Phase Diagrams of Binary Mixtures and Gibbs Phase Rule

Flashcards covering solid-liquid and liquid-gas phase diagrams for binary mixtures, the lever rule, distillation principles, and the Gibbs Phase Rule based on Lecture 5 by Prof Sharon Cooper.

Eutectic point ($e$)

The minimum melting point of a mixture, where the liquid mixture is in equilibrium with solid A and solid B.

Eutectic composition

The specific mixture composition at the eutectic point which melts and freezes without changing its composition.

Frozen eutectic structure

A solid consisting of microdomains of solid A and microdomains of solid B.

Lever rule

A rule used to determine the relative amounts of liquid and solid phases in equilibrium, given by the formula $n_{\beta} l_{\beta} = n_{\beta} l_{\beta}$, where $n_{\beta}$ and $n_{\beta}$ are the number of moles of each phase.

Water-NaCl eutectic

A mixture of water ($77\,\text{wt.\%}$) and NaCl ($23\,\text{wt.\%}$) that has a eutectic point at $-21\,^{\circ}\text{C}$.

Traditional solder

A mixture with a eutectic composition of $67\,\text{wt.\%}$ tin ($T_m = 232\,^{\circ}\text{C}$) and $33\,\text{wt.\%}$ lead ($T_m = 327\,^{\circ}\text{C}$) resulting in a melting point of $183\,^{\circ}\text{C}$.

Deep eutectic solvents

Solvents with exceptionally low melting points compared to their pure components, such as a 1:2 mole ratio of choline chloride ($T_m = 302\,^{\circ}\text{C}$) and urea ($T_m = 133\,^{\circ}\text{C}$) which melts at $12\,^{\circ}\text{C}$.

Raoult's Law

A law for binary mixtures stating that the partial pressure of a component is proportional to its mole fraction in the liquid, expressed as $p_A = x_A p_A^*$.

Simple distillation

A process where vapour is withdrawn from a boiling mixture and condensed to separate components.

Fractional distillation

A process where the boiling and condensation cycle is repeated successively, causing the vapour to become progressively richer in the more volatile component.

Gibbs Phase Rule

A rule arising from the requirement of equal chemical potential across all equilibrium phases, used to determine the degrees of freedom ($F$) in a system.

Degrees of Freedom ($F$)

The number of independent variables (such as composition, pressure, or temperature) that can be varied without changing the number of phases in equilibrium.

$\beta$ phase

The solid phase (e.g., solid B) that starts to form when a binary mixture enters the two-phase region of a phase diagram upon cooling.

$\alpha$ phase

The liquid phase in a solid-liquid phase diagram that becomes richer in one component as the other component solidifies.

Vapour enrichment

The phenomenon where the mole fraction of the more volatile component in the gas phase ($y_A$) is higher than its mole fraction in the liquid phase ($x_A$).