General Chemistry Exam 2 Study Guide

Atomic Structure and Quantum Theory

Electron Configuration and Quantum Numbers

Understanding atomic structure is fundamental in chemistry. Electrons occupy orbitals defined by quantum numbers, which describe their energy, shape, and orientation.

• Principal Quantum Number (n): Indicates the energy level (shell) of an electron.

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

• Magnetic Quantum Number (ml): Specifies the orientation of the orbital.

• Spin Quantum Number (ms): Describes the spin direction of the electron.

• Example: For n = 5, possible values of l are 0, 1, 2, 3, 4.

Key Equations:

• $E = h\nu$ (Energy of a photon)

• $\Delta E = 2.18 \times 10^{-18} \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)$ (Energy change for electron transitions in hydrogen)

Bohr Model and Quantum Mechanics

The Bohr model describes electrons in fixed orbits around the nucleus, but quantum mechanics shows electrons exist in probability clouds (orbitals).

• Bohr Model: Electrons transition between energy levels, emitting or absorbing photons.

• Quantum Mechanical Model: Electrons have wave-particle duality and are described by wavefunctions.

• Example: When an electron moves from n = 4 to n = 2, energy is emitted as a photon.

Chemical Bonding and Reactions

Balancing Chemical Equations

Balancing equations ensures the conservation of mass and charge in chemical reactions.

• Steps:

  1. Write the unbalanced equation.

  2. Count atoms of each element on both sides.

  3. Add coefficients to balance atoms.

  4. Check that all atoms and charges are balanced.

• Example: $3NO_2 + H_2O_2 \rightarrow 2HNO_3 + NO$

Types of Chemical Reactions

• Precipitation Reactions: Formation of an insoluble product (precipitate) from soluble reactants.

• Redox Reactions: Transfer of electrons between species; involves changes in oxidation states.

• Acid-Base Reactions: Transfer of protons (H+) between reactants.

• Example: $Fe_2O_3 + 3C \rightarrow 4Fe + 3CO_2$ (Redox reaction)

Stoichiometry

Stoichiometry involves calculating the amounts of reactants and products in chemical reactions.

• Mole Concept: 1 mole = $6.022 \times 10^{23}$ particles.

• Key Equations:

  • $\text{Molarity} = \frac{\text{mol solute}}{\text{L solution}}$

  • $\text{Percent yield} = \frac{\text{actual}}{\text{theoretical}} \times 100$

• Example: Calculating grams of KNO3 needed for a solution of given molarity.

States of Matter and Gas Laws

Properties of Gases

Gases have unique properties described by the kinetic molecular theory and gas laws.

• Kinetic Molecular Theory:

  • Gases consist of tiny particles in constant, random motion.

  • Collisions are elastic; no energy is lost.

  • Volume of particles is negligible compared to container.

  • No attractive or repulsive forces between particles.

• Ideal Gas Law: $PV = nRT$

• Partial Pressure: $P_{\text{total}} = P_1 + P_2 + P_3 + \ldots$

• Example: Calculating the pressure exerted by a gas in a container.

Gas Stoichiometry and Molar Volume

• Standard Temperature and Pressure (STP): 0°C and 1 atm; 1 mole of gas occupies 22.4 L.

• Gas Collection Over Water: Account for vapor pressure of water when collecting gases.

• Example: Calculating the amount of hydrogen gas collected over water.

Deviations from Ideal Gas Behavior

Real gases deviate from ideal behavior at high pressures and low temperatures due to intermolecular forces and finite particle volume.

• Van der Waals Equation: Adjusts the ideal gas law for real gases.

• Example: Explaining why a gas sample does not behave ideally under certain conditions.

Solutions and Solubility

Types of Solutions and Solubility Rules

Solutions are homogeneous mixtures of solute and solvent. Solubility depends on the nature of the solute and solvent.

• Electrolytes: Substances that conduct electricity when dissolved in water.

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

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

• Non-Electrolytes: Do not dissociate (e.g., sugar).

• Example: Comparing the conductivity of different ionic compounds in water.

Concentration Units

• Molarity (M): $\text{M} = \frac{\text{mol solute}}{\text{L solution}}$

• Percent by Mass: $\text{percent} = \frac{\text{part}}{\text{whole}} \times 100$

• Parts per Million (ppm): $\text{ppm} = \frac{\text{part}}{\text{whole}} \times 10^6$

• Example: Calculating the concentration of AlBr3 in a solution.

Thermochemistry and Energy

Energy Changes in Chemical Reactions

Chemical reactions involve energy changes, often in the form of heat or light.

• Endothermic Reactions: Absorb energy from surroundings.

• Exothermic Reactions: Release energy to surroundings.

• Example: Thermite reaction producing molten metal.

Calculating Energy and Work

• Key Equations:

  • $q = mC\Delta T$ (heat transfer)

  • $\Delta E = q + w$ (change in internal energy)

Electrochemistry and Redox Reactions

Oxidation States and Redox Processes

Redox reactions involve the transfer of electrons, changing the oxidation states of elements.

• Oxidation: Loss of electrons; increase in oxidation state.

• Reduction: Gain of electrons; decrease in oxidation state.

• Example: Determining the change in oxidation state for iron in a reaction.

Experimental Techniques and Calculations

Preparation of Solutions

Preparing solutions of known concentration is a common laboratory procedure.

• Steps:

  1. Calculate the required mass or volume of solute.

  2. Dissolve in solvent and dilute to final volume.

  3. Use appropriate glassware for accuracy.

• Example: Preparing 0.0500 M CuSO4 from a 1.00 M stock solution.

Chromium Removal from Water

Chromium can be removed from water by precipitation as Cr(OH)3 using NaOH.

• Key Equation: $\text{Volume NaOH} = \frac{\text{mol Cr}^{3+}}{\text{M NaOH}}$

Tables and Constants

Vapor Pressure of Water

The vapor pressure of water varies with temperature and is important for gas collection experiments.

Temperature (°C)	Vapor Pressure (mmHg)
0	4.6
10	9.2
20	17.5
25	23.8
30	31.8
40	55.3
45	71.9

Additional info: Table values inferred from standard vapor pressure data.

Useful Constants

• Avogadro's number: $6.022 \times 10^{23}$ particles/mol

• Gas constant: $R = 0.0821$ L·atm/(mol·K)

• Standard pressure: 1 atm = 760 mmHg

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

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

Quantum Mechanics and Light

Wave-Particle Duality

Light and electrons exhibit both wave-like and particle-like properties, as demonstrated by key experiments.

• Photoelectric Effect: Light can eject electrons from a metal surface, showing particle behavior.

• Double-Slit Experiment: Electrons produce interference patterns, showing wave behavior.

• Electromagnetic Waves: Wavelength and frequency are inversely related; energy increases with frequency.

• Example: Comparing the energy and wavelength of two waves.

Extra Credit: Gas Effusion and Molecular Formula

Effusion and Graham's Law

Effusion rate of a gas is inversely proportional to the square root of its molar mass.

• Graham's Law: $\text{Rate}_1/\text{Rate}_2 = \sqrt{M_2/M_1}$

• Application: Determining the molecular formula of an unknown gas from effusion data.