Question

For the following reaction,
\[ 2\,\mathrm{Pb_3O_4(s)} \rightleftharpoons 6\,\mathrm{PbO(s)} + \mathrm{O_2(g)} \] The correct option showing the number of phases (P), number of components (C) and degrees of freedom (F) is:

• A. P = 3, C = 2, F = 1
• B. P = 3, C = 3, F = 2
• C. P = 2, C = 3, F = 3
• D. P = 2, C = 2, F = 2

Hint:

Two distinct solids plus one gas give P = 3; three species tied by one reaction give C = 2; apply F = C - P + 2.

Answer 1

The Correct Option is A

Step 1: Count the phases present at equilibrium.
The system has \(\mathrm{Pb_3O_4(s)}\) as one solid phase and \(\mathrm{PbO(s)}\) as a second, chemically distinct solid phase (they don't mix into a single solid solution), plus \(\mathrm{O_2(g)}\) as a single gas phase (all gases mix into one phase). So \(P=3\).

Step 2: Count the number of independent components.
There are 3 chemical species: \(\mathrm{Pb_3O_4}\), \(\mathrm{PbO}\), and \(\mathrm{O_2}\), related by exactly one chemical equilibrium (the reaction itself). So:
\[ C = (\text{species}) - (\text{independent reactions}) = 3-1=2 \]
There is no extra concentration constraint since the solids are separate pure phases, not a single mixed phase.

Step 3: Apply the Gibbs phase rule.
\[ F = C-P+2 \]
Substituting \(C=2\), \(P=3\):
\[ F = 2-3+2=1 \]

Step 4: Sanity-check the result physically.
With one degree of freedom, once temperature is fixed, the equilibrium dissociation pressure of \(\mathrm{O_2}\) over the \(\mathrm{Pb_3O_4/PbO}\) mixture is automatically fixed, exactly the expected behaviour for a univariant three-phase equilibrium, analogous to \(\mathrm{CaCO_3(s) \rightleftharpoons CaO(s)+CO_2(g)}\), also \(P=3,C=2,F=1\).

Final Answer:
\(P=3\), \(C=2\), \(F=1\), option (A). \[ \boxed{P=3,\ C=2,\ F=1} \]