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In this case it really doesn't matter with which you start C or H, but mostly start with the simplest numbered: C. (Here the molecular coefficient is SET to a = 1 for C3H8, later it can be changed to a higer value when other coefficient are not a whole number)

Never start with the oxygen, it is in two products and can't be solved first.

aC3H8 + bO2 --> pCO2 + qH2O

C: 3a = p , if SET a=1, then p=3

H: 8a = 2q , if SET a=1, then q=4

So far:

1C3H8 + bO2 --> 3CO2 + 4H2O leaving b to be solved to a (whole) natural number

Then:

O: 2b = 2p + q = 6 + 4 then b = 5

Solved:

C3H8 + 5O2 --> 3CO2 + 4H2O

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Q: When C3H8 is combined with O2 in a reaction the two end products are carbon dioxide and water What element should you first look at in balancing this equation?
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