# How would you balance the following equation: C3H8 + O2 --> CO3 + H20?

Dec 16, 2015

$\textcolor{b l u e}{2} {C}_{3} {H}_{8} + \textcolor{b l u e}{13} {O}_{2} \rightarrow \textcolor{b l u e}{6} C {O}_{3} + \textcolor{b l u e}{8} {H}_{2} O$

#### Explanation:

$\textcolor{b l u e}{n} {C}_{3} {H}_{8} + \textcolor{b l u e}{m} {O}_{2} \rightarrow \textcolor{b l u e}{p} C {O}_{3} + \textcolor{b l u e}{q} {H}_{2} O$

We are looking for minimal integer solutions for:

$3 n = p$
$8 n = 2 q$
$2 m = 3 p + q$

We can try a few values for $n$
$n = 1$

$3 \left(1\right) = p$ ...okay
$8 \left(1\right) = 2 q \rightarrow q = 4$ ...okay
$2 m = 3 \left(3\right) + 4$ ...No; would require $m$ to be a fraction

$n = 2$

$3 \left(2\right) = 6 = p$ ...okay
$8 \left(2\right) = 2 q \rightarrow q = 8$ ...okay
$2 m = 3 \left(6\right) + 8 \rightarrow m = 13$ ...okay

and we have our solution.