Thermodynamics: Chemical Potentials for Ideal and Non-Ideal Systems

Vocabulary-style flashcards defining key thermodynamics terms, equations, and standard states for ideal and non-ideal systems as presented in Lecture 6 by Prof. Sharon Cooper.

Chemical Potential ($\mu$)

The molar Gibbs energy ($G_m$) for a single component, or the partial molar Gibbs energy for multiple components; it signifies the potential for change.

Phase Stability

In a one-component system, the phase that possesses the lowest chemical potential ($\mu$) will be the most thermodynamically stable.

Gibbs-Duhem Equation

At constant $T$ and $p$, this equation shows that the chemical potentials do not vary independently: $\sum n_i d ext{\mu}_i = 0$.

Gaseous Standard State ($p^o$)

The state corresponding to the pure gas at $1\, ext{bar}$ pressure.

Configurational Entropy

The source of variation in chemical potential ($\mu$) arising from increased accessible volume, represented by the term $RT \ln(p/p^o)$.

Liquid Standard State ($*$)

The standard state corresponding to the pure liquid, where the pure liquid is in equilibrium with its vapour.

Ideal Solution (or Ideal Liquid Mixture)

A solution where interactions between molecules are identical irrespective of their identity, characterized by $\Delta H_{\text{mix}} = 0$.

Raoult's Law

An empirical law stating that for a solvent $A$, the partial pressure is $p_A = x_A p_A^*$, which holds increasingly well as $x_A \rightarrow 1$.

Non-Ideal Solution

A mixture where interactions between like and unlike molecules are different, resulting in $\Delta H_{\text{mix}} \neq 0$.

Henry's Law

A relationship obeyed by dilute solutes ($x_B \ll 0.1$) where the vapour pressure of solute $B$ is $p_B = x_B K_B$, and $K_B$ is the Henry's law constant.

Ideal Dilute Solution

A solution where the solvent behaves ideally according to Raoult's Law ($x_A \rightarrow 1$) and the solute obeys Henry's Law.

Molality ($m$)

The concentration of a solution expressed as moles of solute per $\text{kg}$ of solvent.

Hypothetical Standard State ($m^o$)

The standard state for an ideal dilute solution, defined as a $1\, ext{molal}$ solution in which molecular interactions are the same as in an infinitely dilute solution.

Activity ($a$)

A dimensionless quantity used to express the chemical potential for non-ideal systems: $\mu_i = \mu_i^o + RT \ln a_i$.

Activity Coefficient ($\gamma$)

A dimensionless factor that measures the deviation from ideality; $\gamma = 1$ for ideal systems and can be calculated as the ratio of actual pressure to Raoult's Law pressure.

Fugacity

The term used for activity in the context of gases when applying standard states at $1\, ext{bar}$, where $\gamma$ is specifically called the fugacity coefficient.