General Chemistry: Thermochemistry, Quantum Mechanics, Electron Configurations, and Periodic Trends

Comprehensive practice flashcards defining core terms across thermochemistry, quantum mechanics, electron configurations, and periodic trends from CHEN 1201.

First Law of Thermodynamics

The principle stating that the total energy of the universe is conserved ($\Delta E_{\text{universe}} = \Delta E_{\text{sys}} + \Delta E_{\text{surr}} = 0$), meaning energy cannot be created or destroyed, only transferred as heat ($q$) or work ($w$) via $\Delta E = q + w$.

State Function vs. Path Function

A state function is a property determined solely by the current state of the system independent of pathway (e.g., $E$, $H$, $P$, $V$, $T$), whereas a path function depends on the specific path taken (e.g., $q$, $w$).

Specific Heat Capacity ($C_s$)

The quantity of heat required to raise the temperature of $1\,\text{g}$ of a substance by $1\,^\circ\text{C}$, formulated as $q = m \cdot C_s \cdot \Delta T$.

Pressure-Volume Work

Mechanical work performed when a system expands or contracts against external pressure, calculated using $w = -P_{\text{ext}}\Delta V$.

Constant-Pressure Calorimetry

A calorimetric method conducted under open atmospheric pressure (e.g., coffee-cup calorimetry) where measured heat exchange directly equals the reaction enthalpy: $q_{\text{rxn}} = \Delta H_{\text{rxn}} = -q_{\text{soln}} = -m_{\text{soln}} \cdot C_{s,\text{soln}} \cdot \Delta T$.

Constant-Volume Calorimetry

A calorimetric method conducted in a rigid bomb container where $\Delta V = 0$ ($w = 0$), meaning measured heat corresponds directly to the change in internal energy: $\Delta E_{\text{rxn}} = q_v = -C_{\text{cal}} \cdot \Delta T$.

Hess's Law

A thermodynamic law stating that if a chemical reaction is expressed as the sum of a series of steps, the overall reaction enthalpy is the algebraic sum of the enthalpy changes for each step ($\Delta H_{\text{overall}} = \sum \Delta H_i$).

Standard Enthalpy of Formation ($\Delta H_f^\circ$)

The enthalpy change occurring when $1.0\,\text{mole}$ of a compound is synthesized from its pure constituent elements in their standard reference states at $1\,\text{atm}$, where $\Delta H_f^\circ \equiv 0$ for elements in their standard state.

Photoelectric Effect

The ejection of electrons from a material when irradiated with photons exceeding a threshold frequency ($\nu_0$), governed by $E = h\nu$ and $KE_{\max} = h\nu - \phi$.

De Broglie Wavelength

The wavelength associated with a matter particle possessing mass ($m$) and velocity ($v$), defined by $\lambda = \frac{h}{mv}$.

Heisenberg Uncertainty Principle

A quantum mechanical principle stating that it is impossible to simultaneously measure the exact position ($\Delta x$) and momentum ($m\Delta v$) of a particle: $\Delta x \cdot m\Delta v \ge \frac{h}{4\pi}$.

Principal Quantum Number ($n$)

The quantum number specifying the orbital size and primary electronic energy shell ($n = 1, 2, 3, \dots$).

Angular Momentum Quantum Number ($l$)

The quantum number determining the geometrical shape of an orbital subshell, ranging as integers from $0$ to $n - 1$ ($l = 0 \rightarrow s$, $l = 1 \rightarrow p$, $l = 2 \rightarrow d$, $l = 3 \rightarrow f$).

Magnetic Quantum Number ($m_l$)

The quantum number defining the 3D spatial orientation of an orbital within a subshell, taking integer values from $-l$ to $+l$ ($2l + 1$ orbitals per subshell).

Spin Quantum Number ($m_s$)

The quantum number specifying the intrinsic spin orientation of an electron, taking values of either $+\frac{1}{2}$ or $-\frac{1}{2}$.

Aufbau Principle

The orbital filling principle stating that electrons occupy the lowest available energy orbitals before populating higher energy levels.

Pauli Exclusion Principle

The fundamental rule stating that no two electrons in an atom can have the exact same set of four quantum numbers, limiting each individual orbital to a maximum of two electrons with opposite spins.

Hund's Rule

The orbital filling rule stating that degenerate orbitals are filled singly with parallel electron spins before pairing occurs.

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

The net positive charge experienced by valence electrons from the nucleus after accounting for shielding by inner core electrons ($Z_{\text{eff}} \approx Z - S$), which increases across a period.

First Ionization Energy ($IE_1$)

The minimum energy required to remove the most loosely held electron from a gaseous atom or ion in its ground state, generally increasing across a period and decreasing down a group.

Electron Affinity ($EA$)

The energy change associated with adding an electron to an isolated gaseous atom to form an anion, generally becoming more exothermic across a period.

Paramagnetism vs. Diamagnetism

Paramagnetic species contain one or more unpaired electrons and are attracted to external magnetic fields; diamagnetic species have all electron spins paired and are weakly repelled.

Lattice Energy ($\Delta H_{\text{latt}}$)

The electrostatic energy required to separate one mole of an ionic crystalline solid into gaseous ions, proportional to $\frac{q_1 q_2}{r}$, where ionic charge magnitudes dominate over ion-ion distance.

First Law of Thermodynamics

The law stating that the total energy of the universe is constant, meaning energy can neither be created nor destroyed; mathematically expressed as $\Delta E_{\text{sys}} = -\Delta E_{\text{surr}}$.

Internal Energy ($E$)

The sum of the kinetic and potential energies of all particles within a system; its change is given by $\Delta E = E_{\text{final}} - E_{\text{initial}} = q + w$.

State Function

A mathematical property whose value depends solely on the current equilibrium state of the system, not on the path taken to reach that state (examples include internal energy $E$, enthalpy $H$, pressure $P$, and temperature $T$).

Pressure-Volume Work ($w$)

Work associated with the expansion or compression of a gas against an external pressure, calculated using the equation $w = -P_{\text{ext}} \Delta V$, where $1\,\text{L}\cdot\text{atm} = 101.325\,\text{J}$.

Heat ($q$)

The transfer of thermal energy between a system and its surroundings caused by a temperature difference; quantified for a single substance by $q = m \cdot C_s \cdot \Delta T$.

Specific Heat Capacity ($C_s$)

The quantity of heat required to raise the temperature of $1\,\text{g}$ of a substance by $1\,^\circ\text{C}$ (or $1\,\text{K}$); for liquid water at $298\,\text{K}$, this value is $4.18\,\text{J}/(\text{g}\cdot^\circ\text{C})$.

Thermal Equilibrium

The condition reached when a system and its surroundings attain the same temperature, resulting in no net heat transfer ($q_{\text{sys}} = -q_{\text{surr}}$).

Calorie (cal)

A unit of energy defined by the exact conversion factor $1\,\text{cal} = 4.184\,\text{J}$, with a nutritional Calorie (Cal) or kilocalorie (kcal) equal to $1000\,\text{cal} = 4184\,\text{J}$.

Enthalpy ($H$)

A thermodynamic state function defined as $H = E + PV$; at constant pressure, the change in enthalpy equals the heat transferred by the system ($\Delta H = q_p$).

Exothermic Reaction

A process that releases heat to its surroundings, characterized by a negative change in enthalpy ($\Delta H < 0$) and a negative reaction heat ($q_{\text{rxn}} < 0$).

Endothermic Reaction

A process that absorbs heat from its surroundings, characterized by a positive change in enthalpy ($\Delta H > 0$) and a positive reaction heat ($q_{\text{rxn}} > 0$).

Bomb Calorimeter

A sealed, constant-volume apparatus used to measure $\Delta E_{\text{rxn}}$ for combustion reactions; because volume is constant ($w = 0$), heat flow satisfies $q_{\text{cal}} = C_{\text{cal}} \cdot \Delta T = -q_{\text{rxn}}$.

Coffee-Cup Calorimeter

A constant-pressure calorimeter made from nested Styrofoam cups used to determine $\Delta H_{\text{rxn}}$ in aqueous solutions, where $q_{\text{soln}} = m_{\text{soln}} \cdot C_{s,\text{soln}} \cdot \Delta T = -q_{\text{rxn}}$.

Hess's Law

The principle stating that if a chemical reaction can be written as the sum of a series of reaction steps, the overall enthalpy change $\Delta H^\circ_{\text{rxn}}$ is the sum of the enthalpy changes of the individual steps.

Standard Enthalpy of Formation ($\Delta H^\circ_f$)

The enthalpy change accompanying the formation of $1\,\text{mol}$ of a compound from its constituent elements in their standard states at $1\,\text{atm}$ and the temperature of interest.

Standard State

The reference state for a substance defined as $1\,\text{atm}$ for a pure gas, the pure stable liquid or solid at $1\,\text{atm}$ and the temperature of interest, or a concentration of exactly $1\,\text{M}$ for a substance in solution.

Electromagnetic Radiation

Energy transmitted through space by oscillating, mutually perpendicular electric and magnetic fields traveling at the speed of light ($c = 3.00 \times 10^8\,\text{m/s}$), related by $c = \nu \lambda$.

Constructive Interference

The phenomenon in wave mechanics where two waves traveling in phase align so their amplitudes reinforce each other, producing a resultant wave of greater amplitude.

Destructive Interference

The phenomenon occurring when waves are out of phase, causing their positive and negative amplitudes to cancel one another out.

Diffraction

The bending and spreading of a wave around the edges of an obstacle or as it passes through a slit of dimension comparable to its wavelength.

Photoelectric Effect

The ejection of electrons from the surface of a metal when light with a frequency equal to or higher than the threshold frequency ($\nu_0$) strikes the surface.

Work Function ($\phi$)

The minimum binding energy required to dislodge an electron from the surface of a specific metal, defined by $\phi = h\nu_0$, where $\nu_0$ is the threshold frequency.

Photon

A discrete packet or quantum of electromagnetic radiation whose energy is proportional to its frequency, calculated as $E = h\nu = \frac{hc}{\lambda}$.

Wave-Particle Duality

The concept in quantum mechanics demonstrating that light and subatomic matter exhibit complementary properties of both continuous waves and discrete particles.

Rydberg Equation

An empirical formula predicting the wavelengths of hydrogen emission lines: $\frac{1}{\lambda} = R \left(\frac{1}{m^2} - \frac{1}{n^2}\right)$, where $n > m$ and $R = 1.097 \times 10^{-2}\,\text{nm}^{-1}$.

Bohr Model

An atomic model postulating that electrons travel around the nucleus in discrete, stationary circular orbits of quantized energy ($E_n = -2.18 \times 10^{-18}\,\text{J}(1/n^2)$) and emit or absorb light during transitions between orbits.

De Broglie Wavelength

The wavelength associated with a moving particle of mass $m$ and velocity $v$, given by the de Broglie equation $\lambda = \frac{h}{mv}$.

Heisenberg's Uncertainty Principle

The quantum physical principle stating that the position ($\Delta x$) and momentum or velocity ($m\Delta v$) of a particle cannot be measured simultaneously with arbitrary precision, governed by $\Delta x \cdot m\Delta v \ge \frac{h}{4\pi}$.

Indeterminacy

The inherent property of subatomic particles asserting that exact physical trajectories cannot be determined; instead, statistical probability distribution maps specify the likelihood of locating a particle.

Schrödinger Equation

The fundamental quantum wave equation $H\psi = E\psi$, where $H$ is the Hamiltonian operator, $\psi$ is the wave function, and $E$ is the energy of the electron.

Principal Quantum Number ($n$)

An integer quantum number ($n = 1, 2, 3, \dots$) that dictates the overall size and primary energy level (shell) of an atomic orbital.

Angular Momentum Quantum Number ($l$)

An integer quantum number ranging from $0$ to $n - 1$ that specifies the three-dimensional geometric shape of an orbital ($l = 0$ corresponds to $s$, $l = 1$ to $p$, $l = 2$ to $d$, and $l = 3$ to $f$).

Magnetic Quantum Number ($m_l$)

An integer quantum number taking values from $-l$ to $+l$ that specifies the three-dimensional spatial orientation of an orbital within a given subshell.

Spin Quantum Number ($m_s$)

A quantum number indicating the intrinsic spin orientation of an electron within an orbital, restricted to the values $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down).

p Orbitals

A set of three mutually perpendicular, two-lobed dumbbell-shaped orbitals ($p_x, p_y, p_z$) corresponding to $l = 1$ with a nodal plane passing through the nucleus.

d Orbitals

A set of five orbitals corresponding to $l = 2$ ($d_{yz}, d_{xy}, d_{xz}, d_{x^2-y^2}, d_{z^2}$), where four display a four-lobed cloverleaf pattern with two nodal planes and one exhibits a two-lobed dumbbell encircled by a toroidal ring.

Degenerate Orbitals

Orbitals belonging to the same atom that possess identical energy levels, such as the three $p$ orbitals in a given subshell or the five $d$ orbitals in a subshell of an isolated atom.

Sublevel Splitting

The separation of orbital energies within the same principal energy level in multi-electron atoms ($E(s) < E(p) < E(d) < E(f)$) caused by electron shielding and orbital penetration.

Aufbau Principle

The rule establishing that electrons fill atomic orbitals in order of increasing energy, populating the lowest-energy available orbital before moving to higher levels ($1s \rightarrow 2s \rightarrow 2p \rightarrow 3s \rightarrow 3p \rightarrow 4s \rightarrow 3d \dots$).

Hund's Rule

The rule dictating that when degenerate orbitals are filled, electrons occupy them singly first with parallel spins to minimize electron-electron repulsion and achieve lower energy before pairing begins.

Pauli Exclusion Principle

The fundamental quantum principle establishing that no two electrons in the same atom can possess identical sets of all four quantum numbers ($n, l, m_l, m_s$); an orbital can hold at most two electrons with opposing spins.

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

The net positive charge experienced by an outer valence electron, estimated as the nuclear charge minus shielding core electrons ($Z_{\text{eff}} \approx Z - \text{core electrons}$); it increases from left to right across a period.

Shielding

The repulsive effect whereby inner-core electrons repel valence electrons, partially shielding them from experiencing the full positive charge of the nucleus.

Penetration

The spatial property of an outer-shell orbital whose probability distribution allows it to get close to the nucleus, feeling less shielding and experiencing a higher $Z_{\text{eff}}$.

Valence Electrons

Electrons located in the outermost shell that participate in chemical bonding; for main-group elements they occupy the outermost $s$ and $p$ subshells, while for transition metals they include outermost $s$ and incomplete $d$ electrons.

Paramagnetic

A characteristic of an atom, ion, or molecule that contains one or more unpaired electrons, causing it to be attracted toward an external magnetic field.

Diamagnetic

A characteristic of an atom, ion, or molecule in which all electrons are completely spin-paired, causing it to show no attraction and be slightly repelled by an external magnetic field.

Isoelectronic Series

A group of atoms or ions that contain identical numbers of electrons and share the same electron configuration, such as $S^{2-}$, $Cl^-$, $K^+$, and $Ca^{2+}$ (each with $18$ electrons).

Atomic Radius

A measure of the size of a neutral atom, typically defined as half the distance between nuclei in identical bonded atoms; it increases down a periodic group and decreases across a period from left to right.

Ionic Radius

The effective radius of an ion in an ionic crystal; cations are smaller than their parent atoms due to lost shells and higher $Z_{\text{eff}}$, while anions are larger than their parent atoms due to added electron-electron repulsion.

First Ionization Energy ($IE_1$)

The minimum energy required to remove the outermost electron from a neutral, gaseous atom in its ground state ($X(g) \rightarrow X^+(g) + e^-$); it generally increases across a period and decreases down a group.

Successive Ionization Energies

The energies required to sequentially remove additional electrons ($IE_1, IE_2, IE_3, \dots$) from an atom, which always increase and display a steep, dramatic jump once all valence electrons are removed and a core shell is broken.

Electron Affinity ($EA$)

The energy change associated with adding an electron to a neutral gaseous atom in its ground state ($X(g) + e^- \rightarrow X^-(g)$), which generally becomes more negative (favorable) across a period.

Metallic Character

The extent to which an element demonstrates metallic properties, particularly the propensity to lose valence electrons to form cations; it increases down a group and decreases across a period from left to right.

Lattice Energy

The energy required to completely separate $1\,\text{mol}$ of an ionic solid into its constituent individual gaseous ions ($MX(s) \rightarrow M^+(g) + X^-(g)$), which increases with higher ionic charge and shorter internuclear distance according to Coulomb's law ($E \propto \frac{q_1 q_2}{r}$).