General Chemistry Study Guide: Atomic Structure, Bonding, and Solutions

Atomic Structure and Quantum Theory

Energy of a Photon

The energy of a photon can be calculated using its wavelength or frequency. This is fundamental to understanding how atoms absorb and emit light.

• Photon Energy Formula: The energy ($E$) of a photon is given by: $E = h\nu$ where $h$ is Planck's constant ($6.626 \times 10^{-34}\ \text{J} \cdot \text{s}$) and $\nu$ is the frequency in Hz.

• Relationship to Wavelength: $E = \dfrac{hc}{\lambda}$ where $c$ is the speed of light ($3.00 \times 10^8\ \text{m/s}$) and $\lambda$ is the wavelength in meters.

• Example: Calculate the energy of a photon with a wavelength of $500\ \text{nm}$. First, convert $500\ \text{nm}$ to meters: $500\ \text{nm} = 5.00 \times 10^{-7}\ \text{m}$. $E = \dfrac{(6.626 \times 10^{-34})(3.00 \times 10^8)}{5.00 \times 10^{-7}} = 3.97 \times 10^{-19}\ \text{J}$

Absorption vs. Emission Spectra

Atoms and molecules absorb and emit light at specific wavelengths, producing characteristic spectra.

• Absorption Spectrum: Shows dark lines or bands where light has been absorbed by electrons moving to higher energy levels.

• Emission Spectrum: Shows bright lines or bands where electrons fall to lower energy levels, emitting photons.

• Application: Used to identify elements in stars and laboratory samples.

Bohr Atom and Electron Transitions

The Bohr model describes electrons in quantized orbits around the nucleus, explaining atomic emission and absorption.

• Key Features:

  • Electrons occupy fixed energy levels (shells).

  • Energy is absorbed or emitted when electrons move between levels.

  • Limitations: Only accurately describes hydrogen-like atoms.

• Calculating Wavelength/Frequency: $\Delta E = E_f - E_i = -2.18 \times 10^{-18} \left( \dfrac{1}{n_f^2} - \dfrac{1}{n_i^2} \right)\ \text{J}$ where $n_i$ and $n_f$ are the initial and final energy levels.

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them.

• Principal Quantum Number ($n$): Indicates the main energy level.

• Angular Momentum Quantum Number ($l$): Indicates the shape of the orbital (s, p, d, f).

• Magnetic Quantum Number ($m_l$): Indicates the orientation of the orbital.

• Spin Quantum Number ($m_s$): Indicates the spin direction of the electron (+1/2 or -1/2).

Electron Configuration and Orbital Diagrams

Electron configurations show the distribution of electrons among orbitals. Orbital diagrams use arrows to represent electron spins.

• Aufbau Principle: Electrons fill the lowest energy orbitals first.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing up.

• Example: The electron configuration of oxygen (8 electrons): $1s^2\ 2s^2\ 2p^4$

Shapes of Atomic Orbitals

Atomic orbitals have characteristic shapes that influence chemical bonding.

• s orbitals: Spherical shape.

• p orbitals: Dumbbell-shaped, oriented along x, y, or z axes.

• d orbitals: Cloverleaf shapes or a donut with a dumbbell.

Electron Configurations of Ions

When atoms form ions, they gain or lose electrons to achieve a stable electron configuration.

• Cations: Lose electrons (e.g., Na → Na+).

• Anions: Gain electrons (e.g., Cl → Cl-).

Chemical Bonding and Molecular Structure

Lewis Structures

Lewis structures represent the arrangement of valence electrons in molecules and polyatomic ions.

• Steps:

  1. Count total valence electrons.

  2. Draw skeletal structure with single bonds.

  3. Distribute remaining electrons to complete octets.

  4. Use double/triple bonds if necessary.

• Example: CO2 has two double bonds between C and O.

Octet Rule and Exceptions

Most atoms aim for eight valence electrons, but there are exceptions.

• Common Exceptions: Hydrogen (2 electrons), Boron (6 electrons), expanded octets (e.g., SF6).

Resonance Structures and Formal Charge

Some molecules have multiple valid Lewis structures (resonance). Formal charge helps determine the most stable structure.

• Formal Charge Formula: Formal charge = (valence electrons) - (nonbonding electrons) - 1/2(bonding electrons)

• Example: Ozone (O3) has two resonance structures.

Bond Energy and Bond Length

Bond energy is the energy required to break a bond; bond length is the distance between nuclei of bonded atoms.

• Relationship: Generally, shorter bonds are stronger (higher bond energy).

• Calculating Reaction Enthalpy: $\Delta H = \sum \text{(bond energies of bonds broken)} - \sum \text{(bond energies of bonds formed)}$

VSEPR Theory and Molecular Geometry

Valence Shell Electron Pair Repulsion (VSEPR) theory predicts the shapes of molecules based on electron pair repulsion.

• Common Geometries:

  • Linear: 180° (e.g., CO2)

  • Trigonal planar: 120° (e.g., BF3)

  • Tetrahedral: 109.5° (e.g., CH4)

  • Trigonal bipyramidal: 90°, 120° (e.g., PCl5)

  • Octahedral: 90° (e.g., SF6)

• Bond Angles: Determined by the number of bonding and lone pairs.

Molecular Polarity

Molecular polarity depends on bond polarity and molecular geometry.

• Polar Molecules: Have an uneven distribution of electron density (e.g., H2O).

• Nonpolar Molecules: Have a symmetrical distribution (e.g., CO2).

Composition and Solutions

Percent Composition

Percent composition expresses the mass percentage of each element in a compound.

• Formula: Percent composition = $\dfrac{\text{mass of element}}{\text{total mass of compound}} \times 100\%$

• Example: In H2O, %H = 11.2%, %O = 88.8%.

Empirical and Molecular Formulas

The empirical formula is the simplest whole-number ratio of elements; the molecular formula gives the actual number of atoms.

• Steps to Determine:

  1. Convert percent composition to grams.

  2. Convert grams to moles.

  3. Divide by the smallest number of moles to get the ratio.

  4. Use molar mass to find the molecular formula.

Electrolytes and Nonelectrolytes

Solutions can be classified based on their ability to conduct electricity.

• Strong Electrolytes: Completely dissociate in water (e.g., NaCl).

• Weak Electrolytes: Partially dissociate (e.g., acetic acid).

• Nonelectrolytes: Do not dissociate (e.g., sugar).

Dissociation Equations

When ionic compounds or acids dissolve in water, they dissociate into ions.

• Example: NaCl(s) → Na+(aq) + Cl-(aq)

• Acid Example: HCl(aq) → H+(aq) + Cl-(aq)

Calculating Molarity

Molarity (M) is the concentration of a solution, defined as moles of solute per liter of solution.

• Formula: $M = \dfrac{\text{moles of solute}}{\text{liters of solution}}$

• Example: 0.5 moles NaCl in 1.0 L solution: $M = 0.5\ \text{M}$

Dilution Calculations

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

• Formula: $M_1V_1 = M_2V_2$ where $M_1$ and $V_1$ are the initial molarity and volume, $M_2$ and $V_2$ are the final molarity and volume.

• Example: To dilute 100 mL of 2.0 M solution to 1.0 M: $2.0 \times 100 = 1.0 \times V_2 \implies V_2 = 200\ \text{mL}$

Summary Table: Types of Solutions

Type	Definition	Example
Strong Electrolyte	Completely dissociates in water	NaCl, HCl
Weak Electrolyte	Partially dissociates in water	CH3COOH
Nonelectrolyte	Does not dissociate in water	C6H12O6 (glucose)