How can I balance an equation with odd numbers of certain elements?

[FTCC.student]

I know this is elementary stuff, but I'm in Gen Chem 1 and this is the only thing I am having trouble with. I am fine balancing most equations, but when there are odd numbers of certain elements I get sort of confused. For example:

C₂H₆ + O₂ \rightarrow CO₂ + H₂O

The Attempt at a Solution

I have tried several times, but the closest I could get was:

2C₂H₆ + 5O₂ \rightarrow 2CO₂ + 6H₂O

It is the Oxygen andHydrogen being uneven that is screwing me up. Right away I realize I have 3 Oxygen on the right and 2 on the left, so the first thing I tried to do was make both sides have 6 oxygen...

C₂H₆ + 3O₂ \rightarrow CO₂ + 4H₂O

But then that leaves me with 8 Hydrogen on the right, and only 6 on the left...I can't think of any ways to get that 6 to equal 8! Then I tried for 12 Oxygen on both sides instead of 6...then my problem is still Hydrogen.

So maybe y'all see what I'm confused about...like I said, this is the only thing I am having trouble with so far in Gen Chem is balancing this specific type of equation, and we have our first test on Tuesday! So hopefully someone can help :)

 

[Borek]

Let's start with 1 molecule of C₂H₆. It is obvious we will produce two CO₂ and three H₂O:

C₂H₆ + xO₂ → 2CO₂ + 3H₂O

Can you find x? It will be a fraction now - but you can multiply everything by some small integer to get rid of the denominator...

 

[FTCC.student]

It would be 3\frac{1}{2}, yes? So I should then multiply by a small integer to get rid of denom, multiply all by 2? Does that include the 3.5?

 

[Borek]

Yes, multiply 3.5 as well.