2O$
10. $Pb(NO_3)_2 \rightarrow PbO + NO_2 + O_2$