Chemistry explores the composition, structure, properties, and transformations of matter. This chapter provides reference standards for atomic particles, electron configurations, periodic trends, chemical bonding, reaction kinetics, the pH scale, and the fundamental gas laws.
2.1 Subatomic Particles
| Particle | Symbol | Charge (e) | Charge (Coulombs) | Rest Mass (kg) | Rest Mass (amu / Da) | Location |
|---|
| Proton | $p^+$ or $^1_1\text{p}$ | $+1$ | $+1.602 \times 10^{-19}\text{ C}$ | $1.6726 \times 10^{-27}\text{ kg}$ | $1.007276\text{ u}$ | Atomic Nucleus |
| Neutron | $n^0$ or $^1_0\text{n}$ | $0$ | $0\text{ C}$ | $1.6749 \times 10^{-27}\text{ kg}$ | $1.008665\text{ u}$ | Atomic Nucleus |
| Electron | $e^-$ or $^0_{-1}\text{e}$ | $-1$ | $-1.602 \times 10^{-19}\text{ C}$ | $9.1094 \times 10^{-31}\text{ kg}$ | $0.0005486\text{ u}$ | Electron Orbitals / Cloud |
2.2 Quantum Numbers & Orbital Architecture
| Quantum Number | Symbol | Permissible Values | Physical Meaning |
|---|
| Principal | $n$ | $1, 2, 3, 4, \dots$ | Energy level and orbital size / radial distance from nucleus. |
| Azimuthal (Angular) | $l$ | $0, 1, \dots, (n-1)$ | Orbital shape ($l=0: s\text{ [sphere]}, l=1: p\text{ [dumbbell]}, l=2: d\text{ [clover]}, l=3: f$). |
| Magnetic | $m_l$ | $-l, \dots, 0, \dots, +l$ | Spatial orientation of the orbital in 3D coordinates. |
| Spin | $m_s$ | $+\frac{1}{2}, -\frac{1}{2}$ | Intrinsic angular momentum (spin orientation: $\uparrow$ or $\downarrow$). |
Fundamental Rules of Electron Filling
- Aufbau Principle: Electrons occupy the lowest-energy orbitals first ($1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p \dots$).
- Pauli Exclusion Principle: No two electrons in the same atom can share identical sets of four quantum numbers ($n, l, m_l, m_s$). Each orbital holds at most 2 electrons with opposite spins.
- Hund's Rule: Every orbital in a subshell is singly occupied with parallel spins before any orbital is doubly occupied.
2.3 Periodic Table Families & Groups
| Group Number | Family Name | Valence Electrons | Key Properties | Representative Elements |
|---|
| Group 1 | Alkali Metals | 1 | Extremely reactive, soft, low melting points, form $+1$ cations, react violently with water. | $\text{Li, Na, K, Rb, Cs}$ |
| Group 2 | Alkaline Earth Metals | 2 | Highly reactive, denser than Group 1, form $+2$ cations, basic oxides. | $\text{Be, Mg, Ca, Sr, Ba}$ |
| Groups 3–12 | Transition Metals | Variable ($d$-block) | High melting points, high electrical conductivity, multiple oxidation states, colored complexes. | $\text{Fe, Cu, Ag, Au, Pt, Ni}$ |
| Group 17 | Halogens | 7 | Highly electronegative, diatomic nonmetals ($\text{F}_2, \text{Cl}_2$), form $-1$ anions (halides). | $\text{F, Cl, Br, I}$ |
| Group 18 | Noble Gases | 8 (2 for He) | Inert, complete valence octet, monatomic gases, extremely low chemical reactivity. | $\text{He, Ne, Ar, Kr, Xe, Rn}$ |
| $f$-Block (Period 6) | Lanthanides | Variable | Rare-earth metallic elements, magnetic properties, high electrical conductance. | $\text{La, Ce, Nd, Sm, Eu}$ |
| $f$-Block (Period 7) | Actinides | Variable | All radioactive, heavy synthetic elements, nuclear fission fuels. | $\text{Th, U, Pu, Am, Cm}$ |
2.4 Periodic Trends
| Periodic Property | Left to Right Across a Period | Top to Bottom Down a Group | Underlying Nuclear Mechanism |
|---|
| Atomic Radius | Decreases ($\rightarrow\downarrow$) | Increases ($\downarrow\uparrow$) | Effective nuclear charge ($Z_{\text{eff}}$) pulls electrons closer across; added shells increase distance down. |
| Ionization Energy | Increases ($\rightarrow\uparrow$) | Decreases ($\downarrow\downarrow$) | Higher $Z_{\text{eff}}$ binds valence electrons tighter; electron shielding weakens grip down group. |
| Electronegativity | Increases ($\rightarrow\uparrow$) | Decreases ($\downarrow\downarrow$) | Pauling scale: Fluorine is highest ($3.98$), Francium lowest ($0.7$). |
| Electron Affinity | Generally increases ($\rightarrow\uparrow$) | Generally decreases ($\downarrow\downarrow$) | Energy released when an electron is attached to a neutral atom in gaseous state. |
| Metallic Character | Decreases ($\rightarrow\downarrow$) | Increases ($\downarrow\uparrow$) | Propensity to lose electrons and form cations. |
2.5 Chemical Bonds & Intermolecular Forces
| Interaction Type | Mechanism | Typical Bond Energy (kJ/mol) | Examples |
|---|
| Ionic Bond | Electrostatic attraction between oppositely charged ions formed by complete electron transfer ($\Delta\chi > 2.0$) | $400 - 4000$ | $\text{NaCl}, \text{MgO}, \text{CaF}_2$ |
| Covalent Bond (Nonpolar) | Equal sharing of electron pairs between atoms with identical or near-identical electronegativities ($\Delta\chi < 0.4$) | $150 - 1100$ | $\text{H}_2, \text{O}_2, \text{CH}_4, \text{N}_2$ |
| Covalent Bond (Polar) | Unequal electron sharing resulting in partial charges ($\delta^+, \delta^-$) where $0.4 \le \Delta\chi \le 2.0$ | $200 - 800$ | $\text{H}_2\text{O}, \text{HCl}, \text{NH}_3$ |
| Metallic Bond | Delocalized "sea of electrons" surrounding stationary positive metal cation lattices | $100 - 800$ | $\text{Fe, Cu, Al, Au}$ |
| Hydrogen Bond | Dipole-dipole attraction between $\text{H}$ covalently bonded to highly electronegative $\text{N, O, F}$ and adjacent lone pair | $10 - 40$ | Water hydrogen bonding, DNA base pairs |
| Dipole-Dipole Force | Electrostatic attraction between permanent molecular dipole moments in polar molecules | $5 - 25$ | $\text{SO}_2, \text{HCl}$ (liquid phase) |
| London Dispersion Force | Temporary, induced instantaneous dipoles present in all molecules (dominant in nonpolar substances) | $0.05 - 40$ | $\text{He, Ar}, \text{CH}_4, \text{I}_2$ |
2.6 Chemical Reaction Classification & Stoichiometry
| Reaction Class | General Form | Archetypal Example |
|---|
| Synthesis (Combination) | $A + B \rightarrow AB$ | $2\text{H}_2(g) + \text{O}_2(g) \rightarrow 2\text{H}_2\text{O}(l)$ |
| Decomposition | $AB \rightarrow A + B$ | $2\text{H}_2\text{O}_2(aq) \rightarrow 2\text{H}_2\text{O}(l) + \text{O}_2(g)$ |
| Single Replacement | $A + BC \rightarrow B + AC$ | $\text{Zn}(s) + 2\text{HCl}(aq) \rightarrow \text{ZnCl}_2(aq) + \text{H}_2(g)$ |
| Double Replacement (Metathesis) | $AB + CD \rightarrow AD + CB$ | $\text{AgNO}_3(aq) + \text{NaCl}(aq) \rightarrow \text{AgCl}(s)\downarrow + \text{NaNO}_3(aq)$ |
| Combustion | $\text{C}_x\text{H}_y + \left(x + \frac{y}{4}\right)\text{O}_2 \rightarrow x\text{CO}_2 + \frac{y}{2}\text{H}_2\text{O}$ | $\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g) + \Delta H$ |
| Neutralization (Acid-Base) | $\text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water}$ | $\text{HCl}(aq) + \text{NaOH}(aq) \rightarrow \text{NaCl}(aq) + \text{H}_2\text{O}(l)$ |
2.7 Acids, Bases & The pH Scale
| Theory | Acid Definition | Base Definition |
|---|
| Arrhenius | Produces hydrogen ions ($\text{H}^+$ / $\text{H}_3\text{O}^+$) in aqueous solution | Produces hydroxide ions ($\text{OH}^-$) in aqueous solution |
| Brønsted-Lowry | Proton donor ($\text{H}^+$ donor) | Proton acceptor ($\text{H}^+$ acceptor) |
| Lewis | Electron-pair acceptor (electrophile) | Electron-pair donor (nucleophile) |
Quantitative pH Equations (at $25^\circ\text{C}$ / $298\text{K}$)
$$\text{pH} = -\log_{10}[\text{H}^+] \qquad \text{pOH} = -\log_{10}[\text{OH}^-] \qquad \text{pH} + \text{pOH} = 14$$
$$\text{Ion-Product Constant of Water: } K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14}$$
$$\text{Henderson-Hasselbalch Buffer Equation: } \text{pH} = \text{p}K_a + \log_{10}\left(\frac{[\text{A}^-]}{[\text{HA}]}\right)$$
2.8 Fundamental Gas Laws
| Law Name | Equation | Constant Variables | Physical Principle |
|---|
| Boyle's Law | $P_1 V_1 = P_2 V_2$ | $T, n$ (Isothermal) | Pressure is inversely proportional to volume. |
| Charles's Law | $\frac{V_1}{T_1} = \frac{V_2}{T_2}$ | $P, n$ (Isobaric) | Volume is directly proportional to absolute temperature ($K$). |
| Gay-Lussac's Law | $\frac{P_1}{T_1} = \frac{P_2}{T_2}$ | $V, n$ (Isochoric) | Pressure is directly proportional to absolute temperature. |
| Avogadro's Law | $\frac{V_1}{n_1} = \frac{V_2}{n_2}$ | $P, T$ | Equal gas volumes at constant $P, T$ contain identical particle counts. |
| Combined Gas Law | $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$ | $n$ | Simultaneous variations of $P, V,$ and $T$ for a closed sample. |
| Ideal Gas Law | $PV = nRT$ | — | Unifies gas dynamics; $R = 0.08206\text{ L}\cdot\text{atm/mol}\cdot\text{K} = 8.314\text{ J/mol}\cdot\text{K}$. |
| Dalton's Law of Partial Pressures | $P_{\text{total}} = \sum P_i = \sum \chi_i P_{\text{total}}$ | $V, T$ | Total pressure is the sum of partial pressures of all gaseous constituents. |