Writing and Balancing Chemical Equations - Chemistry

1. Fundamental Concepts

Chemical Equation: A symbolic representation of a chemical reaction showing reactants (left) and products (right).

Law of Conservation of Mass: Mass is neither created nor destroyed. Therefore, the number of atoms of each element must be equal on both sides of the equation.
Subscripts vs. Coefficients:

Subscripts: Indicate the number of atoms in a molecule (e.g., $H_2O$). Do not change these when balancing.

Coefficients: Indicate the number of molecules (e.g., $2H_2O$). Change these to balance the equation.

2. Key Concepts

Skeleton Equation: An unbalanced equation showing only the formulas of the reactants and products.

Balanced Equation: An equation where the total number of atoms for each element is equal on both sides.

State Symbols: Abbreviations in parentheses indicating the physical state of the substance:

$(s)$ : Solid
$(l)$ : Liquid
$(g)$ : Gas
$(aq)$ : Aqueous solution

3. Examples

Example 1 (Basic)

Problem: Write and balance the chemical equation for the combustion of methane ( $$CH_4$$ ) in oxygen ( $$O_2$$ ) to form carbon dioxide ( $$CO_2$$ ) and water ( $$H_2O$$ ).

Step-by-Step Solution:

Write the unbalanced equation: $$CH_4 + O_2 \rightarrow CO_2 + H_2O$$
Balance carbon atoms: $$CH_4 + O_2 \rightarrow CO_2 + H_2O$$ (1 carbon atom on each side)
Balance hydrogen atoms: $$CH_4 + O_2 \rightarrow CO_2 + 2H_2O$$ (4 hydrogen atoms on each side)
Balance oxygen atoms: $$CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O$$ (4 oxygen atoms on each side)

Validation: Check the number of atoms on both sides: - Left: 1 C, 4 H, 4 O - Right: 1 C, 4 H, 4 O ✓

Example 2 (Intermediate)

Problem: Write and balance the chemical equation for the reaction between iron(III) oxide ( $$Fe_2O_3$$ ) and aluminum ( $$Al$$ ).

Step-by-Step Solution:

Write the unbalanced equation: $$Fe_2O_3 + Al \rightarrow Al_2O_3 + Fe$$
Balance iron atoms: $$Fe_2O_3 + Al \rightarrow Al_2O_3 + 2Fe$$ (2 iron atoms on each side)
Balance aluminum atoms: $$Fe_2O_3 + 2Al \rightarrow Al_2O_3 + 2Fe$$ (2 aluminum atoms on each side)
Balance oxygen atoms: $$Fe_2O_3 + 2Al \rightarrow Al_2O_3 + 2Fe$$ (3 oxygen atoms on each side)

Validation: Check the number of atoms on both sides: - Left: 2 Fe, 3 O, 2 Al - Right: 2 Fe, 3 O, 2 Al ✓

4. Problem-Solving Techniques

Write the Skeleton Equation: Ensure all chemical formulas are correct (check charges for ionic compounds).

Count Atoms: Create a table to count atoms of each element on both sides.

Balance Element by Element:

Leave Hydrogen (H) and Oxygen (O) for last, as they often appear in multiple compounds.

Balance Polyatomic Ions (like $SO_4^{2-}$ ) as a single unit if they appear unchanged on both sides.

Use Coefficients: Multiply the entire molecule by a coefficient to adjust the count.

Check and Simplify: Ensure the coefficients are in the lowest possible whole number ratio.