Stoichiometry of Chemical Reactions: Writing, Balancing, and Classifying Equations

Writing and Balancing Chemical Equations

Introduction to Chemical Equations

Chemical equations are symbolic representations of chemical reactions, showing the identities and relative quantities of reactants and products. They are fundamental for describing chemical changes and ensuring the conservation of mass.

• Balanced chemical equation: Shows equal numbers of each type of atom on both sides of the reaction.

• Physical states: Indicated by (s) for solid, (l) for liquid, (g) for gas, and (aq) for aqueous solution.

• Law of Conservation of Mass: The total number of atoms of each element must be the same on both sides of the equation.

Example: The combustion of methane:

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

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

Steps for Balancing Chemical Equations

1. Determine the physical states of reactants and products.

2. Write the unbalanced chemical equation.

3. Balance the number of atoms of each element, starting with the most complex molecule.

4. Leave pure elements (not in a molecule) to the last.

Example Table: Balancing CH4 Combustion

Element	Reactants	Products	Balanced?
C	1	1	Yes
H	4	2 × 2 = 4	Yes
O	2 × 2 = 4	2 + (2 × 1) = 4	Yes

Balancing by Inspection and Using Fractions

• Balance by inspection: Adjust coefficients to achieve equal numbers of atoms.

• Fractions may be used as intermediate coefficients, then multiplied to obtain whole numbers.

Example: $\mathrm{C_2H_6 + \frac{7}{2}O_2 \rightarrow 3H_2O + 2CO_2}$ Multiply by 2: $\mathrm{2C_2H_6 + 7O_2 \rightarrow 6H_2O + 4CO_2}$

Additional Information in Chemical Equations

• Physical states are indicated with abbreviations.

• Special conditions (e.g., heat) may be shown above/below the arrow (Δ).

Example: $\mathrm{CaCO_3(s) \xrightarrow{\Delta} CaO(s) + CO_2(g)}$

Classifying Chemical Reactions

Precipitation Reactions

Precipitation reactions occur when dissolved substances react to form one or more solid products. These are often double displacement (metathesis) reactions.

• Molecular equation: $\mathrm{CaCl_2(aq) + 2AgNO_3(aq) \rightarrow Ca(NO_3)_2(aq) + 2AgCl(s)}$

• Ionic equation: $\mathrm{Ca^{2+}(aq) + 2Cl^-(aq) + 2Ag^+(aq) + 2NO_3^-(aq) \rightarrow Ca^{2+}(aq) + 2NO_3^-(aq) + 2AgCl(s)}$

• Net ionic equation: $\mathrm{2Ag^+(aq) + 2Cl^-(aq) \rightarrow 2AgCl(s)}$

Solubility and Precipitation

• Solubility: Maximum concentration of a substance that can be achieved under specified conditions.

• Soluble: Substances with large solubility.

• Insoluble: Substances with low solubility, readily precipitate.

• Precipitate: Solid formed when concentration exceeds solubility.

Solubility Rules Table (Main Purpose: Classification)

Ion	Solubility	Exceptions
NO3-, Na+, K+, NH4+	Soluble	None
Cl-, Br-, I-	Soluble	Compounds with Ag+, Hg22+, Pb2+
SO42-	Soluble	Compounds with Ba2+, Pb2+, Ca2+, Sr2+
CO32-, PO43-	Insoluble	Compounds with group 1 ions and NH4+
OH-	Insoluble	Compounds with group 1 ions, Ba2+

Acid-Base Reactions

Definition and Examples

An acid-base reaction involves the transfer of a hydrogen ion (H+) from one species to another. Acids yield hydronium ions (H3O+) in water, while bases yield hydroxide ions (OH-).

• Strong acids: Completely ionize in water (e.g., HCl, HNO3, H2SO4).

• Weak acids: Partially ionize (e.g., CH3COOH).

• Strong bases: Ionic hydroxides (e.g., NaOH, KOH) that dissociate completely.

• Weak bases: Partially react with water (e.g., NH3).

Example: $\mathrm{HCl(aq) + H_2O(l) \rightarrow H_3O^+(aq) + Cl^-(aq)}$

Polyprotic Acids

• Monoprotic acids: One ionizable hydrogen atom per molecule.

• Polyprotic acids: More than one ionizable hydrogen atom, ionize in steps.

Example:

• $\mathrm{H_2SO_4(aq) \rightarrow H^+(aq) + HSO_4^-(aq)}$

• $\mathrm{HSO_4^-(aq) \rightarrow H^+(aq) + SO_4^{2-}(aq)}$

Neutralization Reactions

Neutralization occurs when an acid reacts with a base to produce a salt and water.

• Net ionic equation: $\mathrm{H^+(aq) + OH^-(aq) \rightarrow H_2O(l)}$

• Example: $\mathrm{Mg(OH)_2(s) + 2HCl(aq) \rightarrow MgCl_2(aq) + 2H_2O(l)}$

Oxidation-Reduction (Redox) Reactions

Definition and Half-Reactions

Redox reactions involve the transfer of electrons between reactants. Oxidation is the loss of electrons, while reduction is the gain of electrons. These processes occur simultaneously.

• Oxidation: Increase in oxidation number.

• Reduction: Decrease in oxidation number.

• Half-reactions: Show electron transfer for each species.

Example:

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

• Half-reactions: $\mathrm{2Na(s) \rightarrow 2Na^+(s) + 2e^-}$ $\mathrm{Cl_2(g) + 2e^- \rightarrow 2Cl^-(s)}$

Oxidizing and Reducing Agents

• Reducing agent: Species that donates electrons (is oxidized).

• Oxidizing agent: Species that accepts electrons (is reduced).

Example: In $\mathrm{2Na(s) + Cl_2(g) \rightarrow 2NaCl(s)}$, Na is the reducing agent, Cl2 is the oxidizing agent.

Practice and Application

Sample Problems

• Balance the following equation: $\mathrm{C_2H_6(g) + O_2(g) \rightarrow CO_2(g) + H_2O(g)}$

• Write net ionic equations for precipitation reactions.

• Predict products of acid-base and redox reactions.

Summary Table: Types of Chemical Reactions

Type	Description	Example
Synthesis	Two or more substances combine to form one product	$\mathrm{2H_2 + O_2 \rightarrow 2H_2O}$
Decomposition	One substance breaks down into two or more products	$\mathrm{2H_2O \rightarrow 2H_2 + O_2}$
Single Displacement	One element replaces another in a compound	$\mathrm{Zn + 2HCl \rightarrow ZnCl_2 + H_2}$
Double Displacement	Exchange of ions between two compounds	$\mathrm{AgNO_3 + NaCl \rightarrow AgCl + NaNO_3}$
Combustion	Substance reacts with oxygen, producing heat and light	$\mathrm{CH_4 + 2O_2 \rightarrow CO_2 + 2H_2O}$

Additional info: These notes expand on the provided slides by including definitions, examples, and tables for clarity and completeness, suitable for exam preparation in General Chemistry.