Chapter 3: Composition of Solutions and Stoichiometry of Chemical Reactions

Balancing Chemical Equations

Chemical equations must be balanced to obey the law of conservation of mass. This ensures that the number of atoms of each element is the same on both sides of the equation.

• Key Point: Adjust coefficients (not subscripts) to balance atoms.

• Example:

Avogadro’s Number as a Unit Conversion

Avogadro’s number () is used to convert between moles and number of particles (atoms, molecules, ions).

• Key Point: $1= 6.022 \times 10^{23}$ particles

• Example: $2\ce{Na}= 2 \times 6.022 \times 10^{23} = 1.204 \times 10^{24}$ atoms

Mole-to-Mole and Gram-to-Gram Conversions

Stoichiometry allows conversion between amounts of reactants and products using balanced equations.

• Key Point: Use molar ratios from the balanced equation for conversions.

• Example: : $2\ce{H_2} moles .

• Formula:

Limiting Reactant Problems

The limiting reactant is the reactant that is completely consumed first, limiting the amount of product formed.

• Key Point: Calculate the amount of product formed from each reactant; the smallest amount determines the limiting reactant.

• Example: If $5\ce{H_2} g react, determine which runs out first using molar masses and stoichiometry.

Percent Yield Calculation

Percent yield compares the actual yield to the theoretical yield.

• Formula:

• Example: If theoretical yield is $10 g, percent yield is .

Electrolytes: Strong, Weak, and Nonelectrolytes

Electrolytes are substances that conduct electricity when dissolved in water.

• Strong Electrolyte: Completely dissociates (e.g., )

• Weak Electrolyte: Partially dissociates (e.g., )

• Nonelectrolyte: Does not dissociate (e.g., )

Ionic and Net Ionic Equations

Ionic equations show all ions in solution; net ionic equations show only the species that change during the reaction.

• Example:

• Ionic Equation:

• Net Ionic Equation:

Redox Reactions: Oxidation and Reduction

Redox reactions involve the transfer of electrons. Oxidation is loss of electrons; reduction is gain of electrons.

• Oxidizing Agent: Causes oxidation (is reduced)

• Reducing Agent: Causes reduction (is oxidized)

• Example:

• Zn is oxidized; Cu2+ is reduced.

Titration Calculations

Titration is used to determine the concentration of a solution by reacting it with a solution of known concentration.

• Formula: (for 1:1 stoichiometry)

• Example: M neutralizes $0.1$ M in equal volumes.

Dilution Calculations

Dilution involves adding solvent to decrease the concentration of a solution.

• Formula:

• Example: To make $100 M solution from M stock: mL stock solution, dilute to $100$ mL.

Chapter 4: Reactions in Aqueous Solutions

Solute and Solvent Identification

A solution consists of a solute (substance dissolved) and a solvent (substance doing the dissolving, usually present in greater amount).

• Example: In saltwater, NaCl is the solute, H2O is the solvent.

Electrolyte Classification

See above for definitions of strong, weak, and nonelectrolytes.

Types of Reactions in Aqueous Solution

Common types include acid-base, precipitation, and redox reactions.

• Acid-Base Reaction: Transfer of H+ ion

• Precipitation Reaction: Formation of an insoluble solid

• Redox Reaction: Transfer of electrons

• Example: (acid-base)

Ionic and Net Ionic Equations

See above for method and examples.

Acids and Bases: Definitions and Identification

Acids donate H+ ions; bases accept H+ ions (Brønsted-Lowry definition).

• Strong Acids: , ,

• Weak Acids:

• Strong Bases: ,

• Weak Bases:

Assigning Oxidation Numbers

Oxidation numbers help track electron transfer in redox reactions.

• Rules: Elements = 0; Group 1 = +1; Group 2 = +2; Oxygen = -2 (except in peroxides); Hydrogen = +1 (with nonmetals), -1 (with metals)

• Example: In , H = +1, O = -2

Identifying Oxidized/Reduced Species and Agents

See above for definitions and examples.

Molarity Calculations

Molarity () is the number of moles of solute per liter of solution.

• Formula:

• Example: moles in $1M = 0.5$ M

Using Molarity as a Conversion Factor

Molarity can convert between volume of solution and moles of solute.

• Example: L of M solution contains moles solute.

Solution Stoichiometry and Dilution

Use molarity and volume to relate amounts of reactants and products in solution reactions.

• Formula: for dilution

Titration Calculations

See above for method and formula.

Chapter 5: Electromagnetic Spectrum and Periodicity

Wavelength, Frequency, and Energy Calculations

Light has both wave and particle properties. The energy, wavelength, and frequency of light are related by fundamental equations.

• Speed of Light:

• Energy of a Photon:

• Where: m/s, J·s

• Example: Calculate energy of a photon with nm: J

Electron Transitions and Energy

Electron transitions between energy levels in atoms result in absorption or emission of photons with specific energies.

• High Energy Transition: Large jump between levels (short wavelength, high frequency)

• Low Energy Transition: Small jump between levels (long wavelength, low frequency)

De Broglie Wavelength of Moving Objects

All matter has wave-like properties, described by the de Broglie equation.

• Formula:

• Where: = mass (kg), = velocity (m/s)

• Example: Calculate for an electron moving at m/s.

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and electrons.

• n: Principal quantum number (energy level, )

• l: Angular momentum quantum number ( to )

• m_l: Magnetic quantum number ( to )

• m_s: Spin quantum number ( or )

Electron Configurations

Electron configurations show the arrangement of electrons in an atom or ion.

• Long-hand: List all occupied orbitals (e.g., )

• Abbreviated: Use noble gas core (e.g., for S)

• Up to n = 5: Include all orbitals up to

Periodic Trends

Properties of elements change predictably across periods and groups.

• Example: Na has a larger atomic radius than Cl; Cl has higher electronegativity than Na.

Additional info: These notes expand on the study guide points with definitions, formulas, and examples for clarity and completeness, suitable for exam preparation in General Chemistry.