Deep-Dive Guides · Phase Equilibria

Phase Equilibria — the complete deep dive

One guide dense enough to take you from "I can state the phase rule" to CSIR-NET Part-C fluency. The organising idea: a phase diagram is a map of where matter is stable, and the Gibbs phase rule tells you exactly how many knobs (T, P, composition) you can turn independently in any region of that map.

Free extract — the opening section of the guide, in full.

0. How to use this guide — the master map ▲ top

Everything in phase equilibria is either "how many degrees of freedom?" (phase rule), "where is the boundary line?" (Clapeyron), or "how much of each phase?" (lever rule). Fix the map first:

Question	Tool	Master relation
Degrees of freedom	Gibbs phase rule	F = C − P + 2
Condensed system (P fixed)	reduced phase rule	F = C − P + 1
Slope of a phase boundary	Clapeyron	dP/dT = ΔH_trans/(TΔV_trans)
Vapour-pressure curve	Clausius–Clapeyron	ln(p₂/p₁) = −(ΔH_vap/R)(1/T₂ − 1/T₁)
Amount of each phase	lever rule	n_α·l_α = n_β·l_β
Vapour composition (ideal)	Raoult + Dalton	p_i = x_ip_i*; y_i = p_i/P
Solute between two solvents	Nernst distribution	K_D = c_org/c_aq

The three questions to ask of any phase problem: (1) How many components C and phases P? — then F follows immediately. (2) Am I on a line, in an area, or at a point of the diagram? (fixes P and thus F). (3) Do I need a boundary slope (Clapeyron), a composition (Raoult), or an amount (lever rule)? Answer these and the calculation is mechanical.

Definitions.Phase (P): a physically distinct, mechanically separable, homogeneous region. Component (C): the minimum number of independent chemical species needed to specify the composition of every phase (= species − independent relations among them). Degrees of freedom (F): the number of intensive variables (T, P, composition) that can be varied independently without changing the number of phases. R = 8.314 J K⁻¹ mol⁻¹.

Read the rest of this guide

The remaining 9 sections — The Gibbs phase rule, One-component systems, Two-component systems, Distillation and more — are part of ChemVidya Full Access, along with the other guides, the books, the study notes and 6,000+ practice questions with worked solutions.

See plans Read it in the app