General Chemistry: Gases, Thermochemistry, and Quantum Theory

Comprehensive practice flashcards covering gas laws, thermochemistry, calorimetry, and quantum electronic structure from General Chemistry lectures.

Specific Heat ($s$)

The amount of heat ($q$) required to raise the temperature of one gram ($1\,\text{g}$) of a substance by one degree Celsius ($1\,^\circ\text{C}$), calculated as $s = \frac{q}{m\Delta t}$ with units of $\text{J}/(\text{g}\cdot^\circ\text{C})$.

Heat Capacity ($C$)

The amount of heat ($q$) required to raise the temperature of a given quantity ($m$) of a substance by one degree Celsius ($1\,^\circ\text{C}$), calculated as $C = ms$ with units of $\text{J}/^\circ\text{C}$.

Total Heat Capacity of a Calorimeter System ($C_{\text{all}}$)

The combined heat capacity when a calorimeter system involves both water and the calorimeter vessel: $C_{\text{all}} = C_{\text{H}_2\text{O}} + C_{\text{calorimeter}}$, where the heat released by the reaction equals the heat absorbed by the surroundings: $q_{\text{all}} = C_{\text{all}}\Delta t = -q_{\text{rxn}}$.

Barometer

A device designed to measure atmospheric pressure using a column of liquid mercury, where standard atmospheric pressure supports a mercury column of height $760\,\text{mmHg}$ ($76\,\text{cm}$ or $1\,\text{atm}$) at sea level.

Manometer

An instrument consisting of a U-tube containing liquid mercury used to measure gas pressures, operating either as a closed-tube manometer ($P_{\text{gas}} = P_h$) or an open-tube manometer ($P_{\text{gas}} = P_h + P_{\text{atm}}$).

Boyle's Law

The gas law stating that at constant temperature and constant amount of gas, the volume ($V$) of a gas is inversely proportional to its pressure ($P$): $P \propto \frac{1}{V}$ or $P_1V_1 = P_2V_2$.

Charles's and Gay-Lussac's Law

The gas law stating that the volume ($V$) of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature in Kelvin: $V \propto T$ or $\frac{V_1}{T_1} = \frac{V_2}{T_2}$, where $T\,(\text{K}) = t\,(^\circ\text{C}) + 273.15$.

Avogadro's Law

The gas law stating that at constant temperature and pressure, the volume ($V$) of a gas is directly proportional to the number of moles ($n$) of the gas: $V \propto n$ or $\frac{V_1}{n_1} = \frac{V_2}{n_2}$.

Ideal Gas Equation

The equation of state summarizing the relationships among pressure, volume, temperature, and amount of gas: $PV = nRT$, where $R = 0.082057\,\text{L}\cdot\text{atm}/(\text{mol}\cdot\text{K})$.

Standard Temperature and Pressure (STP)

The standard set of baseline conditions for gases, defined as $0\,^\circ\text{C}$ ($273.15\,\text{K}$) and $1\,\text{atm}$, where $1\,\text{mole}$ of an ideal gas occupies $22.414\,\text{L}$.

Gas Density Equation ($d$)

The relationship used to determine the density of a gas in grams per liter ($\text{g/L}$) from its molar mass ($\mathcal{M}$), pressure ($P$), and temperature ($T$): $d = \frac{P\mathcal{M}}{RT}$.

Dalton's Law of Partial Pressures

The principle stating that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures that each gas would exert alone: $P_{\text{total}} = \sum P_i = P_1 + P_2 + \dots$.

Mole Fraction ($X_i$)

A dimensionless concentration unit representing the number of moles of one component ($n_i$) divided by the total moles of all components ($n_T$) in a mixture: $X_i = \frac{n_i}{n_T}$, where $P_i = X_i P_T$.

Kinetic Molecular Theory of Gases

A theoretical model explaining gas behavior based on four core postulates: gas molecules have negligible volume compared to container volume, travel continuously in random directions with elastic collisions, exert no intermolecular forces, and have average kinetic energy proportional to absolute temperature ($\text{KE} = \frac{1}{2}mu^2$).

Root-Mean-Square Speed ($u_{\text{rms}}$)

A statistical average of molecular speeds defined by $u_{\text{rms}} = \sqrt{\frac{3RT}{\mathcal{M}}}$, where $R = 8.314\,\text{J}/(\text{K}\cdot\text{mol})$ and molar mass $\mathcal{M}$ is expressed in $\text{kg/mol}$.

Gas Diffusion

The gradual mixing of molecules of one gas with molecules of another gas by virtue of their random kinetic thermal motion.

Gas Effusion

The process by which a gas under pressure escapes from one compartment of a container into an evacuated space by passing through a tiny pinhole.

Graham's Law of Effusion

The law stating that the rate of effusion of a gas is inversely proportional to the square root of its molar mass: $\frac{r_1}{r_2} = \frac{t_2}{t_1} = \sqrt{\frac{\mathcal{M}_2}{\mathcal{M}_1}}$.

Van der Waals Equation

An equation of state that models real nonideal gas behavior: $(P + \frac{an^2}{V^2})(V - nb) = nRT$, where $a$ accounts for attractive intermolecular forces and $b$ accounts for the finite volume of gas molecules.

Gas Laws Reminder Triangle

A mnemonic linking the ideal gas equation variables ($PV = nRT$) to the fundamental gas laws: connecting $P$ and $V$ for Boyle's law, $V$ and $T$ for Charles's law, and $V$ and $n$ for Avogadro's law.

General Gas Law Ratio

The relation $\frac{P_1V_1}{n_1T_1} = \frac{P_2V_2}{n_2T_2} = R$, which demonstrates that because the universal constant $R$ is invariant, holding any two variables constant directly derives Boyle's, Charles's, or Avogadro's laws.

Open System

A thermodynamic system that can exchange both matter and energy (usually as heat) across its boundary with the surroundings.

Closed System

A thermodynamic system that can exchange energy across its boundary with the surroundings, but cannot exchange mass.

Isolated System

A thermodynamic system that cannot exchange either mass or energy with its surroundings.

Exothermic Process

Any process that gives off heat to the surroundings, resulting in a negative heat flow ($q < 0$) and a negative enthalpy change ($\Delta H < 0$).

Endothermic Process

Any process in which heat is absorbed by the system from the surroundings, resulting in a positive heat flow ($q > 0$) and a positive enthalpy change ($\Delta H > 0$).

State Function

A thermodynamic property that depends solely on the current equilibrium state of the system, regardless of the pathway taken to reach that state (e.g., $\Delta U = U_{\text{final}} - U_{\text{initial}}$).

First Law of Thermodynamics

The law of conservation of energy stating that energy can be converted from one form to another but cannot be created or destroyed: $\Delta U_{\text{system}} + \Delta U_{\text{surroundings}} = 0$ or $\Delta U = q + w$.

Pressure-Volume Work ($w$)

The work resulting from gas expansion or compression against a constant external pressure: $w = -P\Delta V$, where expansion ($\Delta V > 0$) corresponds to work done by the system on the surroundings ($w < 0$), with $1\,\text{L}\cdot\text{atm} = 101.3\,\text{J}$.

Enthalpy ($H$)

A thermodynamic state function defined as $H = U + PV$, which quantifies the heat change of a process occurring at constant pressure: $\Delta H = q_p$.

Total System Energy Change Equation ($\Delta E$)

The formula $\Delta E = \Delta H - P\Delta V$, which combines constant-pressure heat flow ($\Delta H$) and mechanical expansion work ($-P\Delta V$) to find the overall internal energy change.

Constant-Pressure Calorimeter

A device (typically consisting of nested Styrofoam cups open to the atmosphere) used to measure the heat of non-combustion reactions: $q_{\text{rxn}} = -(q_{\text{water}} + q_{\text{cal}})$, where $\Delta H = q_{\text{rxn}}$.

Constant-Volume Calorimeter (Bomb Calorimeter)

A rigid, constant-volume apparatus ($\Delta V = 0$) immersed in water used to determine heats of combustion: $q_{\text{rxn}} = -(q_{\text{water}} + q_{\text{bomb}})$, where $\Delta H \approx q_{\text{rxn}}$.

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

The heat change resulting from the formation of one mole of a compound from its constituent elements in their standard states at $1\,\text{atm}$ and $25\,^\circ\text{C}$, with $\Delta H^\circ_f = 0$ for any element in its most stable allotropic form.

Hess's Law

The law stating that the enthalpy change for a chemical reaction is identical whether the reaction takes place in a single step or a series of steps, because enthalpy is a state function.

Direct Method for Enthalpy of Reaction

The calculation of $\Delta H^\circ_{\text{rxn}}$ using tabulated standard enthalpies of formation via: $\Delta H^\circ_{\text{rxn}} = \sum m\Delta H^\circ_f(\text{products}) - \sum n\Delta H^\circ_f(\text{reactants})$, where $m$ and $n$ are stoichiometric coefficients.

Indirect Method for Enthalpy of Reaction

A strategy using Hess's law to determine an unknown enthalpy of reaction by algebraically manipulating (reversing reactions and multiplying coefficients) and summing known thermochemical equations.

Enthalpy of Solution ($\Delta H_{\text{soln}}$)

The heat generated or absorbed when a solute dissolves completely in a solvent, given by $\Delta H_{\text{soln}} = U + \Delta H_{\text{hydr}}$, where $U$ is the lattice energy and $\Delta H_{\text{hydr}}$ is the heat of hydration.

Wavelength ($\lambda$)

The linear distance between identical points on successive waves (such as crest-to-crest or trough-to-trough), related to frequency and wave speed by $\lambda = \frac{c}{\nu}$.

Frequency ($\nu$)

The number of complete wave cycles that pass a fixed point per second, expressed in units of reciprocal seconds ($\text{s}^{-1}$) or Hertz ($1\,\text{Hz} = 1\,\text{cycle/s}$).

Photoelectric Effect

The ejection of electrons from the surface of a metal when struck by light with a frequency at or above a characteristic threshold frequency.

Work Function ($W$)

The minimum energy required to liberate an electron from the surface of a specific metal, related to kinetic energy by $\text{KE} = h\nu - W$.

Photon

A discrete packet or particle of electromagnetic radiation possessing energy equal to $E = h\nu = \frac{hc}{\lambda}$, where $h = 6.63 \times 10^{-34}\,\text{J}\cdot\text{s}$.

Line Emission Spectrum

A discontinuous spectrum of distinct, discrete wavelengths produced when light emitted by excited atoms passes through a slit and a prism onto a detector.

Balmer Series

The series of lines in the hydrogen atomic emission spectrum located in the visible and ultraviolet regions resulting from transitions that terminate at principal quantum level $n_f = 2$.

De Broglie Wavelength

The wavelength associated with any material particle having mass $m$ and velocity $u$, formulated as $\lambda = \frac{h}{mu}$.

Heisenberg Uncertainty Principle

The quantum mechanical principle stating that it is impossible to determine simultaneously both the exact position ($x$) and momentum ($p$) of a particle, governed by $\Delta x \Delta p \ge \frac{h}{4\pi}$.

Pauli Exclusion Principle

The quantum rule stating that no two electrons in an atom can have the exact same set of all four quantum numbers ($n, \ell, m_\ell, m_s$), meaning an orbital can accommodate at most two electrons with opposing spins.

Aufbau Principle

The principle stating that as protons are added one by one to build up the elements, electrons are added successively into the lowest-energy available atomic orbitals.

Diamagnetic Substance

A substance in which all electron spins are paired (such as ground-state $\text{Zn}$ or $\text{Ca}$), resulting in no net magnetic moment and slight repulsion by an external magnetic field.