Writing and Balancing Chemical Equations

Writing and Balancing Chemical Equations

Introduction to Chemical Reactions and Equations

Chemical reactions are processes in which substances (reactants) are transformed into new substances (products) through the breaking and forming of chemical bonds. Chemical equations are symbolic representations of these reactions, providing information about the identities and quantities of reactants and products involved.

• Chemical Reaction: A process where one or more substances are converted into different substances, involving chemical changes in matter.

• Chemical Equation: A concise way of describing a chemical reaction using chemical formulas and symbols.

• Example: Combustion of methane: $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

Types of Chemical Reactions

• Combustion Reaction: A reaction in which a substance combines with oxygen to form one or more oxygen-containing compounds, often releasing energy as heat and light.

• Example: Combustion of natural gas (methane): $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

Representing Chemical Equations

Chemical equations show the reactants on the left and the products on the right, separated by an arrow ($\rightarrow$). The physical states of substances are indicated in parentheses:

• (s): Solid

• (l): Liquid

• (g): Gas

• (aq): Aqueous (dissolved in water)

Example: $\mathrm{CH_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

Determining the Number of Atoms in Reactants and Products

To ensure a chemical equation is correct, the number of atoms of each element must be the same on both sides of the equation (Law of Conservation of Mass).

• Count the number of atoms for each element in the reactants and products.

• If the numbers do not match, the equation must be balanced.

Example: $\mathrm{H_2(g) + O_2(g) \rightarrow H_2O(g)}$ Reactants: 2 H, 2 O Products: 2 H, 1 O The equation is not balanced for oxygen.

Balancing Chemical Equations

Balancing chemical equations ensures the same number of each type of atom appears on both sides. This is achieved by adjusting the coefficients (numbers in front of formulas), not the subscripts (numbers within formulas).

• Steps to Balance:

  1. Write the unbalanced equation with correct formulas.

  2. Count the number of atoms of each element on both sides.

  3. Add coefficients to balance the atoms, starting with the most complex substance.

  4. Balance elements that appear in only one reactant and one product first.

  5. Balance free elements (uncombined elements) last.

  6. Check your work by recounting atoms for each element.

• Do not change subscripts as this alters the identity of the substance.

Example: $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

Balancing Equations: Step-by-Step Examples

• Example 1: $\mathrm{CH_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$ Step 1: Balance C: 1 on both sides. Step 2: Balance H: 4 on left, 2 on right. Add coefficient 2 before $\mathrm{H_2O}$. Step 3: Balance O: 2 on left, 4 on right. Add coefficient 2 before $\mathrm{O_2}$. Balanced Equation: $\mathrm{CH_4(g) + 2O_2(g) \rightarrow CO_2(g) + 2H_2O(g)}$

• Example 2: $\mathrm{Fe_2O_3(s) + C(s) \rightarrow Fe(s) + CO_2(g)}$ Step 1: Balance Fe: 2 on left, 1 on right. Add coefficient 2 before Fe. Step 2: Balance C: 1 on left, 1 on right. Step 3: Balance O: 3 on left, 2 on right. Add coefficient 3 before CO2 and 3 before C. Balanced Equation: $\mathrm{Fe_2O_3(s) + 3C(s) \rightarrow 2Fe(s) + 3CO_2(g)}$

Balancing Equations with Fractional Coefficients

Sometimes, balancing requires the use of fractional coefficients, especially for diatomic molecules like $\mathrm{O_2}$. After balancing, multiply all coefficients by the denominator to obtain whole numbers.

• Example: Combustion of butane ($\mathrm{C_4H_{10}}$): $\mathrm{2C_4H_{10}(g) + 13O_2(g) \rightarrow 8CO_2(g) + 10H_2O(g)}$

• Example: Combustion of ethane ($\mathrm{C_2H_6}$): $\mathrm{2C_2H_6(g) + 7O_2(g) \rightarrow 4CO_2(g) + 6H_2O(g)}$

Balancing Equations Involving Polyatomic Ions

When polyatomic ions appear unchanged on both sides of the equation, balance them as units to simplify the process.

• Example: Reaction between aqueous strontium chloride and lithium phosphate: $\mathrm{3SrCl_2(aq) + 2Li_3PO_4(aq) \rightarrow Sr_3(PO_4)_2(s) + 6LiCl(aq)}$

• Steps:

  1. Write correct formulas for all reactants and products.

  2. Balance polyatomic ions as a group if they appear on both sides.

  3. Balance remaining atoms as needed.

Summary Table: States of Matter Abbreviations

Abbreviation	State
(s)	Solid
(l)	Liquid
(g)	Gas
(aq)	Aqueous (dissolved in water)

Key Points to Remember

• Always use correct chemical formulas for all substances.

• Balance equations by adjusting coefficients, not subscripts.

• Check that the number of atoms for each element is equal on both sides.

• Indicate physical states for all reactants and products.

• For reactions involving polyatomic ions, balance them as units if they remain unchanged.

Practice Problems

• Write and balance the equation for the reaction between solid silicon dioxide and solid carbon to produce solid silicon carbide and carbon monoxide gas.

• Write and balance the equation for the combustion of gaseous ethane ($\mathrm{C_2H_6}$) in oxygen.

Additional info: These notes are based on lecture slides and include expanded academic context for clarity and completeness.