[Rmerckx]

This is a question I got in molecular Physical Chemistry. This course deals with statistical thermodynamics. I have to determine the degree of dissociation of PO in the temperature range 200K-2000 K at a pressure of 1000 Pa. Anyone who can help me with this exercise? I don't see the reaction scheme. My thoughts were : 4PO P_4 + 2O_2 But this gives me a 4Th order equation which i can't solve. or 2PO  P_2+O_2
thanks !

[Corribus]

Can you provide the actual wording of the question (verbatim)?

[Enthalpy]

I've run Propep, a software for chemical equilibria in flames, on 16g oxygen and 31g phosphorus at 1kPa. Here under are the molar fractions.

========== 2000K ==========

O                    1.3200e-005
O2                   3.8964e-006
P                    1.0580e-003
PO                   8.0473e-001
PO2                  9.1652e-002
P2                   6.4740e-002
P2O3                 3.7638e-002
P2O4                 1.4476e-004
P2O5                 1.7093e-005
P3                   2.1799e-006
P3O6                 8.6031e-007
P4                   6.3651e-007

All gaseous.

========== 1000K ==========

PO                   2.0054e-005
PO2                  6.0515e-007
P2                   7.2306e-002
P2O3                 2.0800e-002
P2O4                 1.1807e-005
P3                   2.5759e-006
P3O6                 2.0438e-004
P4                   4.7768e-001
P4O6                 2.0417e-007
P4O7                 9.8869e-003
P4O8                 1.1812e-001
P4O9                 2.7708e-001
P4O10                2.3877e-002

All gaseous.

========== 500K ==========

P2                   9.4437e-008
P4                   5.5551e-001
P4O7                 1.5300e-004
P4O8                 2.5238e-002
P4O9                 3.9715e-001
P4O10                2.1943e-002

All gaseous.

========== 390K ==========

P4                   5.9817e-001
P4O7                 1.3182e-006
P4O8                 6.4889e-004
P4O9                 2.0281e-002
P4O10                5.9193e-004
Condensed species
P4O10(cr)            3.8031e-001

========== 200K ==========

Software fails. I suppose all products are solid or liquid, then Propep can't solve.

=========================

You can trust Propep's results when available. Especially, it finds autonomously the right produced species from its included base, which must be pretty complete for P and O. Though, it finds strictly equilibria, be there a credible reaction path to them or not. For instance, I suppose PO stays untouched at 200K, but from the equilibrium it's absent.

I can't imagine how to obtain by hand the above results. At some temperatures the alternatives to PO are PO₂, P₂ and P₂O₃, and others it's P₄, P₄O₉ and P₄O₈, still at other T solid P₄O₁₀ meddles in.

[Rmerckx]

Can you provide the actual wording of the question (verbatim)?

This is the actual question:
Questions in series B deal with calculating equilibrium constants of gas phase reactions using
statistical thermodynamics and using them to determine an equilibrium composition.
Determine the degree of dissociation of PO in the temperature range 200–2000 K at a pressure
of 1000 Pa.

[Enthalpy]

That's better. "Dissociation" means into oxygen and phosphorus, from the available PO. Once you've chosen the molecular formula for oxygen and phosphorus, it's a simple equilibrium, not influenced by the other combinations provided you suppose some pressure.

I still fear that the person who asked this just ignores how many compounds are possible, so to get a good mark you'll need more diplomacy than what I am capable of.