Chem quiz unit2 Ultimate Study Guide

Electromagnetic Radiation and the Nature of Light

• Light is electromagnetic energy propagating as waves at the speed of light in a vacuum, $c = 3.00 \times 10^8\,\text{m}\,\text{s}^{-1}$.

• Fundamental wave equations:

  • Wave speed relation: $c = \lambda \nu$ (or $c = f \lambda$), where $\lambda$ represents wavelength and $\nu$ (or $f$) represents frequency in $\text{Hz}$ or $\text{s}^{-1}$ .

  • Photon energy relation: $E = h \nu$ (or $E = h f$), where Planck's constant is $h = 6.63 \times 10^{-34}\,\text{J}\cdot\text{s}$.

• Wavelength and frequency are inversely related; frequency and energy are directly proportional.

• Electromagnetic spectrum in order of increasing energy/frequency and decreasing wavelength: Radio waves $\rightarrow$ Microwaves $\rightarrow$ Infrared (IR) $\rightarrow$ Visible light $\rightarrow$ Ultraviolet (UV) $\rightarrow$ X-rays $\rightarrow$ Gamma rays.

• The visible spectrum ranges from red to violet (ROYGBIV) across wavelengths of approximately $780\,\text{nm}$ down to $380\,\text{nm}$.

Atomic Spectra and the Bohr Model

• Continuous spectra exhibit an uninterrupted band of all wavelengths, while line spectra contain discrete, quantized wavelengths characteristic of specific elements.

• Emission spectra are generated when excited electrons drop to lower principal energy levels ($n$), releasing photons corresponding to the energy difference between levels.

• Absorption spectra display dark gaps produced when cold vapor absorbs specific frequencies from continuous light.

• Spectral series transitions in Hydrogen:

  • Transitions dropping to $n = 1$ release high-energy photons in the ultraviolet (UV) region.

  • Transitions dropping to $n = 2$ release photons in the visible light region.

  • Transitions dropping to $n \ge 3$ release lower-energy photons in the infrared (IR) region.

• Principal energy levels converge (decrease in spacing) as distance from the nucleus increases.

Quantum Mechanical Model and Quantum Numbers

• Heisenberg's Uncertainty Principle states that it is impossible to simultaneously measure both the precise position and velocity of an electron.

• Orbitals define regions of probability where up to $2$ electrons can reside.

• The four quantum numbers:

  • Principal Quantum Number ($n$): Positive integers ($n = 1, 2, 3\dots$) indicating the main energy level. Maximum orbitals per level = $n^2$; maximum electrons = $2n^2$.

  • Angular Momentum Quantum Number ($l$): Integer values from $0$ to $n - 1$ defining orbital geometry:

  • $l = 0$: spherical $s$-orbital ($1$ orbital per subshell).

  • $l = 1$: dumbbell-shaped $p$-orbital ($3$ degenerate orbitals: $p_x, p_y, p_z$).

  • $l = 2$: clover-shaped $d$-orbital ($5$ degenerate orbitals).

  • $l = 3$: tetrahedral-shaped $f$-orbital ($7$ degenerate orbitals).

  • Magnetic Quantum Number ($m_l$): Integers ranging from $-l$ to $+l$, determining the spatial orientation of the orbital.

  • Spin Quantum Number ($m_s$): Values of $+\frac{1}{2}$ or $-\frac{1}{2}$, defining opposing electron spins.

Electron Configuration Principles and Transition Elements

• Aufbau Principle: Orbitals fill in order of increasing potential energy, with lower-energy levels filled first.

• Pauli Exclusion Principle: No two electrons in an atom may share identical sets of all four quantum numbers; an orbital holds at most $2$ electrons with opposite spins.

• Hund's Rule: Degenerate orbitals are each singly occupied with parallel spins before pairing begins.

• Condensed electron configurations list the preceding noble gas symbol in brackets followed by valence electrons (e.g., Sulfur: $[\text{Ne}]\,3s^2\,3p^4$).

• First-row transition metal cations ($\text{Sc}$ to $\text{Cu}$) lose outer $4s$ electrons before $3d$ electrons when forming ions.

• Zinc ($\text{Zn}$) has a filled $3d^{10}$ sublevel and forms only $+2$ ions without variable oxidation states, excluding it from transition element classification.

• Ground-state exceptions to the Aufbau principle:

  • Chromium ($\text{Cr}$, $Z = 24$): $[\text{Ar}]\,4s^1\,3d^5$ (favored half-filled $d$-sublevel).

  • Copper ($\text{Cu}$, $Z = 29$): $[\text{Ar}]\,4s^1\,3d^{10}$ (favored completely filled $d$-sublevel).

Periodic Trends and Reactivity

• Elements are arranged by increasing atomic number ($Z$); elements in the same group possess the same valence electron configuration and similar chemical properties.

• Atomic Radius:

  • Increases down a group due to the addition of occupied principal energy levels.

  • Decreases left-to-right across a period due to increasing nuclear charge pulling electrons closer.

• Ionic Radius:

  • Cations are smaller than their parent atoms due to loss of valence electrons and outermost occupied shells.

  • Anions are larger than their parent atoms due to increased electron-electron repulsion.

  • In isoelectronic series, ionic radius decreases as nuclear charge increases (e.g., $\text{Mg}^{2+} < \text{Na}^+$; $\text{S}^{2-} < \text{P}^{3-}$).

• Shielding Effect:

  • Increases down a group due to more intervening inner energy levels.

  • Remains constant across a period because the count of core electron shells is identical.

• Electronegativity and Electron Affinity:

  • Both trends decrease down a group and increase across a period toward the upper right of the table.

  • Fluorine ($\text{F}$) possesses the highest electronegativity.

• Chemical Reactivity:

  • Metals increase in reactivity toward the bottom-left corner (Francium, $\text{Fr}$, is the most reactive metal).

  • Nonmetals increase in reactivity toward the top-right corner (Fluorine, $\text{F}$, is the most reactive nonmetal).

Ionization Energy Trends, Discontinuities, and Calculations

• First Ionization Energy (IE): Minimum energy required to remove one electron from a neutral gaseous atom in the ground state:   $X_{(g)} + \text{energy} \rightarrow X^+_{(g)} + e^-$

• General trends: IE decreases down a group (increased distance and shielding) and increases across a period (increased nuclear charge).

• Period discontinuities:

  • Group 2 to Group 13/3 (e.g., $\text{Be}$ to $\text{B}$): The single $p$ electron in Group 13 is shielded by the inner $s^2$ subshell and resides at higher energy, requiring less energy to remove.

  • Group 15 to Group 16 (e.g., $\text{N}$ to $\text{O}$): Mutual electron-electron repulsion between paired electrons in the $p$ orbital of Group 16 lowers the energy required to remove an electron relative to the half-filled $p^3$ subshell of Group 15.

• Successive Ionization Energies: Sequentially increase due to higher proton-to-electron ratios; major leaps in energy indicate the removal of an electron from a complete inner noble gas core.

• Calculating Ionization Energy from spectral convergence:

  • Spectral lines converge at the continuum limit ($n = \infty$), representing the complete removal of an electron.

  • For Hydrogen, lines converge at $\lambda = 9.12 \times 10^{-8}\,\text{m}$.

  • Frequency calculation:     $f = \frac{c}{\lambda} = \frac{3.00 \times 10^8\,\text{m}\,\text{s}^{-1}}{9.12 \times 10^{-8}\,\text{m}} = 3.29 \times 10^{15}\,\text{s}^{-1}$

  • Photon energy:     $E = h f = (6.63 \times 10^{-34}\,\text{J}\cdot\text{s})(3.29 \times 10^{15}\,\text{s}^{-1}) = 2.18 \times 10^{-18}\,\text{J}$

  • Molar first ionization energy:     $IE = 1.31 \times 10^3\,\text{kJ}\,\text{mol}^{-1}$

Electromagnetic Radiation and the Nature of Light

• Light behaves like both a wave and a stream of tiny energy packets (called photons). It moves through empty space at $c = 3.00 \times 10^8\,\text{m}\,\text{s}^{-1}$.

• Main light equations:

  • Wave speed: $c = \lambda \nu$ , where $\lambda$ is the wave length and $\nu$ is the wave frequency (how many waves pass each second). c= the speed of light.

  • Photon energy: $E = h \nu$, where Planck's constant is $h = 6.63 \times 10^{-34}\,\text{J}\cdot\text{s}$ .

• Wavelength and frequency are opposites: as waves get longer, fewer pass by each second. Higher frequency means higher energy.

• Light types from lowest energy to highest energy: Radio waves $\rightarrow$ Microwaves $\rightarrow$ Infrared (heat) $\rightarrow$ Visible light $\rightarrow$ Ultraviolet $\rightarrow$ X-rays $\rightarrow$ Gamma rays.

• Rainbow colors in visible light range from red (longest wave, lowest energy, about $780\,\text{nm}$) to violet (shortest wave, highest energy, about $380\,\text{nm}$).

Atomic Spectra and the Bohr Model

• A continuous spectrum is a smooth rainbow of all colors blended together. A line spectrum has only separate, sharp lines of color made by one kind of atom.

• Emission lines appear when electrons get excited and drop down to lower energy levels, giving off light.

• Absorption lines appear as dark missing bands when cool gas soaks up specific light colors from a bright source.

• Hydrogen light drops:

  • Drops to level $n = 1$ release high-energy ultraviolet light.

  • Drops to level $n = 2$ release visible light you can see.

  • Drops to level $n = 3$ or higher release lower-energy infrared light.

• Energy steps get closer together the farther they are from the center (nucleus) of the atom.

Quantum Mechanical Model and Quantum Numbers

• Heisenberg's Uncertainty Principle says we cannot know both the exact spot and the exact speed of an electron at the same time.

• Orbitals are 3D zones of space where an electron is most likely to hang out. Each zone can hold up to $2$ electrons.

• Four numbers give the address of an electron:

  • Main shell ($n$): Whole numbers ($n = 1, 2, 3\dots$) telling how far the electron is from the center. Maximum electrons in a shell = $2n^2$.

  • Subshell shape ($l$): Values from $0$ up to $n - 1$:

  • $l = 0$: round sphere shape ($s$-orbital, holds up to $2$ electrons).

  • $l = 1$: dumbbell shape ($p$-orbital, $3$ paths, holds up to $6$ electrons).

  • $l = 2$: four-leaf clover shape ($d$-orbital, $5$ paths, holds up to $10$ electrons).

  • $l = 3$: complex flower shape ($f$-orbital, $7$ paths, holds up to $14$ electrons).

  • Tilt/Direction ($m_l$): Shows which direction in 3D space the orbital points (from $-l$ to $+l$).

  • Spin ($m_s$): Either $+\frac{1}{2}$ or $-\frac{1}{2}$, showing whether the electron spins up or down.

Electron Configuration Principles and Transition Elements

• Aufbau rule: Electrons fill the lowest energy rooms first.

• Pauli rule: No two electrons in an atom can have the exact same address; an orbital holds at most $2$ electrons, and they must spin in opposite ways.

• Hund's rule: When orbitals have the same energy, electrons sit alone with the same spin before they pair up.

• Short notation: Put the nearest earlier noble gas in brackets, then write the leftover outer electrons (for example, Sulfur: $[\text{Ne}]\,3s^2\,3p^4$).

• When transition metals make positive ions, they lose their outer $4s$ electrons before losing any $3d$ electrons.

• Zinc ($\text{Zn}$) has a completely full $3d$ set and only makes a $+2$ ion, so it does not count as a true transition metal.

• Odd rules for extra stability:

  • Chromium ($\text{Cr}$): fills as $[\text{Ar}]\,4s^1\,3d^5$ because a half-full $d$ set is extra stable.

  • Copper ($\text{Cu}$): fills as $[\text{Ar}]\,4s^1\,3d^{10}$ because a completely full $d$ set is extra stable.

Periodic Trends and Reactivity

• Elements are sorted by proton count ($Z$). Elements in the same up-and-down column share similar outer electrons and act in similar ways.

• Atom size:

  • Gets bigger going down a column because new outer electron rings are added.

  • Gets smaller going left to right across a row because more positive protons in the middle pull the electron cloud tighter.

• Ion size:

  • Positive ions (cations) lose electrons, losing outer space, so they are smaller than their parent atoms.

  • Negative ions (anions) gain electrons, which crowd each other and push outward, so they are bigger than their parent atoms.

• Shielding: Inside electrons block the pull of the nucleus. Shielding grows going down a column and stays about the same across a row.

• Pull on electrons (Electronegativity and Electron Affinity):

  • Both grow moving up and to the right on the table.

  • Fluorine ($\text{F}$) pulls on electrons the strongest.

• How easily elements react:

  • Metals react more easily toward the bottom-left corner (Francium, $\text{Fr}$, is the most reactive metal).

  • Nonmetals react more easily toward the top-right corner (Fluorine, $\text{F}$, is the most reactive nonmetal).

Ionization Energy Trends, Discontinuities, and Calculations

• First Ionization Energy: The energy needed to pull one electron away from a gas atom: $X_{(g)} \rightarrow X^+_{(g)} + e^-$.

• General rule: Gets smaller going down a column (electrons are farther out and easier to steal) and gets bigger going left to right across a row (nucleus holds electrons tighter).

• Small dips in the trend:

  • Group 2 to Group 13 (like $\text{Be}$ to $\text{B}$): The lone $p$ electron sits in a higher energy subshell and is shielded by the $s$ pair, so it takes less work to pull off.

  • Group 15 to Group 16 (like $\text{N}$ to $\text{O}$): In Group 16, two electrons share the same orbital. They repel each other, making one easier to push out.

• Big energy jumps: Once all outer electrons are removed, taking an electron from the full inner core takes a huge jump in energy.

• Finding Ionization Energy from light lines:

  • Color lines crowd together at the edge where an electron breaks completely free from the atom.

  • For Hydrogen, lines crowd together at wavelength $\lambda = 9.12 \times 10^{-8}\,\text{m}$.

  • Frequency step: $f = \frac{c}{\lambda} = \frac{3.00 \times 10^8\,\text{m}\,\text{s}^{-1}}{9.12 \times 10^{-8}\,\text{m}} = 3.29 \times 10^{15}\,\text{s}^{-1}$

  • Energy for one atom: $E = h f = (6.63 \times 10^{-34}\,\text{J}\cdot\text{s})(3.29 \times 10^{15}\,\text{s}^{-1}) = 2.18 \times 10^{-18}\,\text{J}$

  • Total energy for one mole of atoms: $IE = 1.31 \times 10^3\,\text{kJ}\,\text{mol}^{-1}$