need help with balancing equation: V2O5 to VO(acac)2

[Noff]

I have a two-step reaction of which I have to make a single balanced equation:

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V2O5 + 2H2SO4+ C2H5OH = 2VOSO4 + 3H2O + CH3CHO

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VOSO4 + 2C5H8O2 + Na2CO3 = VO(C5H7O2)2 + Na2SO4 + H2O + CO2

How may I proceed?

[expert]

V₂O₅ + 2H₂SO₄+ C₂H₅OH = 2VOSO₄ + 3H₂O + CH₃CHO
VOSO₄ + 2C₅H₈O₂ + Na₂CO₃ = VO(C₅H₇O₂)₂ + Na₂SO₄ + H₂O + CO₂


This is a 2-step process requiring different conditions: the first needs acid and the second needs base, so combined process is formal, not real.
To combine simply treat it as a math equation and on the next stage add chemistry.

From the second equation we have:
VOSO₄ = - 2C₅H₈O₂ - Na₂CO₃ + VO(C₅H₇O₂)₂ + Na₂SO₄ + H₂O + CO₂

put this into the first equation:
V₂O₅ + 2H₂SO₄+ C₂H₅OH = 2(- 2C₅H₈O₂ - Na₂CO₃ + VO(C₅H₇O₂)₂ + Na₂SO₄ + H₂O + CO₂) + 3H₂O + CH₃CHO

Adjust:

V₂O₅ + 2H₂SO₄+ C₂H₅OH = - 4C₅H₈O₂ - 2Na₂CO₃ + 2VO(C₅H₇O₂)₂ + 2Na₂SO₄ + 2H₂O + 2CO₂ + 3H₂O + CH₃CHO

V₂O₅ + 2H₂SO₄+ C₂H₅OH + 4C₅H₈O₂ + 2Na₂CO₃ = 2VO(C₅H₇O₂)₂ + 2Na₂SO₄ + 2CO₂ + 5H₂O + CH₃CHO

You can use it as a total equation or you can further adjust it to chemistry by eliminating reaction between H₂SO₄ and Na₂CO₃:
H₂SO₄ + Na₂CO₃ = Na₂SO₄ + H₂O + CO₂ or
2H₂SO₄ + 2Na₂CO₃ = 2Na₂SO₄ + 2H₂O + 2CO₂

Let’s identify and subtract the above reaction from both sides of the equation:

V₂O₅ + C₂H₅OH + 4C₅H₈O₂ = 2VO(C₅H₇O₂)₂ + 3H₂O + CH₃CHO

That’s the answer!

[Noff]

Thanks mate; 'just this morning, I thought about treating it as a standard algebraic equation; and the acid and base part I should have realised.

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V2O5 + 2H2SO4+ C2H5OH = 2VOSO4 + 3H2O + CH3CHO

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VOSO4 + 2C5H8O2 + Na2CO3 = VO(C5H7O2)2 + Na2SO4 + H2O + CO2

This is a 2-step process requiring different conditions: the first needs acid and the second needs base, so combined process is formal, not real.
To combine simply treat it as a math equation and on the next stage add chemistry.

From the second equation we have:

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VOSO4 = - 2C5H8O2 - Na2CO3 + VO(C5H7O2)2 + Na2SO4 + H2O + CO2

put this into the first equation:

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V2O5 + 2H2SO4+ C2H5OH = 2(- 2C5H8O2 - Na2CO3 + VO(C5H7O2)2 + Na2SO4 + H2O + CO2) + 3H2O + CH3CHO

Adjust:

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V2O5 + 2H2SO4+ C2H5OH = - 4C5H8O2 - 2Na2CO3 + 2VO(C5H7O2)2 + 2Na2SO4 + 2H2O + 2CO2 + 3H2O + CH3CHO

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V2O5 + 2H2SO4+ C2H5OH + 4C5H8O2 + 2Na2CO3 = 2VO(C5H7O2)2 + 2Na2SO4 + 2CO2 + 5H2O + CH3CHO

You can use it as a total equation or you can further adjust it to chemistry by eliminating reaction between

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H2SO4

and

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Na2CO3

:

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H2SO4 + Na2CO3 = Na2SO4 + H2O + CO2

or

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2H2SO4 + 2Na2CO3 = 2Na2SO4 + 2H2O + 2CO2

Let’s identify and subtract the above reaction from both sides of the equation:

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V2O5 + C2H5OH + 4C5H8O2 = 2VO(C5H7O2)2  + 3H2O + CH3CHO

That’s the answer!