General Chemistry Exam Review: Atomic Structure, Quantum Mechanics, Chemical Reactions, and Solution Chemistry

Atomic Structure and Electron Configuration

Electron Configuration of Ions

Electron configuration describes the arrangement of electrons in an atom or ion. For ions, electrons are added or removed according to the charge.

• Magnesium ion (Mg2+): Loses two electrons from its neutral state, resulting in the configuration $1s^2 2s^2 2p^6$.

• Example: Mg: $1s^2 2s^2 2p^6 3s^2$; Mg2+: $1s^2 2s^2 2p^6$

Electron Configuration and Element Identification

Electron configurations can be used to identify elements and ions. For example, $1s^2 2s^2 2p^6 3s^2 3p^1$ corresponds to Al+.

• Key Point: The number of electrons matches the atomic number minus the charge.

Quantum Mechanics and Atomic Theory

Frequency and Wavelength of Light

The frequency ($\nu$) of light is related to its wavelength ($\lambda$) by the equation:

• $c = \lambda \nu$

• Where $c$ is the speed of light ($3.00 \times 10^8$ m/s).

• Example: For $\lambda = 540$ nm, $\nu = \frac{c}{\lambda}$

Photon Emission in Hydrogen Atom

When an electron relaxes from a higher energy level to a lower one, it emits a photon. The frequency of the photon is given by:

• $E = h\nu$

• Where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s).

• Example: Transition from $n=2$ to $n=1$ in hydrogen emits a photon with a specific frequency.

Uncertainty Principle

The Heisenberg Uncertainty Principle states that it is impossible to know both the exact position and momentum of a particle simultaneously.

• Key Point: $\Delta x \cdot \Delta p \geq \frac{h}{4\pi}$

• Example: The more precisely position is known, the less precisely momentum can be known.

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and electrons:

• Principal quantum number ($n$): Energy level (integer, $n \geq 1$)

• Angular momentum quantum number ($l$): Shape of orbital ($0 \leq l < n$)

• Magnetic quantum number ($m_l$): Orientation ($-l \leq m_l \leq l$)

• Spin quantum number ($m_s$): Spin ($+1/2$ or $-1/2$)

• Example: $n=3, l=2, m_l=2, m_s=+1/2$ is valid.

Angular Nodes in Orbitals

Angular nodes are regions where the probability of finding an electron is zero due to the angular part of the wavefunction.

• d orbitals: Number of angular nodes = $l$ (for d, $l=2$)

• Example: d orbital has 2 angular nodes.

Chemical Bonding and Reactions

Net Ionic Equations

Net ionic equations show only the species that participate in the chemical change.

• Example: NH4+ (aq) + NO3- (aq) → NH4NO3 (aq)

Precipitation Reactions

When two solutions are mixed, a precipitate may form if an insoluble product is produced.

• Example: AgNO3 + BaCl2 → AgCl (precipitate) + Ba(NO3)2

Electrolytes

Electrolytes are substances that conduct electricity when dissolved in water. Strong electrolytes dissociate completely.

• Strong electrolytes: Ionic compounds like BaI2, NaCl, K2SO4

• Weak electrolytes: Weak acids and bases, e.g., CH3COOH

Conductivity of Liquids

Conductivity depends on the presence of ions. Pure water and some liquids do not conduct electricity well.

• Example: Mercury is a metal and conducts electricity; water is a poor conductor unless ions are present.

Solution Chemistry and Stoichiometry

Molarity Calculations

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

• $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$

• Example: Dissolving 0.90 g of LiBrO2 in 86.80 mL water: calculate moles, then divide by volume in liters.

Stoichiometry of Precipitate Formation

Stoichiometry allows calculation of the mass of precipitate formed in a reaction.

• Example: Pb(NO3)2 + KI → PbI2 (precipitate) + 2KNO3

• Calculate moles of Pb(NO3)2 and use molar mass of PbI2 to find mass.

Ion Counting in Solutions

Some compounds produce more ions per formula unit when dissolved.

• Example: FeCl3 dissociates into 4 ions: Fe3+ and 3Cl-

Physical Chemistry: Energy and Wavelength

Photon Counting and Energy

The energy of a photon is given by $E = h\nu$. The number of photons in a pulse of energy is:

• $\text{Number of photons} = \frac{\text{Total energy}}{E_{\text{photon}}}$

de Broglie Wavelength

All matter has wave-like properties. The de Broglie wavelength is:

• $\lambda = \frac{h}{mv}$

• Where $m$ is mass, $v$ is velocity.

• Example: For a 60 kg person running at 10 m/s, $\lambda = \frac{6.626 \times 10^{-34}}{60 \times 10}$

Speed of Electron for Given Wavelength

The speed required for an electron to have a certain wavelength is found using the de Broglie equation.

• $v = \frac{h}{m\lambda}$

• Example: For $\lambda = 200$ pm, $m = 9.11 \times 10^{-31}$ kg

HTML Table: Comparison of Electrolytes

Compound	Type	Electrolyte Strength
BaI2	Ionic	Strong
CH3COOH	Weak acid	Weak
NaCl	Ionic	Strong
CH3OH	Molecular	None

HTML Table: Quantum Numbers

Quantum Number	Symbol	Possible Values	Physical Meaning
Principal	n	1, 2, 3, ...	Energy level
Angular Momentum	l	0 to n-1	Orbital shape
Magnetic	ml	-l to +l	Orbital orientation
Spin	ms	+1/2, -1/2	Electron spin

Additional info:

• Some questions reference calculations (e.g., molarity, photon energy) that require use of standard chemistry equations.

• All topics are foundational for a first-year college General Chemistry course.