General Chemistry Study Guide: Periodic Properties, Chemical Bonding, Molecular Geometry, and Gases

Chapter 7: Periodic Properties of the Elements

7.2 Effective Nuclear Charge

The effective nuclear charge (Zeff) is the net positive charge experienced by an electron in a multi-electron atom. It accounts for both the attraction to the nucleus and the repulsion from other electrons.

• Definition: The effective nuclear charge is calculated as $Z_{eff} = Z - S$, where Z is the atomic number and S is the screening constant.

• Trend: Zeff increases across a period and slightly increases down a group.

• Example: For a 3p electron in phosphorus (Z = 15), the effective nuclear charge is less than 15 due to electron shielding.

7.3 Sizes of Atoms and Ions

The atomic radius is a measure of the size of an atom, typically the distance from the nucleus to the outermost electron shell. Ionic radii refer to the size of ions.

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

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

• Example: Na+ is smaller than Na; Cl- is larger than Cl.

7.4 Ionization Energy and Electron Affinity

Ionization energy is the energy required to remove an electron from a gaseous atom. Electron affinity is the energy change when an electron is added to a gaseous atom.

• Ionization Energy Trend: Increases across a period, decreases down a group.

• Electron Affinity Trend: Generally becomes more negative across a period.

• Equation: $M(g) \rightarrow M^+(g) + e^-$ (Ionization)

• Example: First ionization energy of sodium is lower than that of chlorine.

Chapter 8: Basic Concepts of Chemical Bonding

8.1 Lewis Symbols and the Octet Rule

Lewis symbols represent valence electrons as dots around the chemical symbol. The octet rule states that atoms tend to gain, lose, or share electrons to achieve eight valence electrons.

• Application: Used to predict bonding in molecules.

• Example: Oxygen has six valence electrons; it forms two bonds to complete its octet.

8.2 Ionic Bonding

Ionic bonding occurs when electrons are transferred from one atom to another, resulting in oppositely charged ions that attract each other.

• Formation: Metal + Nonmetal → Ionic compound

• Equation: $Na + Cl \rightarrow Na^+ + Cl^- \rightarrow NaCl$

• Properties: High melting points, conduct electricity when molten.

8.3 Covalent Bonding

Covalent bonding involves the sharing of electron pairs between atoms, typically nonmetals.

• Single, Double, Triple Bonds: One, two, or three pairs of electrons shared.

• Example: $H_2O$ has two single covalent bonds.

8.4 Bond Polarity and Electronegativity

Bond polarity arises from differences in electronegativity, the ability of an atom to attract electrons in a bond.

• Polar Covalent Bond: Unequal sharing of electrons.

• Electronegativity Trend: Increases across a period, decreases down a group.

• Example: $HCl$ is polar; $Cl$ is more electronegative than $H$.

8.5 Drawing Lewis Structures

Lewis structures show how atoms are bonded and the arrangement of valence electrons.

• Steps: Count valence electrons, arrange atoms, connect with bonds, complete octets.

• Example: $CO_2$ has two double bonds between C and O.

8.6 Resonance Structures

Resonance structures are multiple valid Lewis structures for a molecule, differing only in electron placement.

• Example: $O_3$ (ozone) has two resonance forms.

8.7 Exceptions to the Octet Rule

Some molecules do not follow the octet rule, such as those with odd numbers of electrons, incomplete octets, or expanded octets.

• Example: $BF_3$ (boron trifluoride) has only six electrons around boron.

8.8 Strengths and Lengths of Single and Multiple Bonds

Bond strength increases and bond length decreases with the number of shared electron pairs.

• Single Bond: Longest and weakest.

• Triple Bond: Shortest and strongest.

• Example: $N_2$ has a triple bond, making it very strong and short.

Chapter 9: Molecular Geometry and Bonding Theories

9.1 Molecular Shapes

The shape of a molecule is determined by the arrangement of atoms and electron pairs around the central atom.

• Common Shapes: Linear, bent, trigonal planar, tetrahedral, trigonal bipyramidal, octahedral.

• Example: $CH_4$ is tetrahedral.

9.2 The VSEPR Model

The Valence Shell Electron Pair Repulsion (VSEPR) model predicts molecular geometry based on repulsion between electron pairs.

• Principle: Electron pairs arrange to minimize repulsion.

• Example: $H_2O$ is bent due to two lone pairs on oxygen.

9.3 Molecular Shape and Molecular Polarity

Molecular polarity depends on both bond polarity and molecular shape.

• Polar Molecules: Have a net dipole moment.

• Nonpolar Molecules: Symmetrical shape cancels dipoles.

• Example: $CO_2$ is linear and nonpolar; $H_2O$ is bent and polar.

9.4 Covalent Bonding and Orbital Overlap

Covalent bonds form when atomic orbitals overlap, allowing electrons to be shared.

• Sigma (σ) Bonds: Head-on overlap.

• Pi (π) Bonds: Side-on overlap.

• Example: $C_2H_4$ (ethene) has a double bond: one σ and one π bond.

9.5 Hybrid Orbitals

Hybridization is the mixing of atomic orbitals to form new, equivalent hybrid orbitals.

• Types: sp, sp2, sp3

• Example: $CH_4$ uses sp3 hybrid orbitals.

9.6 Multiple Bonds

Multiple bonds consist of one sigma bond and one or more pi bonds.

• Double Bond: One σ and one π bond.

• Triple Bond: One σ and two π bonds.

• Example: $N_2$ has a triple bond.

Chapter 10: Gases

10.1 Physical Characteristics of Gases

Gases have unique physical properties: they expand to fill their container, are compressible, and have low densities.

• Example: Air in a balloon expands to fill the shape of the balloon.

10.2 The Gas Laws

The gas laws describe the relationships between pressure, volume, temperature, and amount of gas.

• 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)

10.3 The Ideal-Gas Equation

The ideal-gas equation combines the gas laws into a single relationship.

• Equation: $PV = nRT$

• Variables: P = pressure, V = volume, n = moles, R = gas constant, T = temperature

• Example: Calculate the volume of 1 mole of gas at STP.

10.4 Gas Mixtures and Partial Pressures

In a mixture of gases, each gas exerts a partial pressure proportional to its amount.

• Dalton's Law: $P_{total} = P_1 + P_2 + ... + P_n$

• Example: Air is a mixture of N2, O2, CO2, etc.

10.5 The Kinetic-Molecular Theory of Gases

The kinetic-molecular theory explains gas behavior in terms of particle motion.

• Postulates: Gases consist of tiny particles in constant, random motion; collisions are elastic.

• Equation: $KE_{avg} = \frac{3}{2}RT$ (per mole)

10.6 Molecular Speeds, Effusion, and Diffusion

Gas particles move at different speeds, and their movement leads to effusion (escape through a small hole) and diffusion (mixing).

• Graham's Law: $\frac{rate_1}{rate_2} = \sqrt{\frac{M_2}{M_1}}$

• Example: Lighter gases effuse faster than heavier gases.