Chemistry Lecture Notes

Electron Configuration and Quantum Chemistry

Electron Configuration Basics

  • Atomic symbols and electrons: This involves the notation of different atomic species (e.g., H, He, Li).

  • Electron arrangement across energy levels:

    • 1st energy level: Holds a maximum of 2 electrons. This is represented by:

    • $1s^2$

    • 2nd energy level: Also has multiple orbitals:

    • $2s^2$, $2p^6$

    • 3rd energy level: Holds $3s$, $3p$, and $3d$ orbitals:

    • Full configuration shown as $3s^2 3p^6 3d^{10}$.

    • 4th energy level: Includes orbitals like $4s$, $4p$, and $4d$…

Aufbau Principle

  • Aufbau Principle: This principle states that electrons occupy the lowest energy orbitals first before filling higher energy levels. Thus, the configuration goes:

    • Example getting to $Sc$:

    • Configuration starts from lowest (1s) to full occupancy of available orbitals:

      • $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^3$.

Hund's Rule

  • Hund's Rule: This rule states that electrons will fill degenerate (same energy) orbitals singly before pairing up.

  • For instance, in a p subshell:

    • Electrons fill $3p$ as:

    • $3p^3$ before any spin-paired arrangement is chosen.

Pauli's Exclusion Principle

  • Pauli's Exclusion Principle: No two electrons in an atom can have identical quantum numbers. In summary:

    • Electrons in the same orbital must have opposite spins (one +1/2 and the other -1/2).

Quantum Numbers

  • Each electron in an atom is described by a set of four quantum numbers:

    1. Principal quantum number ($n$): Indicates energy levels (1-7).

    2. Angular momentum quantum number ($l$): Indicates the type of orbital (0 = s, 1 = p, 2 = d, 3 = f).

    3. Magnetic quantum number ($m_l$): Specifies the orientation of the orbital.

    4. Spin quantum number ($m_s$): Represents the direction of the electron spin (either +1/2 or -1/2).

Molecular Orbitals and Bonding

  • Molecular Orbits: When two atomic orbitals overlap, they form molecular orbitals, allowing electrons to move between two atoms, e.g., hydrogen molecule $H_2$:

    • Overlapping of $1s$ orbitals creates a bond allowing for electron sharing:

    • $H-H$ represents shared electrons between two hydrogen atoms.

Acid-Base Chemistry

  • Acids and Bases: Understanding the classification as strong or weak bases and acids.

    • Example Reaction: $NH_3$ acts as a weak base.

  • Acid-Base Reaction example:

    • $NH3 + HCl ightarrow NH4^+ + Cl^-$

    • Reaction showcases the formation of the ammonium ion under acidic conditions.

pH Calculations

  • pH and pOH Relationship:

    • pH+pOH=14pH + pOH = 14

    • pH=−extlog[H3O+]pH = - ext{log}[H_3O^+]

    • Calculation example:

    • Given: [OH−]=10−5.13[OH^-] = 10^{-5.13}; compute pH:

      • Find pH using a logarithmic relationship with ion concentrations.

  • Buffer Solutions:

    • A buffer is composed of a weak acid and its conjugate base:

    • Example: HNO<em>2HNO<em>2 and NaNO</em>2NaNO</em>2

  • Equilibrium Reaction:

    • HNO<em>2+H</em>2O<br>ightleftharpoonsNO<em>2−+H</em>3O+HNO<em>2 + H</em>2O <br>ightleftharpoons NO<em>2^- + H</em>3O^+

Important Equations

  • Kw=[H+][OH−]=1imes10−14K_w = [H^+][OH^-] = 1 imes 10^{-14}

  • K<em>aK<em>a and K</em>bK</em>b relationships involving logarithmic functions are crucial for buffer and acid-base equilibrium adjustments.