Chemical Equations and Stoichiometry: Writing, Balancing, and Calculations

Chemical Equations and Chemical Reactions

Introduction to Chemical Equations

Chemical changes are represented by chemical equations, which show the transformation of reactants into products. These equations are fundamental tools in chemistry for describing what happens during a chemical reaction.

• Reactants: Substances present at the start of a reaction (left side of the arrow).

• Products: Substances formed as a result of the reaction (right side of the arrow).

Example chemical equations:

• $\mathrm{H_2 + O_2 \rightarrow H_2O}$

• $\mathrm{CH_4 + O_2 \rightarrow CO_2 + H_2O}$

• $\mathrm{NaOH + HCl \rightarrow H_2O + NaCl}$

In chemical reactions, bonds are broken and new bonds are formed. It is crucial to recognize that atoms are neither created nor destroyed during a chemical reaction. This principle is known as the Law of Conservation of Mass.

Key Features of Chemical Equations

• Physical States: Indicated by symbols to the lower right of each formula:

  • (s): Solid

  • (l): Liquid

  • (g): Gas

  • (aq): Aqueous (dissolved in water)

• Chemical Equation Coefficients: Numbers in front of formulas indicate the relative number of molecules or moles involved in the reaction.

Example with physical states and coefficients:

• $\mathrm{HCl(aq) + NaHCO_3(s) \rightarrow CO_2(g) + H_2O(l) + NaCl(aq)}$

Writing and Balancing Chemical Equations

Steps for Writing and Balancing

To accurately represent a chemical reaction, follow these steps:

1. Identify the Reaction: Determine the reactants, products, and their physical states.

2. Write the Unbalanced Equation: Write the formulas for all reactants and products.

3. Balance the Equation: Adjust coefficients to ensure the same number of each type of atom appears on both sides of the equation. Do not change the chemical formulas of the reactants or products.

Tips for Balancing:

• Start with the most complex molecule (the one with the most atoms).

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

• Balance hydrogen and oxygen atoms last.

• Check your work to ensure mass balance.

Example: Balancing a Chemical Equation

Consider the combustion of methane:

• Unbalanced: $\mathrm{CH_4 + O_2 \rightarrow CO_2 + H_2O}$

• Balanced: $\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$

Stoichiometry: Quantitative Relationships in Chemical Reactions

Introduction to Stoichiometry

Stoichiometry is the calculation of the quantities of reactants and products involved in a chemical reaction. The coefficients in a balanced chemical equation represent the relative minimum number of molecules or moles needed for the reaction to occur.

Steps in Stoichiometric Calculations

1. Write and balance the chemical equation.

2. Convert the given mass of a substance to moles using its molar mass.

3. Use the mole ratio from the balanced equation to relate moles of one substance to moles of another.

4. Convert moles of the desired substance to mass, if required.

Example Problem: Combustion of Propane

If propane ($\mathrm{C_3H_8}$) reacts with oxygen to produce water and carbon dioxide, how much $\mathrm{O_2}$ is needed to react with 96.1 g of propane?

• Balanced equation: $\mathrm{C_3H_8 + 5O_2 \rightarrow 3CO_2 + 4H_2O}$

• Convert 96.1 g $\mathrm{C_3H_8}$ to moles: $\frac{96.1\ \mathrm{g}}{44\ \mathrm{g/mol}} = 2.18$ moles $\mathrm{C_3H_8}$

• Mole ratio: 1 mole $\mathrm{C_3H_8}$ : 5 moles $\mathrm{O_2}$

• Moles of $\mathrm{O_2}$ needed: $2.18 \times 5 = 10.9$ moles $\mathrm{O_2}$

Sample Problems and Applications

Practice Problems

• Aluminum and Cobalt(II) Nitrate: Aluminum metal reacts with aqueous cobalt(II) nitrate to form aqueous aluminum nitrate and cobalt metal. Find the stoichiometric coefficient for aluminum in the balanced equation using the lowest whole-number coefficients.

• Radium Phosphate and Sulfuric Acid: Radium phosphate reacts with sulfuric acid to form radium sulfate and phosphoric acid. Find the coefficient for sulfuric acid in the balanced equation using the lowest whole-number coefficients.

Sample Problem 2: Acid Rain Formation

A component of acid rain is nitric acid, which forms when nitrogen dioxide reacts with oxygen and water:

• $4\ \mathrm{NO_2(g)} + O_2(g) + 2\ \mathrm{H_2O(l)} \rightarrow 4\ \mathrm{HNO_3(aq)}$

If a power plant produces 16 kg of $\mathrm{NO_2}$ per year, and there is sufficient $\mathrm{O_2}$ and $\mathrm{H_2O}$, what mass of $\mathrm{HNO_3}$ can form?

1. Convert 16 kg $\mathrm{NO_2}$ to moles: $\frac{16,000\ \mathrm{g}}{46\ \mathrm{g/mol}} = 348$ moles $\mathrm{NO_2}$

2. Mole ratio: 4 moles $\mathrm{NO_2}$ : 4 moles $\mathrm{HNO_3}$ (1:1 ratio)

3. Moles $\mathrm{HNO_3}$ formed: 348 moles

4. Mass $\mathrm{HNO_3}$: $348 \times 63\ \mathrm{g/mol} = 21,924$ g = 21.9 kg

Summary Table: Physical State Symbols

Symbol	Meaning
(s)	Solid
(l)	Liquid
(g)	Gas
(aq)	Aqueous (dissolved in water)

Key Terms and Definitions

• Chemical Equation: A symbolic representation of a chemical reaction.

• Reactant: A starting substance in a chemical reaction.

• Product: A substance formed as a result of a chemical reaction.

• Stoichiometry: The calculation of reactants and products in chemical reactions.

• Mole Ratio: The ratio of moles of one substance to moles of another as indicated by the coefficients in a balanced equation.

• Law of Conservation of Mass: States that mass is neither created nor destroyed in a chemical reaction.

Additional info: Some example problems and calculations have been expanded for clarity and completeness.