Balancing Chemical Equations and Oxidation Numbers

Balancing Chemical Equations

Introduction to Balancing Equations

Balancing chemical equations is a fundamental skill in chemistry, ensuring that the law of conservation of mass is obeyed. This law states that atoms are neither created nor destroyed in a chemical reaction, so the number of each type of atom must be the same on both sides of the equation.

• Step 1: Write the Equation in Word Form List all reactants on the left and products on the right. Example: Calcium carbonate + Hydrochloric acid → Calcium chloride + Water + Carbon dioxide

• Step 2: Write the Chemical Formulas Replace the names with correct chemical formulas. Example: $\mathrm{CaCO_3} + \mathrm{HCl} \rightarrow \mathrm{CaCl_2} + \mathrm{H_2O} + \mathrm{CO_2}$

• Step 3: Balance the Equation Adjust the coefficients (stoichiometric numbers) so that the number of each atom is equal on both sides. Example:

  • Count atoms on each side:

  Element	Reactants	Products
  Ca	1	1
  C	1	1
  O	3	3 (2 in CO2 + 1 in H2O)
  Cl	1	2
  H	1	2

  • Balance H and Cl by multiplying HCl by 2:

  $\mathrm{CaCO_3} + 2\mathrm{HCl} \rightarrow \mathrm{CaCl_2} + \mathrm{H_2O} + \mathrm{CO_2}$

• Step 4: Indicate Physical States Use (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solution. Example: $\mathrm{CaCO_3}(s) + 2\mathrm{HCl}(aq) \rightarrow \mathrm{CaCl_2}(aq) + \mathrm{H_2O}(l) + \mathrm{CO_2}(g)$

Worked Example: Aluminium and Hydrochloric Acid

1. Word Equation: Aluminium + Hydrochloric acid → Aluminium chloride + Hydrogen

2. Formula Equation: $\mathrm{Al} + \mathrm{HCl} \rightarrow \mathrm{AlCl_3} + \mathrm{H_2}$

3. Balancing Steps:

   • Balance Cl: $\mathrm{Al} + 3\mathrm{HCl} \rightarrow \mathrm{AlCl_3} + \mathrm{H_2}$

   • Balance H: Multiply HCl by 6 and H2 by 3: $\mathrm{Al} + 6\mathrm{HCl} \rightarrow \mathrm{AlCl_3} + 3\mathrm{H_2}$

   • Balance Cl again: Double AlCl3: $\mathrm{Al} + 6\mathrm{HCl} \rightarrow 2\mathrm{AlCl_3} + 3\mathrm{H_2}$

   • Balance Al: Multiply Al by 2: $2\mathrm{Al} + 6\mathrm{HCl} \rightarrow 2\mathrm{AlCl_3} + 3\mathrm{H_2}$

Key Point: Balancing equations is a stepwise process. Adjust only the coefficients, not the chemical formulas.

Practice Problem

Balance the following equation:

$\mathrm{P_4O_{10}}(s) + \mathrm{H_2O}(l) \rightarrow \mathrm{H_3PO_4}(aq)$

Hint: Work step by step, balancing P, then H, then O.

Oxidation Numbers

Introduction to Oxidation Numbers

Oxidation numbers are a bookkeeping tool used to keep track of electron transfer in chemical reactions, especially in redox (oxidation-reduction) processes. They do not represent actual charges on atoms but help identify which species are oxidized or reduced.

• Oxidation: Increase in oxidation number

• Reduction: Decrease in oxidation number

Rules for Assigning Oxidation Numbers

1. The oxidation number of an element in its uncombined form is 0.

2. The sum of oxidation numbers in a neutral molecule is 0; in an ion, it equals the ion's charge.

3. Hydrogen is +1 when bonded to non-metals, -1 when bonded to metals.

4. Group 1 elements are always +1; Group 2 elements are always +2.

5. Halogens are usually -1 (fluorine is always -1), except when combined with oxygen or a more electronegative halogen.

6. Oxygen is usually -2, except in peroxides (-1) or when bonded to fluorine (+2).

Worked Examples

• Example 1: Lithium Oxide ($\mathrm{Li_2O}$)

  • Let x = oxidation number of Li

  • Oxygen is -2 (rule 6)

  • Equation: $2x + (-2) = 0$

  • $2x = +2 \Rightarrow x = +1$

  • Therefore, Li is +1 in $\mathrm{Li_2O}$

• Example 2: Permanganate Ion ($\mathrm{MnO_4^-}$)

  • Let x = oxidation number of Mn

  • Oxygen is -2 (rule 6)

  • Equation: $x + 4(-2) = -1$

  • $x - 8 = -1 \Rightarrow x = +7$

  • Therefore, Mn is +7 in $\mathrm{MnO_4^-}$

Practice Problem

Determine the oxidation number of the underlined element in:

• $\underline{C}_6H_6$ (benzene)

• $\underline{Al}H_3$ (aluminum hydride)

Redox Equations

Introduction to Redox Equations

Redox (reduction-oxidation) equations involve the transfer of electrons between species. Balancing these equations requires ensuring both mass and charge are conserved.

• Half-Equations: Show either the oxidation or reduction process separately.

• Example: Iron and Potassium Permanganate Reaction

  • Oxidation half: $\mathrm{Fe^{3+} + e^- \rightarrow Fe^{2+}}$

  • Reduction half: $\mathrm{MnO_4^-} + \mathrm{H^+} \rightarrow \mathrm{Mn^{2+}} + \mathrm{H_2O}$

• Both atoms and charges must be balanced in the final equation.

Summary of Learning Outcomes

• Be able to balance chemical equations fully.

• Be able to calculate oxidation numbers for individual atoms in a compound.

• Understand the meaning of oxidation and reduction in terms of electron transfer and oxidation numbers.

Additional info: These concepts are foundational for understanding more advanced topics in general and organic chemistry, including reaction mechanisms and redox processes in organic molecules.