Atom Balance: C & O for CO and O2 Reaction

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SUMMARY

The discussion centers on the atom balance for carbon (C) and oxygen (O) in the reaction involving one mole of carbon monoxide (CO) and half a mole of oxygen (O2), resulting in products CO2, CO, O2, and O. The initial attempt at a solution reveals a system of equations that appears unsolvable due to having two equations and four unknowns. However, the unique solution emerges when considering the final state without CO, indicating an incomplete reaction, and recognizing that O2 cannot be negative while O does not occur.

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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?
 
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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.
 
Strange question. How is atom balance defined?
 

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