General Chemistry Study Guide: Solutions, Acid-Base, Redox, Atomic Structure, and Quantum Mechanics

Solutions and Concentrations

Solution Preparation and Molarity

Solutions are homogeneous mixtures of two or more substances. The concentration of a solution is often expressed in terms of molarity (M), which is the number of moles of solute per liter of solution.

• Molarity (M): $M = \frac{\text{moles of solute}}{\text{liters of solution}}$

• Example: Dissolving 7.25 g of cobalt(II) sulfate (CoSO4, molar mass 154.99 g/mol) in enough water to make 275.0 mL of solution. Calculate the molar concentration of sulfate ions.

• Dilution: When a solution is diluted, the number of moles of solute remains constant. $M_1V_1 = M_2V_2$

• Example: A 300.0 mL sample of KOH stock solution is diluted to 600.0 mL. If the diluted solution has a concentration of 0.210 M, what was the original concentration?

Precipitation Reactions and Net Ionic Equations

When two solutions are mixed, a precipitate may form if an insoluble compound is produced. The net ionic equation shows only the species that actually change during the reaction.

• Example: Mixing calcium chloride and sodium sulfate forms a precipitate of calcium sulfate. Calculate the mass of precipitate formed.

• Net Ionic Equation: Shows only the ions and molecules directly involved in the reaction.

Acid–Base Chemistry

Acids, Bases, and Spectator Ions

Acids donate protons (H+), and bases accept protons. In reactions, some ions do not participate and are called spectator ions.

• Bronsted–Lowry Definition: An acid is a proton donor, a base is a proton acceptor.

• Example: Ammonia (NH3) acts as a base by accepting a proton from water.

• Spectator Ions: Ions that do not participate in the actual chemical change.

pH Calculations and Neutralization

pH is a measure of the hydrogen ion concentration in a solution. Neutralization occurs when an acid and a base react to form water and a salt.

• pH Formula: $\text{pH} = -\log[\text{H}^+]$

• Example: Calculate the pH of a solution containing 3.50 × 10–4 M Ba(OH)2.

• Neutralization: $\text{acid} + \text{base} \rightarrow \text{salt} + \text{water}$

• Example: Calculate the mass of HCl needed to neutralize a given volume of NaOH.

Redox and Reaction Types

Oxidation and Reduction

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

• Oxidizing Agent: The species that is reduced (gains electrons).

• Reducing Agent: The species that is oxidized (loses electrons).

• Example: In Zn(s) + CuSO4(aq) → ZnSO4(aq) + Cu(s), Zn is oxidized and Cu2+ is reduced.

Assigning Oxidation Numbers

Oxidation numbers help track electron transfer in redox reactions.

• Rules: Elements in their standard state have an oxidation number of 0. Oxygen is usually –2, hydrogen is +1, and the sum of oxidation numbers in a compound equals the charge.

• Example: Assign oxidation numbers to sulfur in SO42– and chlorine in ClO4–.

Light, Energy, and the Bohr Model

Electromagnetic Radiation and Energy Calculations

Light exhibits both wave and particle properties. The energy of a photon is related to its frequency and wavelength.

• Key Equations:

  • $c = \lambda \nu$ (speed of light = wavelength × frequency)

  • $E = h\nu$ (energy of a photon)

  • $E = \frac{hc}{\lambda}$

• Example: Calculate the wavelength of microwave radiation with a given frequency.

• Example: Calculate the energy of a photon with a wavelength of 410 nm.

Bohr Model and Energy Levels

The Bohr model describes electrons in quantized energy levels around the nucleus. Transitions between levels involve absorption or emission of energy.

• Energy Level Formula (Hydrogen): $E_n = -\frac{R_H}{n^2}$

• Transition Energy: $\Delta E = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$

• Example: Calculate the energy difference between n = 5 and n = 2 in hydrogen.

Quantum Mechanics and Electron Configuration

de Broglie Wavelength

Particles such as electrons have wave-like properties. The de Broglie equation relates a particle's momentum to its wavelength.

• de Broglie Equation: $\lambda = \frac{h}{mv}$

• Example: Calculate the wavelength of an electron moving at a given speed.

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 (–l to +l)

• Spin Quantum Number (ms): Spin (+½ or –½)

• Allowed Sets: Not all combinations are allowed; for example, l cannot be equal to or greater than n.

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals, following the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

• Example: Write ground-state electron configurations for Fe, Br–, and V.

• Valence Electrons: Electrons in the outermost shell, important for chemical reactivity.

• Exceptions: Some elements (e.g., chromium) have electron configurations that differ from the expected order due to stability of half-filled or fully filled subshells.

Atomic Orbitals and Nodes

Atomic orbitals have regions called nodes where the probability of finding an electron is zero. The number of nodes increases with the principal quantum number n.

• Types of Nodes: Radial (spherical) and angular (planar).

• Relationship: Number of nodes = n – 1.

Atomic Structure Concepts

• Electrons have both wave and particle properties (wave-particle duality).

• Heisenberg uncertainty principle: It is impossible to know both the exact position and momentum of an electron simultaneously.

• Each orbital can hold up to two electrons with opposite spins.

• 4p orbitals are higher in energy than 3d orbitals.

Useful Constants and Conversion Factors

• Speed of light, $c = 2.998 \times 10^8$ m/s

• Planck's constant, $h = 6.626 \times 10^{-34}$ J·s

• Avogadro's number, $N_A = 6.022 \times 10^{23}$ mol–1

• Rydberg constant, $R_H = 2.179 \times 10^{-18}$ J

Prefix	Symbol	Meaning	Value
kilo	k	103	1,000
centi	c	10–2	0.01
milli	m	10–3	0.001
micro	μ	10–6	0.000001
nano	n	10–9	0.000000001
pico	p	10–12	0.000000000001
femto	f	10–15	0.000000000000001

Periodic Table

The periodic table organizes elements by increasing atomic number and similar chemical properties. Groups (columns) have similar valence electron configurations, which determine chemical reactivity.

Additional info: The periodic table and constants are essential reference tools for solving general chemistry problems, including those involving stoichiometry, atomic structure, and quantum mechanics.