General Chemistry I: Practice Problems and Key Concepts Study Guide

Atoms, Elements, and Atomic Structure

Atomic Symbols and Isotopes

Atoms are represented by symbols that indicate the element, atomic number, and mass number. Isotopes are atoms of the same element with different numbers of neutrons.

• Atomic Number (Z): Number of protons in the nucleus; defines the element.

• Mass Number (A): Total number of protons and neutrons.

• Isotopic Symbol: AZX, where X is the element symbol.

• Example: 188O has 8 protons and 10 neutrons.

Subatomic Particles

• Protons: Positively charged particles in the nucleus.

• Neutrons: Neutral particles in the nucleus.

• Electrons: Negatively charged particles in orbitals around the nucleus.

• Number of Electrons: In a neutral atom, equals the number of protons.

Electron Configuration

Describes the arrangement of electrons in an atom's orbitals.

• Follows the Aufbau principle, Pauli exclusion principle, and Hund's rule.

• Example: The electron configuration of Ca is 1s22s22p63s23p64s2.

Chemical Quantities and Calculations

Atomic Mass and Moles

• Atomic Mass Unit (amu): 1 amu = 1/12 the mass of a carbon-12 atom.

• Mole: Amount of substance containing Avogadro's number (6.022 × 1023) of particles.

• Conversions:

  • Mass (g) ↔ Moles ↔ Number of atoms/molecules

  • $\text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}$

  • $\text{Number of particles} = \text{Moles} \times 6.022 \times 10^{23}$

• Example: Calculate the number of atoms in 2.78 g of Ba.

Quantum Mechanical Model of the Atom

Quantum Numbers

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

• Principal Quantum Number (n): Energy level (n = 1, 2, 3, ...)

• Angular Momentum Quantum Number (l): Shape of orbital (l = 0 to n-1)

• Magnetic Quantum Number (ml): Orientation of orbital (ml = -l to +l)

• Spin Quantum Number (ms): Electron spin (+1/2 or -1/2)

Electron Orbitals and Shells

• Orbitals: Regions in space where electrons are likely to be found.

• Shells: Defined by n; each shell contains n2 orbitals.

• Subshells: s, p, d, f (l = 0, 1, 2, 3)

• Maximum electrons per shell: 2n2

• Example: The third shell (n = 3) contains 9 orbitals and can hold 18 electrons.

Periodic Properties of the Elements

Periodic Trends

• Ionization Energy: Energy required to remove an electron from an atom.

• Atomic Radius: Size of an atom; increases down a group, decreases across a period.

• Electron Configuration and Magnetism: Atoms with unpaired electrons are paramagnetic; all electrons paired are diamagnetic.

• Effective Nuclear Charge (Zeff): Net positive charge experienced by valence electrons.

Light and the Electromagnetic Spectrum

Wavelength, Frequency, and Energy

• Wavelength (λ): Distance between successive crests of a wave (in meters).

• Frequency (ν): Number of waves passing a point per second (in Hz).

• Speed of Light (c): $c = 3.00 \times 10^8$ m/s

• Relationship: $c = \lambda \nu$

• Energy of a Photon: $E = h \nu$ where $h = 6.626 \times 10^{-34}$ J·s

• Example: Calculate the wavelength of light with a frequency of $3.63 \times 10^{14}$ Hz.

Photoelectric Effect and Electron Transitions

• Absorption of a photon can cause an electron to move to a higher energy level.

• Shortest wavelength corresponds to the largest energy transition.

Significant Figures and Scientific Notation

• Significant Figures: Digits in a measurement that are known with certainty plus one estimated digit.

• Rules: All nonzero digits are significant; zeros between nonzero digits are significant; leading zeros are not significant; trailing zeros in a decimal number are significant.

• Example: 0.00250 has three significant figures.

Practice Problems and Applications

• Determine the number of protons, neutrons, and electrons in isotopes.

• Predict charges of ions based on group number.

• Calculate mass, moles, and number of atoms using atomic mass and Avogadro's number.

• Write electron configurations for ions and atoms.

• Draw orbital filling diagrams for valence electrons.

Sample Table: Quantum Numbers and Orbitals

Quantum Number	Symbol	Possible Values	Physical Meaning
Principal	n	1, 2, 3, ...	Energy level, shell
Angular Momentum	l	0 to n-1	Subshell (s, p, d, f)
Magnetic	ml	-l to +l	Orbital orientation
Spin	ms	+1/2, -1/2	Electron spin direction

Additional info: These study notes are based on a set of practice exam questions covering atomic structure, quantum mechanics, periodic trends, and basic calculations in general chemistry. The notes expand on the key concepts tested in the questions and provide formulas, definitions, and examples for exam preparation.