In one line
Phase rule numericals are solved by carefully counting P and C for the given equilibrium and then applying F = C − P + 2 (or F′ = C − P + 1 for condensed systems at constant pressure).
Explained simply
These questions are like a three-step checklist: count the separate parts (phases), count the minimum ingredients (components), and plug into the formula. Most mistakes happen in counting, not in the formula.
How it works
- Write the system clearly with physical states: (s), (l), (g), (aq).
- P: each solid = 1 phase; all gases together = 1 phase; each immiscible liquid = 1 phase; one solution = 1 phase.
- C: number of species − independent reactions − extra restrictions.
- Choose the rule: F = C − P + 2 normally; F′ = C − P + 1 if the question says condensed system or constant pressure (alloys).
- State the type: invariant, univariant, bivariant.
Key formula
\( F = C - P + 2 \qquad F' = C - P + 1 \)
Quick example
| System | P | C | F |
|---|---|---|---|
| Ice ⇌ water ⇌ vapour | 3 | 1 | 1 − 3 + 2 = 0 |
| Water ⇌ vapour | 2 | 1 | 1 |
| CaCO3(s) ⇌ CaO(s) + CO2(g) | 3 | 2 | 1 |
| NH4Cl(s) ⇌ NH3(g) + HCl(g) (closed, no extra gas) | 2 | 1 | 1 |
| NH4Cl(s) ⇌ NH3(g) + HCl(g) with extra NH3 | 2 | 2 | 2 |
| 3Fe(s) + 4H2O(g) ⇌ Fe3O4(s) + 4H2(g) | 3 | 3 | 2 |
| Saturated NaCl solution + solid NaCl + vapour | 3 | 2 | 1 |
| Pb–Ag at eutectic (constant pressure) | 3 | 2 | F′ = 2 − 3 + 1 = 0 |
| Pb–Ag melt only (constant pressure) | 1 | 2 | F′ = 2 |
Fe–steam case: N = 4 species, R = 1, C = 3; phases: Fe(s), Fe3O4(s), gas mixture = 3.
Common mistakes
- Counting H2O(g) and H2(g) as two phases.
- Forgetting the 1 : 1 restriction in NH4Cl decomposition.
- Using the full rule for an alloy question that clearly says constant pressure.
How MU asks it
"Calculate the number of phases, components and degrees of freedom for the following systems" (1 mark each, total 3–4 marks), or "Find F at the eutectic point of the Pb–Ag system." For full marks write P, C, the formula and F for each system on separate lines; a one-line reason for C (reaction or restriction) is what separates full marks from partial.