Untitled Flashcard Set

Day 1: Gas Laws, Gas Stoichiometry, and the Nature of Light

1. Kinetic Molecular Theory and Real vs. Ideal Gas Behavior

   • Postulates of Kinetic Molecular Theory (KMT):

   • Gas particles are in constant, random, straight-line motion.

   • The volume of individual gas particles is negligible relative to the total volume occupied by the gas.

   • Intermolecular attractive and repulsive forces between gas particles are negligible.

   • Collisions between particles and with container walls are completely elastic; total kinetic energy is conserved.

   • The average kinetic energy of gas particles is directly proportional to absolute temperature in Kelvin ($KE_{\text{avg}} \propto T$).

2. The Gas Laws and Stoichiometry

   • Combined Gas Law:

   • Relates pressure ($P$), volume ($V$), and temperature ($T$) for a constant number of moles ($n$):
         $\frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2}$

   • Ideal Gas Law:

   • Equation of state relating all macroscopic variables:
         $PV = nRT$

   • Where $P$ is pressure, $V$ is volume in $dm^3$, $n$ is moles of gas, $R$ is the universal gas constant ($8.314\,J\,mol^{-1}\,K^{-1}$ or $0.08206\,atm\,dm^3\,mol^{-1}\,K^{-1}$), and $T$ is absolute temperature in Kelvin.

   • Dalton's Law of Partial Pressures:

   • Total pressure of a non-reacting gas mixture equals the sum of the partial pressures:
         $P_{\text{total}} = P_A + P_B + P_C + \dots$

   • Partial pressure is proportional to the mole fraction ($X_i$):
         $X_A = \frac{n_A}{n_{\text{total}}}$
         $P_A = X_A P_{\text{total}}$

   • Gas Stoichiometry:

   • Use balanced chemical equations to determine stoichiometric mole ratios.

   • Convert between gas volumes and molar quantities using $PV = nRT$ at non-standard conditions, or standard molar volume at specified conditions.

3. Properties and Energetics of Light

   • Wave-Particle Duality:

   • Wave properties: wavelength ($\lambda$), frequency ($\nu$), and interference patterns.

   • Particle properties: quantized energy packets called photons, observed in the photoelectric effect.

   • Wavelength-Frequency Relationship:

   • Relates the speed of light ($c = 3.00 \times 10^8\,m\,s^{-1}$) to wavelength and frequency:
         $c = \lambda \nu$

   • Photon Energy Quantization:

   • Relates the energy of a single photon to its frequency or wavelength:
         $E = h\nu$
         $E = \frac{hc}{\lambda}$

   • Where $h$ is Planck's constant ($6.626 \times 10^{-34}\,J\,s$).

Day 2: Atomic Models, Quantum Mechanics, and Periodic Trends

1. Atomic Models and Quantum Mechanics

   • Potential Energy and Electron Position:

   • Electrostatic attraction between the positively charged nucleus and negatively charged electrons dictates potential energy ($PE$).

   • An electron located closer to the nucleus resides at a lower (more negative) potential energy state.

   • Absorbing energy promotes an electron further from the nucleus to a higher $PE$ level.

   • Bohr Model and Emission Spectra:

   • Atomic line spectra arise from quantized transitions between discrete electronic energy levels ($n$).

   • Photon emission occurs when an electron transitions from a higher state ($n_i$) to a lower state ($n_f$):
         $\Delta E = -R_H \left(\frac{1}{n_f^2} - \frac{1}{n_i^2}\right)$

   • The emitted photon carries an energy precisely equal to the change in energy ($\Delta E = h\nu$).

   • Quantum Mechanical Model and Quantum Numbers:

   • Principal quantum number ($n$): main energy shell ($n = 1, 2, 3, \dots$).

   • Angular momentum quantum number ($l$): orbital shape and subshell ($l = 0, 1, \dots, n-1$; where $l=0$ is s, $l=1$ is p, $l=2$ is d).

   • Magnetic quantum number ($m_l$): spatial orientation of the orbital ($m_l = -l, \dots, 0, \dots, +l$).

   • Spin quantum number ($m_s$): intrinsic spin orientation ($m_s = +\frac{1}{2}$ or $-\frac{1}{2}$).

   • Orbital Geometries:

   • s orbitals: spherical ($l=0$).

   • p orbitals: dumbbell-shaped with a nodal plane at the nucleus ($l=1$; three degenerate orbitals: $p_x, p_y, p_z$).

   • d orbitals: four cloverleaf orientations and one dumbbell with an equatorial ring ($l=2$; five degenerate orbitals).

2. Orbital Filling Rules and Electron Configurations

   • Governing Principles:

   • Aufbau Principle: electrons occupy the lowest-energy orbitals available first.

   • Pauli Exclusion Principle: no two electrons in an atom can have the same four quantum numbers; an orbital holds at most two electrons with opposite spins.

   • Hund's Rule: degenerate orbitals are each occupied singly with parallel spins before any orbital is doubly occupied.

   • Configurations and Valence Electrons:

   • Write configurations in order of orbital energy ($1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, \dots$).

   • Valence electrons: electrons in the outermost principal energy shell ($n_{\text{max}}$).

   • Core electrons: inner-shell electrons that shield the nucleus.

3. Periodic Trends and Ion Formation

   • Effective Nuclear Charge ($Z_{\text{eff}}$):

   • The net positive charge pulling on valence electrons:
         $Z_{\text{eff}} \approx Z - S$

   • Where $Z$ is the actual nuclear charge (atomic number) and $S$ is the shielding constant (approximated by the number of core electrons).

   • Across a period: $Z$ increases while core shielding remains approximately constant, causing $Z_{\text{eff}}$ to increase.

   • Down a group: valence electrons occupy higher principal energy levels ($n$) with greater distance from the nucleus.

   • Periodic Trends:

   • Atomic Radius: decreases across a period (increasing $Z_{\text{eff}}$ pulls valence shells tighter) and increases down a group (electrons occupy higher values of $n$).

   • First Ionization Energy: increases across a period (stronger $Z_{\text{eff}}$ binds valence electrons more tightly) and decreases down a group (valence electrons are further away, experience greater shielding, and are easier to remove).

   • Octet Rule and Ion Charges:

   • Elements gain or lose electrons to achieve an octet ($ns^2 np^6$) of valence electrons, matching a stable noble gas configuration.

   • Group 1 metals form $+1$ cations; Group 2 metals form $+2$ cations; Group 13 metals form $+3$ cations.

   • Group 15 nonmetals form $-3$ anions; Group 16 nonmetals form $-2$ anions; Group 17 halogens form $-1$ anions.