Balancing Chemical Reactions and Stoichiometry: Core Concepts and Practice

Balancing Chemical Reactions

Law of Mass Conservation

The Law of Mass Conservation states that in a chemical reaction, the total mass of the reactants at the beginning is equal to the total mass of the products at the end. This principle is fundamental to all chemical equations and is attributed to Antoine-Laurent Lavoisier, who is often called the "Father of Modern Chemistry."

• Atoms are neither created nor destroyed in chemical reactions.

• The number and type of atoms must be the same on both sides of the reaction equation.

• Balancing equations ensures mass and atom conservation.

Example: The reaction of hydrogen and oxygen to form water must be balanced so that the number of hydrogen and oxygen atoms is the same on both sides.

Properties and Uses of Sodium and Chlorine

Sodium (Na)	Chlorine (Cl2)
Reacts violently with water	Used as a bleach and disinfectant
Used as a coolant in some nuclear reactors	Used as a chemical weapon (WWI, Iraq War, Syria)

Example: Sodium and chlorine react to form sodium chloride (table salt).

Balancing Chemical Equations: Examples

To balance a chemical equation, adjust the coefficients so that the number of each type of atom is the same on both sides.

• Sodium and Chlorine:

  • Unbalanced: $\mathrm{Na(s) + Cl_2(g) \rightarrow NaCl(s)}$

  • Balanced: $2\mathrm{Na(s) + Cl_2(g) \rightarrow 2NaCl(s)}$

• Hydrogen and Oxygen:

  • Unbalanced: $\mathrm{O_2(g) + H_2(g) \rightarrow H_2O(g)}$

  • Balanced: $2\mathrm{H_2(g) + O_2(g) \rightarrow 2H_2O(g)}$

• Nitrogen and Hydrogen (Ammonia Synthesis):

  • Unbalanced: $\mathrm{N_2(g) + H_2(g) \rightarrow NH_3(g)}$

  • Balanced: $\mathrm{N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)}$

• Combustion of Hydrocarbons:

  • Pentane: $\mathrm{C_5H_{12}(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

  • Octane: $\mathrm{C_8H_{18}(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

  • Ethylene: $\mathrm{C_2H_4(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

Example: For ethylene combustion, the balanced equation is $\mathrm{C_2H_4(g) + 3O_2(g) \rightarrow 2CO_2(g) + 2H_2O(g)}$. The sum of coefficients is 1 + 3 + 2 + 2 = 8.

Balancing Ionic Equations

Some reactions occur in aqueous solution and involve ions. These must also be balanced for both atoms and charge.

• Example: $\mathrm{Fe(NO_3)_2(aq) + Na_3PO_4(aq) \rightarrow Fe_3(PO_4)_2(aq) + NaNO_3(aq)}$

• Balance both the number of atoms and the charges.

Stoichiometry

Introduction to Stoichiometry

Stoichiometry is the quantitative study of reactants and products in a chemical reaction. It allows chemists to predict the amounts of substances consumed and produced.

• Based on balanced chemical equations.

• Uses mole ratios to relate quantities of reactants and products.

Molar Interpretation of Balanced Equations

Balanced equations can be interpreted in terms of moles, masses, and molecules.

• Example: $2\mathrm{H_2(g) + O_2(g) \rightarrow 2H_2O(l)}$

• 2 moles of H2 react with 1 mole of O2 to produce 2 moles of H2O.

• Masses can be calculated using molar masses:

  • Molar mass of H2: 2.02 g/mol

  • Molar mass of O2: 32.00 g/mol

  • Molar mass of H2O: 18.02 g/mol

Calculation: If 2.00 mol H2 reacts with 1.00 mol O2:

• Mass of H2: $2.00 \times 2.02 = 4.04$ g

• Mass of O2: $1.00 \times 32.00 = 32.00$ g

• Mass of H2O produced: $2.00 \times 18.02 = 36.04$ g

Stoichiometry Practice Problems

• Ammonia Synthesis: $\mathrm{N_2(g) + 3H_2(g) \rightarrow 2NH_3(g)}$

  • How many moles of N2 will react with 1.20 mol H2? Use the ratio 1:3.

  • How much NH3 will be formed?

• Decomposition of Dinitrogen Pentoxide: $2\mathrm{N_2O_5(g) \rightarrow 2N_2(g) + 5O_2(g)}$

  • Find moles from mass: $n = \frac{m}{M}$

  • How many moles is 25.0 g N2O5? Molar mass = 108.02 g/mol.

  • How many moles N2 and O2 are formed from 0.231 mol N2O5?

Percent Yield

Percent yield measures the efficiency of a reaction:

• $\text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100\%$

• Used to compare the amount of product obtained to the amount predicted by stoichiometry.

Summary Table: Key Stoichiometric Relationships

Concept	Equation/Relationship	Example
Mole-Mass Conversion	$n = \frac{m}{M}$	Find moles from grams
Mole Ratio	From balanced equation	2 mol H2 : 1 mol O2 : 2 mol H2O
Percent Yield	$\text{Percent Yield} = \frac{\text{Actual}}{\text{Theoretical}} \times 100\%$	15.0 g O2 formed vs. calculated

Additional info:

• Balancing equations is a foundational skill for all chemistry students and is required for accurate stoichiometric calculations.

• Stoichiometry connects chemical equations to laboratory measurements and real-world chemical processes.