Exam III Review

Chapter 5: Electronic Structure and Periodicity

Electron Configurations of Ions

Understanding how electrons are arranged in ions is crucial for predicting chemical properties and reactivity.

• Electron Configuration: The distribution of electrons among the orbitals of an atom or ion.

• For cations: Electrons are removed first from the highest principal quantum number (n) orbital.

• For anions: Electrons are added to the lowest available energy orbital.

• Example: Na+ has the same electron configuration as Ne: 1s2 2s2 2p6.

Atomic and Ionic Radius Trends

Atomic and ionic radii vary systematically across the periodic table due to changes in nuclear charge and electron shielding.

• Atomic Radius: Decreases across a period (left to right), increases down a group.

• Ionic Radius: Cations are smaller than their parent atoms; anions are larger.

• Isoelectronic Series: For ions with the same number of electrons, the more positive the charge, the smaller the radius.

• Example: The ionic radius of Na+ is smaller than that of Cl- and larger than that of Al3+.

Slater's Rules for Effective Nuclear Charge (Zeff)

Slater's rules provide a method to estimate the effective nuclear charge experienced by an electron in a multi-electron atom.

• Effective Nuclear Charge (Zeff): The net positive charge experienced by an electron, accounting for shielding by other electrons.

• Formula: $Z_{eff} = Z - S$ where $Z$ is the atomic number and $S$ is the shielding constant.

• Application: Explains trends in atomic size, ionization energy, and electron affinity.

Chapter 6: Molecular Orbital Theory and Hybridization

General Molecular Orbital (MO) Theory

Molecular Orbital Theory describes the distribution of electrons in molecules in terms of molecular orbitals that can extend over the entire molecule.

• Bonding and Antibonding Orbitals: Constructive overlap forms bonding orbitals; destructive overlap forms antibonding orbitals.

• Bond Order: $\text{Bond Order} = \frac{1}{2}(\text{number of bonding electrons} - \text{number of antibonding electrons})$

• Example: O2 has a bond order of 2 and is paramagnetic due to unpaired electrons in π* orbitals.

Homomolecular and Heteromolecular Diatomics MO Theory

• Homomolecular Diatomics: Molecules composed of two identical atoms (e.g., N2, O2).

• Heteromolecular Diatomics: Molecules composed of two different atoms (e.g., CO, NO).

• Energy Ordering: For lighter elements (up to N2), σ2p is higher in energy than π2p; for heavier elements, the order reverses.

Hybridization of Atomic Orbitals

Hybridization is the mixing of atomic orbitals to form new hybrid orbitals suitable for the pairing of electrons to form chemical bonds.

• sp: Linear geometry, 180° bond angle.

• sp2: Trigonal planar geometry, 120° bond angle.

• sp3: Tetrahedral geometry, 109.5° bond angle.

• sp3d: Trigonal bipyramidal geometry, 90° and 120° bond angles.

• sp3d2: Octahedral geometry, 90° bond angles.

• Example: The central atom in BF3 is sp2 hybridized.

Multiple Bonding

• σ (Sigma) Bonds: Formed by head-on overlap of orbitals.

• π (Pi) Bonds: Formed by side-on overlap of p orbitals.

• Double Bond: Consists of one σ and one π bond.

• Triple Bond: Consists of one σ and two π bonds.

Chapter 12: Thermochemistry

Thermochemical Definitions

Thermochemistry deals with the heat changes that accompany chemical reactions.

• System: The part of the universe being studied.

• Surroundings: Everything outside the system.

• Enthalpy (H): The heat content of a system at constant pressure.

The First Law of Thermodynamics

• Statement: Energy cannot be created or destroyed, only transferred or transformed.

• Mathematical Form: $\Delta E = q + w$ where $\Delta E$ is the change in internal energy, $q$ is heat, and $w$ is work.

P-V Expansion Work

• Work Done by a Gas: $w = -P_{ext} \Delta V$

• Sign Convention: Work done by the system is negative.

Heat Capacity and Specific Heat

• Heat Capacity (C): Amount of heat required to raise the temperature of a substance by 1 K.

• Specific Heat (c): Amount of heat required to raise 1 g of a substance by 1 K.

• Formula: $q = mc\Delta T$

Calorimetry

• Calorimetry: Experimental technique to measure heat changes in chemical reactions.

• Example: Mixing HCl and NaOH in a calorimeter to measure the heat of neutralization.

Enthalpy (ΔH)

• ΔH: Change in enthalpy at constant pressure.

• ΔHf°: Standard enthalpy of formation; enthalpy change when 1 mole of a compound forms from its elements in their standard states.

• ΔHrxn: Enthalpy change for a reaction; can be calculated using Hess's Law.

Thermochemical Equations and Hess's Law

• Thermochemical Equation: A balanced chemical equation that includes the enthalpy change.

• Hess's Law: The enthalpy change for a reaction is the same, regardless of the number of steps.

• Formula: $\Delta H_{rxn} = \sum \Delta H_f^{\circ} (\text{products}) - \sum \Delta H_f^{\circ} (\text{reactants})$

Chapter 9: Gases and Their Properties

Concepts of Pressure, Temperature, Volume, and Moles

• Pressure (P): Force per unit area; measured in atmospheres (atm), pascals (Pa), or torr.

• Temperature (T): Measure of average kinetic energy; measured in Kelvin (K).

• Volume (V): Space occupied by a gas; measured in liters (L).

• Moles (n): Amount of substance; 1 mole = 6.022 × 1023 particles.

Gas Laws

• Boyle's Law: $P_1V_1 = P_2V_2$ (at constant T and n)

• Charles's Law: $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ (at constant P and n)

• Avogadro's Law: $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ (at constant P and T)

• Ideal Gas Law: $PV = nRT$

• R (Gas Constant): 0.0821 L·atm·mol-1·K-1

Deviations from Ideality: van der Waals Equation

• Real Gases: Deviate from ideal behavior at high pressures and low temperatures.

• van der Waals Equation: $\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT$

• a and b: Constants that account for intermolecular forces and finite molecular size.

Gas Densities and Molar Mass

• Density (d): $d = \frac{PM}{RT}$ where M is molar mass.

• Application: Used to identify gases and calculate molar mass from experimental data.

Kinetic Molecular Theory (KMT)

• Postulates:

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

  • Collisions are elastic; total kinetic energy is conserved.

  • Average kinetic energy is proportional to temperature (in K).

  • Volume of particles is negligible compared to the volume of the container.

• Root Mean Square Speed: $u_{rms} = \sqrt{\frac{3RT}{M}}$

Graham's Law of Effusion and Diffusion

• Effusion: The process by which gas molecules escape through a small hole.

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

• Application: Lighter gases effuse and diffuse faster than heavier gases.

Sample Table: Thermochemical Data

The following table summarizes standard enthalpies of formation and combustion for selected compounds (values in kJ/mol):

Compound/Reaction	ΔHf° (kJ/mol)	ΔHcomb° (kJ/mol)
CH4(g)	-74.8	-890.3
C2H6(g)	-84.7	-1560.0
CO2(g)	-393.5	—
H2O(l)	-285.8	—
H2(g)	0	—

Additional info: Table values are representative; consult your textbook or data tables for more precise values.

Key Examples and Applications

• Calculating Enthalpy Change: Use standard enthalpies of formation and Hess's Law to determine ΔH for reactions.

• Predicting Hybridization: Use steric number (number of atoms bonded + lone pairs) to determine hybridization of central atom.

• Gas Law Problems: Apply the ideal gas law and related equations to solve for unknowns such as pressure, volume, or temperature.

• Effusion and Diffusion: Use Graham's Law to compare rates for different gases.