Physical Chemistry: Multicomponent Systems and Thermodynamics

Vocabulary flashcards covering solutions, partial characteristics, ideal and non-ideal thermodynamics, osmosis, chemical equilibrium, Gibbs phase rule, external fields, and nonequilibrium states.

Solution

A homogeneous system consisting of two or more mixed components having variable concentrations.

Solvent

The component that constitutes the major part of a solution.

Solute

Any dissolved substance in a solution other than the solvent.

Molar Concentration ($c_i$)

The ratio of the number of moles of component $i$ to the volume $V$ of solution ($c_i = \frac{n_i}{V}$), with SI unit $\text{mole}\cdot\text{m}^{-3}$ or $\text{mole}\cdot\text{dm}^{-3}$.

Particle Concentration ($C_i$)

The number of particles of component $i$ per unit volume of solution ($C_i = \frac{N_i}{V}$), expressed in dimensions of $\text{m}^{-3}$ or $\text{dm}^{-3}$.

Mole Fraction ($x_i$)

The ratio of the number of moles of component $i$ to the total number of moles of all components in the solution ($x_i = \frac{n_i}{\sum_k n_k}$).

Mole Ratio ($r_i$)

The number of moles of solute $i$ per mole of solvent ($r_i = \frac{n_i}{n_1}$).

Molality ($m_i$)

The number of moles of component $i$ per kilogram of solvent, defined as $m_i = \frac{1000 \, n_i}{n_1 M_1}$, where $M_1$ is the molecular weight of the solvent.

Partial Volume ($v_i$)

The partial derivative of volume with respect to the amount of component $i$ at constant temperature, pressure, and amounts of all other components ($v_i = \left(\frac{\partial V}{\partial n_i}\right)_{T, P, \{n_j\}}$).

Chemical Potential ($\mu_i$)

The partial Gibbs free energy of a given component, defined as $\mu_i \equiv g_i = u_i - T s_i + P v_i$.

Partial Entropy ($s_i$)

The derivative of chemical potential with respect to temperature with a negative sign, given by $s_i = -\left(\frac{\partial \mu_i}{\partial T}\right)_{P, \{n_k\}}$.

Average Molar Quantity

An extensive thermodynamic property calculated per mole of mixture regardless of component type, such as average molar entropy $s = \frac{S}{n} = \sum_i x_i s_i$ or average molar volume $v = \frac{V}{n} = \sum_i x_i v_i$.

Ideal Solution

A solution in which the chemical potential of each component obeys $\mu_i = \mu_i^0 + RT \ln(x_i)$, where the standard chemical potential $\mu_i^0$ depends only on temperature and pressure.

Thermodynamic Factor of Compression ($\beta_i$)

A temperature-dependent factor describing the pressure dependence of partial volume in an ideal solution via $v_i = v_i^* (1 - \beta_i P)$, independent of pressure and composition.

Entropy of Mixing ($\Delta S$)

The increase in entropy resulting from preparing an ideal solution from individual pure components, given for a binary ideal solution by $\Delta S = -R [x \ln(x) + (1-x) \ln(1-x)]$.

Activity ($a_i$)

An effective concentration parameter introduced by G. N. Lewis to account for non-ideal behavior in the chemical potential formula $\mu_i = \mu_i^0 + RT \ln(a_i)$.

Activity Coefficient ($\gamma_i$)

The coefficient relating the activity of a component to its concentration ($a_i = \gamma_i c_i$), approaching $1$ in highly dilute solutions.

Osmotic Coefficient ($\phi$)

A thermodynamic parameter used to express the chemical potential of a non-ideal solvent as $\mu_1 = \mu_1^0 - \phi RT \sum_{i \neq 1} r_i$.

Osmotic Pressure ($\Pi$)

The extra hydrostatic pressure established at equilibrium when a solution is separated from its pure solvent by a membrane permeable only to the solvent.

van 't Hoff's Law

The relationship stating that for an ideal dilute solution, osmotic pressure is given by $\Pi = RT \sum_{i \neq 1} c_i$.

Chemical Variable ($\xi$)

The parameter specifying the extent or number of runs of a chemical reaction, defined by $d\xi = \frac{dn_i}{\nu_i}$.

Stoichiometric Coefficient ($\nu_i$)

The coefficient indicating the relative number of molecules of component $i$ produced or consumed in a chemical reaction equation.

Law of Mass Action

The condition of chemical equilibrium for reactions in dilute solutions expressed in concentrations as $K(P, T) = \prod_i c_i^{\nu_i}$.

Degree of Dissociation ($\alpha$)

The fraction of dissolved electrolyte that dissociates into ions, defined as $\alpha = \frac{c - c_{\text{BA}}}{c}$.

Ostwald's Law of Dilution

The relationship $\frac{\alpha^2 c}{1 - \alpha} = K$ for a $1:1$ electrolyte, demonstrating that the degree of dissociation $\alpha$ approaches $1$ as concentration $c$ decreases.

Gibbs Phase Rule

The thermodynamic law stating that in an equilibrium heterogeneous system with $k$ components, the number of phases $n$ cannot exceed $k + 2$ ($n \le k + 2$).

Thermodynamic Degrees of Freedom ($f$)

The number of independent thermodynamic variables that can be altered without disturbing phase equilibrium, given by $f = k + 2 - n$.

Total Chemical Potential ($\tilde{\mu}_i$)

The sum of the internal chemical potential $\mu_i$ and the potential energy of component $i$ in an external field ($\tilde{\mu}_i = \mu_i + u_{\text{pot}}$).

Electrochemical Potential

The total chemical potential of a charged species in an electric field, given by $\tilde{\mu}_i = \mu_i + z_i F \varphi$.

Barometric Formula

The hydrostatic differential relationship $dP = -\rho g \, dh$ describing fluid pressure variation in a gravitational field.

Leontovich Approach

A method of evaluating thermodynamic potentials of nonequilibrium states by modeling them as quasistatic equilibrium states under an additional external field $X$.