Comprehensive University Chemistry: Structure, Bonding, and Reactivity

Fundamental Principles of Atomic Structure

• Coulomb's Law is a primary foundation of chemistry. It states that the electrostatic force of attraction, $F$, is expressed as:
  $F \propto \frac{q_+ \times q_-}{r^2}$
  where $q_+$ and $q_-$ represent the charges on the objects (such as the nucleus, electrons, or ions) and $r^2$ is the square of the distance between their centers. This law implies that force increases with charge and decreases as distance between centers increases.

• Atomic number ($Z$) of an element is defined as the number of protons located in the nucleus of its atom.

• Mass number of an isotope is defined as the sum of the number of protons and the number of neutrons in the nucleus.

• Isotopes are defined as atoms of the same element that contain the same number of protons but different numbers of neutrons. Consequently, they share the same atomic number but possess different mass numbers.

• Relative atomic mass ($\text{A}_r$) of an element is the average mass of the atoms of that element relative to $\frac{1}{12}\text{th}$ the mass of a carbon-12 atom, taking into account the natural abundance of each isotope.

• Relative isotopic mass is the mass of a single atom of an isotope relative to $\frac{1}{12}\text{th}$ the mass of a carbon-12 atom.

• Relative molecular mass ($\text{M}_r$) is the sum of all relative atomic masses of the constituent atoms in a substance. For ionic substances, this is frequently referred to as relative formula mass.

• Molar mass is the mass of one mole of a substance, expressed in grams per mole ($\text{g}\,\text{mol}^{-1}$). It is numerically equivalent to the relative molecular mass.

• First ionisation energy is the amount of energy required per mole to remove one electron from each gaseous atom to form a singly positive ion.

• Second ionisation energy is the energy change per mole during the removal of an electron from a singly positive gaseous ion to produce a doubly positive ion.

• First electron affinity is the energy change per mole when one electron is added to a gaseous atom to form a singly negative ion:
  $\text{E(g)} + \text{e}^- \rightarrow \text{E}^-\text{(g)}$

• Second electron affinity is the energy change per mole for the addition of an electron to a singly negative gaseous ion to form a doubly negative ion:
  $\text{E}^-\text{(g)} + \text{e}^- \rightarrow \text{E}^{2-}\text{(g)}$

• Orbitals fill in a specific order: $1s$, $2s$, $2p$, $3s$, $3p$, $4s$, $3d$, $4p$, $5s$, $4d$, $5p$, $6s$. Each orbital holds a maximum of two electrons. Chromium ($[\text{Ar}]\,4s^1\,3d^5$) and Copper ($[\text{Ar}]\,4s^1\,3d^{10}$) are exceptions to standard filling rules due to the stability of half-filled or full $d$ orbitals.

• Mass Spectrometry: This process involves vaporizing an element and bombarding it with high-energy electrons to form positive ions. These ions are accelerated through an electric potential, deflected by mass, and detected. Relative atomic mass is calculated as:
  $\text{A}_r = \frac{\sum (\text{mass of isotope} \times \text{percentage abundance})}{100}$

Chemical Bonding and Molecular Structure

• Ionic Bond: The electrostatic attraction between a cation (formed by electron loss) and an anion (formed by electron gain). High charge density cations (small radius, high charge) are polarising, while large anions are polarisable, potentially leading to covalent character.

• Covalent Bond: Formed when two atoms share a pair of electrons via orbital overlap. Head-on overlap results in a sigma ($\sigma$) bond; side-by-side overlap results in a pi ($\pi$) bond. A double bond consists of one $\sigma$ and one $\pi$ bond.

• Dative Covalent Bond: A covalent bond where one atom provides both electrons for the shared pair.

• Metallic Bond: The attraction between a lattice of positive ions and a "sea" of delocalised electrons.

• Electronegativity: A measure of an atom's attraction for a pair of electrons in a covalent bond. Large differences (greater than approximately $1.5$) typically lead to ionic bonding.

• Intermolecular Forces:

  • Hydrogen Bonds: Attraction between a $\delta+$ hydrogen atom and a $\delta-$ fluorine, oxygen, or nitrogen atom.
  • Van der Waals Forces: Includes dipole-dipole forces (between polar molecules) and dispersion (induced dipole-induced dipole) forces. Dispersion force strength relates to the number of electrons.

• Molecular Shapes (Electron Pair Repulsion Theory):

  • 2 bond pairs: Linear ($180^\circ$).
  • 3 bond pairs: Triangular planar ($120^\circ$).
  • 4 bond pairs: Tetrahedral ($109.5^\circ$).
  • 3 bond pairs + 1 lone pair: Pyramidal ($107^\circ$).
  • 2 bond pairs + 2 lone pairs: V-shaped/Bent ($104.5^\circ$).
  • 5 bond pairs: Trigonal bipyramidal.
  • 6 bond pairs: Octahedral.
  • Lone pairs exert greater repulsion than bond pairs.

Periodicity and Main Group Chemistry

• Period 3 Trends:

  • Atomic radius decreases across the period as nuclear charge increases, pulling electrons closer.
  • Melting points: Sodium, magnesium, and aluminium are metallic (increasing strength with charge density). Silicon is giant atomic (very high). Phosphorus ($\text{P}_4$), sulphur ($\text{S}_8$), and chlorine ($\text{Cl}_2$) are simple molecular, with sulphur having the highest melting point among these three due to more electrons.
  • Electrical conductivity: Metals and graphite conduct via delocalised electrons. Ionic solids like $\text{NaCl}$ only conduct when molten or in solution.

• Group 1 and 2 Properties:

  • Reactivity increases down the groups as ionisation energy decreases.
  • Flame colors: Lithium (carmine red), Sodium (yellow), Potassium (lilac), Calcium (brick red), Strontium (crimson red), Barium (green).
  • Group 2 Solubilities: Sulphate solubility decreases down the group ($\text{MgSO}_4$ is soluble; $\text{BaSO}_4$ is insoluble). Hydroxide solubility increases down the group.
  • Thermal Stability: Stability of nitrates and carbonates increases down the groups. Group 2 nitrates decompose to metal oxide, $\text{NO}_2$, and oxygen. Group 1 nitrates (except lithium) decompose to metal nitrite and oxygen.

• Group 7 (Halogens):

  • Strength as oxidising agents decreases down the group ($\text{Cl}_2 > \text{Br}_2 > \text{I}_2$).
  • Disproportionation: A reaction where an element is simultaneously oxidised and reduced, such as chlorine in alkali:
    $\text{Cl}_2 + 2\text{OH}^- \rightarrow \text{Cl}^- + \text{ClO}^- + \text{H}_2\text{O}$
  • Halide tests: Addition of $\text{AgNO}_3\text{(aq)}$ followed by ammonia. $\text{AgCl}$ is a white precipitate soluble in dilute ammonia; $\text{AgBr}$ is cream and soluble in concentrated ammonia; $\text{AgI}$ is yellow and insoluble in ammonia.

Formulae, Equations, and Motes

• The Avogadro Constant: The number of carbon atoms in exactly $12\,\text{g}$ of carbon-12, valued at $6.02 \times 10^{23}\,\text{mol}^{-1}$.

• Moles and Molar Volume:

  • $\text{Moles} = \frac{\text{mass (g)}}{\text{molar mass (g}\,\text{mol}^{-1}\text{)}}$
  • $\text{Moles (solution)} = \text{concentration (mol}\,\text{dm}^{-3}\text{)} \times \text{volume (dm}^3\text{)}$
  • $\text{Moles (gas at RTP)} = \frac{\text{volume (dm}^3\text{)}}{24\,\text{dm}^3\,\text{mol}^{-1}}$

• Empirical Formula: The simplest whole-number ratio of elements in a compound. If calculated values end in $.5$ or $.25$, multiply the entire ratio by $2$ or $4$ respectively to obtain integers.

• Percentage Yield:
  $\%\,\text{Yield} = \frac{\text{actual yield (g)}}{\text{theoretical yield (g)}} \times 100\%$

Energetics

• Standard Conditions: Pressure of $1\,\text{atmosphere}$, temperature (usually $298\,\text{K}$), concentration of $1.00\,\text{mol}\,\text{dm}^{-3}$, and substances in their most stable states.

• Definitions:

  • $\Delta H_f^\theta$ (Formation): Enthalpy change when one mole of a compound is formed from its elements in standard states.
  • $\Delta H_c^\theta$ (Combustion): Enthalpy change when one mole of a substance is burned completely in oxygen.
  • $\Delta H_{neut}$ (Neutralisation): Enthalpy change when acid and base react to produce one mole of water.

• Hess's Law: The enthalpy change for a reaction is independent of the route taken.
  $\Delta H_{reaction} = \sum \Delta H_{f\text{ (products)}} - \sum \Delta H_{f\text{ (reactants)}}$

• Bond Enthalpy: The average energy required to break one mole of covalent bonds in a gaseous species.
  $\Delta H = \sum \text{(bonds broken)} - \sum \text{(bonds made)}$

• Born-Haber Cycle: A reaction cycle relating the enthalpy of formation of an ionic solid to atomisation, ionisation, electron affinity, and lattice energy. Lattice energy ($\Delta H_{latt}$) is the energy change when one mole of ionic solid is made from gaseous ions.

Kinetics

• Collision Theory: Rate is determined by collision frequency, collision orientation, and the fraction of molecules with energy exceeding the activation energy ($E_a$).

• Maxwell-Boltzmann Distribution: A graph of molecular energies. Increasing temperature shifts the peak to the right and flattens it, increasing the area (and thus the number of molecules) beyond the activation energy threshold.

• Catalysts: Provide an alternative reaction route with lower activation energy. They do not change the total enthalpy change ($\Delta H$).

• Rate Equations: For a reaction $x\text{M} + y\text{N} \rightarrow \text{products}$:
  $\text{Rate} = k[\text{M}]^a[\text{N}]^b$

  • $k$ is the rate constant, which varies with temperature.
  • The order of reaction is the sum of partial orders ($a + b$).
  • Half-life ($t_{1/2}$) for a first-order reaction is constant.

Chemical Equilibria

• Le Chatelier's Principle: When a change is applied to a system at equilibrium, the position of equilibrium shifts to counteract the change.

  • Temperature: Increase moves equilibrium in the endothermic direction.
  • Pressure: Increase moves equilibrium toward the side with fewer gas molecules.
  • Catalyst: Speeds up reaching equilibrium but does not shift the position.

• Equilibrium Constants:

  • $\text{K}_c = \frac{[\text{C}]^x[\text{D}]^y}{[\text{A}]^m[\text{B}]^n}$
  • $\text{K}_p$ uses partial pressures ($p = \text{mole fraction} \times \text{total pressure}$). Solids and liquids are excluded from equilibrium constant expressions.
  • Equilibrium constants are only affected by temperature changes.

Acid-Base Equilibria

• Definitions:

  • Bronsted-Lowry acid: Proton donor; base: Proton acceptor.
  • $\text{K}_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}\,\text{mol}^2\,\text{dm}^{-6}$ at $25^\circ\text{C}$.
  • $\text{pH} = -\log_{10}[\text{H}^+]$.

• Weak Acids and Buffers:

  • $\text{K}_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$. For weak acids, $[\text{H}^+] = \sqrt{\text{K}_a \times [\text{HA}]}$.
  • Buffer Solution: Resist pH change upon addition of small amounts of acid or base. For an acidic buffer:
    $[\text{H}^+] = \text{K}_a \times \frac{[\text{weak acid}]}{[\text{salt}]}$

Organic Chemistry

• Organic Analysis:

  • Alkenes ($\text{C=C}$): Decolourise bromine water.
  • Alcohols/Acids ($\text{OH}$): React with $\text{PCl}_5$ to produce steamy $\text{HCl}$ fumes.
  • Aldehydes: Form a silver mirror with ammoniacal silver nitrate (Tollens' reagent) or a red precipitate with Fehling's solution.
  • Carbonyls: Form an orange/red precipitate with $2,4$-DNP.
  • Iodoform Test: Yellow precipitate of $\text{CHI}_3$ indicates $\text{CH}_3\text{C=O}$ or $\text{CH}_3\text{CH(OH)}$ groups.

• Isomerism:

  • Structural: Same molecular formula, different structural arrangement.
  • Geometric ($cis/trans$): Due to restricted rotation around $\text{C=C}$.
  • Optical: Non-superimposable mirror images containing a chiral center; rotate plane-polarised light.

• Mechanisms:

  • $S_N2$: Dominant for primary halogenoalkanes; involves a one-step transition state.
  • $S_N1$: Dominant for tertiary halogenoalkanes; involves a two-step process forming a carbocation intermediate.
  • Electrophilic Addition: Reaction of alkenes with halogens or hydrogen halides.
  • Electrophilic Substitution: Nitration of benzene using concentrated $\text{HNO}_3$ and $\text{H}_2\text{SO}_4$ at $50^\circ\text{C}$.

Transition Metal Chemistry

• Characteristics: Variable oxidation states, formation of complex ions, coloured ions, and catalytic activity. Transition metals possess partly filled $d$ shells.

• Complex Ions: Ligands (e.g., $\text{H}_2\text{O}$, $\text{NH}_3$, $\text{CN}^-$) form dative covalent bonds with the metal ion. Electronic $d$-orbital splitting causes light absorption in the visible spectrum.

• Reaction with Alkali:

  • $\text{Cr}^{3+}$: Green precipitate, dissolves in excess $\text{NaOH}$ to green solution.
  • $\text{Fe}^{2+}$: Dirty green precipitate, turns brown on standing.
  • $\text{Fe}^{3+}$: Foxy red/brown precipitate.
  • $\text{Cu}^{2+}$: Blue precipitate, dissolves in excess $\text{NH}_3$ to deep blue solution.

• Vanadium Oxidation States:

  • $+5$ ($\text{VO}_2^+$): Yellow
  • $+4$ ($\text{VO}^{2+}$): Blue
  • $+3$ ($\text{V}^{3+}$): Green
  • $+2$ ($\text{V}^{2+}$): Lavender

Questions & Discussion

• State the masses and charges relative to a proton of protons, neutrons, and electrons.

  • Answer: Proton: Mass $1$, charge $+1$; Neutron: Mass $1$, charge $0$; Electron: Mass $\frac{1}{1860}$, charge $-1$.

• How many neutrons are in an atom of \prescript{23}{11}{\text{Na}}?

  • Answer: $23 - 11 = 12$.

• Explain why the second ionisation energy of sodium is much higher than the first.

  • Answer: The first electron is removed from the third shell, while the second is removed from the second shell, which is closer to the nucleus and less shielded.

• Why is the second electron affinity of oxygen endothermic?

  • Answer: Energy is required to overcome the repulsion of adding a negative electron to a negative ion.

• How do you distinguish between propanal and propanone?

  • Answer: Propanal reacts with ammoniacal silver nitrate to form a silver mirror; propanone does not.

• What is the effect of adding alkali to the $\text{CrO}_4^{2-}/\text{Cr}_2\text{O}_7^{2-}$ equilibrium?

  • Answer: It removes $\text{H}^+$ ions, shifting the equilibrium to the left.