Atom Balance: C & O for CO and O2 Reaction

[xzibition8612]

Homework Statement

One mole of CO and 1/2 mole of oxygen are mixed and the products consist of CO₂, CO, O₂, and O. Write the atom balance for C and O.

Homework Equations

Mass conservation

The Attempt at a Solution

1/2(O₂)+CO₂ -> aCO₂ +bCO+cO₂ +dO.
a, b, c, d are unknowns.

I make a table:

Element Reactants Products
C 1 a+b
O 2 2a+b+2c+d

Its unsolvable. 2 equations and 4 unknowns. But the answer is CO₂ <-> CO+1/2(O₂)

How?

 

[mfb]

It is solvable with a unique solution, if you consider a final state without CO (CO would just indicate your reaction was not complete) and take into account that O₂ cannot be negative and O won't happen.

 

[Borek]

Strange question. How is atom balance defined?