Comprehensive Study Guide: History of Chemistry, Atomic Structure, and Chemical Bonding

Atomic Structure

• Sub-Atomic Particles:

  • Electron:
  • Charge: $-1.6022 \times 10^{-19}\,\text{C}$ (Relative charge: $-1$).
  • Mass: $9.1095 \times 10^{-31}\,\text{kg}$.
  • Discovered by J.J. Thomson.
  • Electromagnetic nature; deflected toward the positive pole in an electric field.
  • Proton:
  • Charge: $+1.6022 \times 10^{-19}\,\text{C}$ (Relative charge: $+1$).
  • Mass: $1.6727 \times 10^{-27}\,\text{kg}$ ($1836$ times heavier than an electron).
  • Deflected toward the negative pole in an electric field.
  • Neutron:
  • Charge: $0\,\text{C}$ (Relative charge: $0$).
  • Mass: $1.6750 \times 10^{-27}\,\text{kg}$ (or $1.67579 \times 10^{-27}\,\text{kg}$).
  • Electrically neutral; passes through electric and magnetic fields undeflected.

• Particle Behavior in a Uniform Electric Field:

  • Electrons curve sharply toward the positive electrode due to their extremely small mass.
  • Protons curve less sharply toward the negative electrode due to their significantly larger mass.
  • Neutrons pass straight through without trajectory curvature.

• Atomic Number ($Z$) and Mass Number ($A$):

  • Atomic Number ($Z$): Total number of protons in the nucleus of an atom. In a neutral atom, number of protons = number of electrons.
  • Mass Number / Nucleon Number ($A$): Total sum of protons and neutrons in the nucleus ($P + N = A$).
  • Cation Electrons = $Z - \text{magnitude of positive charge}$.
  • Anion Electrons = $Z + \text{magnitude of negative charge}$.

• Atomic and Ionic Radii Trends:

  • Atomic Radius: Average distance from the nucleus to the outermost boundary of the electron cloud.
  • Across a Period (Left to Right):
  • Atomic and ionic radii decrease due to increasing effective nuclear charge ($Z_{\text{eff}}$) while inner-shell shielding remains constant.
  • Down a Group (Top to Bottom):
  • Atomic and ionic radii increase due to the addition of principal energy levels (shells) and increased inner-shell shielding.
  • Cation vs. Parent Atom:
  • Cations are always smaller than their parent neutral atoms due to increased $Z_{\text{eff}}$ and reduced electron-electron repulsions in the valence shell.
  • Anion vs. Parent Atom:
  • Anions are always larger than their parent neutral atoms due to increased electron-electron repulsions expanding the valence electron cloud.

• Quantum Numbers:

  • Principal Quantum Number ($n$):
  • Values: $n = 1, 2, 3, 4 \dots$
  • Specifies the main energy level (Bohr shell), size of the orbital, and the period number in the periodic table.
  • Azimuthal / Angular Momentum Quantum Number ($l$):
  • Values: $l = 0, 1, 2 \dots (n - 1)$.
  • Defines orbital shape and subshell ($l = 0 \rightarrow s$, $l = 1 \rightarrow p$, $l = 2 \rightarrow d$, $l = 3 \rightarrow f$).
  • Magnetic Quantum Number ($m$):
  • Values: $m = -l \dots 0 \dots +l$ (total $2l + 1$ orientations).
  • Specifies spatial orientation of degenerate orbitals. Explains Zeeman effect (splitting of spectral lines in magnetic fields) and Stark effect (splitting in electric fields).
  • Subshell Orientations:
    • $s$ ($l=0$): $m = 0$ (1 orbital, spherically symmetrical).
    • $p$ ($l=1$): $m = -1, 0, +1$ (3 degenerate orbitals: $p<em>x, p</em>y, p_z$).
    • $d$ ($l=2$): $m = -2, -1, 0, +1, +2$ (5 degenerate orbitals: $d<em>{xy}, d</em>{yz}, d<em>{xz}, d</em>{x^2-y^2}, d_{z^2}$).
    • $f$ ($l=3$): $m = -3, -2, -1, 0, +1, +2, +3$ (7 degenerate orbitals).
  • Spin Quantum Number ($s$):
  • Values: $s = +\frac{1}{2}$ (represented as $\uparrow$, clockwise) and $s = -\frac{1}{2}$ (represented as $\downarrow$, anti-clockwise).
  • Discovered by Goudsmit (1925); describes intrinsic axial spin of an electron generating an axial magnetic moment.

• Shell and Subshell Electron Capacities:

  • K Shell ($n=1$): $l=0$ ($1s$), $1$ orbital, max $2\,\text{e}^-$.
  • L Shell ($n=2$): $l=0$ ($2s$), $l=1$ ($2p$), $4$ orbitals, max $8\,\text{e}^-$.
  • M Shell ($n=3$): $l=0$ ($3s$), $l=1$ ($3p$), $l=2$ ($3d$), $9$ orbitals, max $18\,\text{e}^-$.
  • N Shell ($n=4$): $l=0$ ($4s$), $l=1$ ($4p$), $l=2$ ($4d$), $l=3$ ($4f$), $16$ orbitals, max $32\,\text{e}^-$.

• Rules for Electronic Configuration:

  • Aufbau Principle: Electrons occupy orbitals of lowest energy first before occupying higher energy levels ($1s < 2s < 2p < 3s < 3p < 4s < 3d \dots$).
  • $n + l$ Rule:
  • Orbitals with lower $n + l$ values have lower energy.
  • If two orbitals share identical $n + l$ values, the orbital with the lower $n$ value has lower energy.
  • Example: For $4s$, $n+l = 4+0 = 4$. For $3d$, $n+l = 3+2 = 5$. Thus, $4s$ fills before $3d$.
  • Pauli Exclusion Principle: No two electrons in the same atom can have the exact same set of all four quantum numbers. If two electrons share identical $n$, $l$, and $m$ values, they must possess opposite spin states ($+\frac{1}{2}$ and $-\frac{1}{2}$).
  • Hund's Rule: When filling degenerate orbitals, electrons occupy them singly with parallel spins before pairing up.
  • Extra stability occurs in half-filled ($d^5$) and completely filled ($d^{10}$) subshells (e.g., Chromium: $[\text{Ar}] 4s^1 3d^5$; Copper: $[\text{Ar}] 4s^1 3d^{10}$).

• Ionization Energy ($IE$):

  • Definition: Minimum energy required to remove the most loosely held electron from an isolated gaseous atom in its ground state.
  • Equations:
  • $\text{Na}(g) \rightarrow \text{Na}^+(g) + 1e^- \quad IE = +496\,\text{kJ}\cdot\text{mol}^{-1}$
  • $\text{Mg}(g) \rightarrow \text{Mg}^+(g) + 1e^- \quad IE = +738\,\text{kJ}\cdot\text{mol}^{-1}$
  • Trends:
  • Across a Period: Increases overall due to increasing $Z_{\text{eff}}$ and decreasing atomic radius.
  • Anomalies: Group IIIA ($p^1$) has lower $IE$ than Group IIA ($s^2$) because removing a $p$ electron requires less energy. Group VA ($p^3$) has higher $IE$ than Group VIA ($p^4$) due to extra stability of half-filled $p$ subshells and spin-pair repulsion in $p^4$.
  • Down a Group: Decreases due to increasing atomic radius and increasing inner-shell screening.
  • Factors Influencing $IE$: Nuclear charge ($\propto IE$), Atomic radius ($\propto \frac{1}{IE}$), Shielding effect ($\propto \frac{1}{IE}$), Spin-pair repulsion (decreases $IE$).
  • Successive Ionization Energies:
  • Large jumps in successive $IE$ data indicate electron removal from an inner principal shell, establishing valence electron count.
  • Example: Sodium $IE<em>1 = 495\,\text{kJ}\cdot\text{mol}^{-1}$, $IE</em>2 = 4560\,\text{kJ}\cdot\text{mol}^{-1}$ (1 valence electron, Group 1).
  • Example: Magnesium $IE<em>1 = 735\,\text{kJ}\cdot\text{mol}^{-1}$, $IE</em>2 = 1445\,\text{kJ}\cdot\text{mol}^{-1}$, $IE_3 = 7730\,\text{kJ}\cdot\text{mol}^{-1}$ (2 valence electrons, Group 2).

• Mass Spectrometry:

  • Measures mass-to-charge ratio ($m/z$) of gaseous ions.
  • Four Steps:
  1. Ionization: Sample vaporized and ionized via electron impact, electrospray, or MALDI.
  2. Acceleration & Mass Analysis: Charged ions accelerated via electric field and deflected in magnetic field based on $m/z$.
  3. Detection: Detector records impact time and ion count.
  4. Data Analysis: Plot of relative abundance ($y$-axis) versus $m/z$ ($x$-axis).
  • Formula for Average Atomic Mass: $\text{Average Atomic Mass} = \frac{\sum (\text{Mass Number} \times \text{Relative Abundance})}{100}$
  • Chlorine Isotope Spectrum: ${}^{35}\text{Cl}$ ($75.76\%$), ${}^{37}\text{Cl}$ ($24.24\%$) $\rightarrow 35.48\,\text{amu}$.
  • Magnesium Isotope Spectrum: ${}^{24}\text{Mg}$ ($79\%$), ${}^{25}\text{Mg}$ ($10\%$), ${}^{26}\text{Mg}$ ($11\%$) $\rightarrow 24.32\,\text{amu}$.

• Semiconductors:

  • Silicon ($Z=14$): Electronic configuration $1s^2 2s^2 2p^6 3s^2 3p^2$ (4 valence electrons).
  • Band Gap: Energy difference between filled valence band and empty conduction band.
  • Doping:
  • $n$-type: Doped with Group 15 elements (e.g., Phosphorus), adding donor electrons to conduction band