Start with the unbalanced equation:
"C"_8"H"_18 + "O"_2 → "CO"_2 + "H"_2"O"
A method that often works is to balance everything other than "O" and "H" first, then balance "O", and finally balance "H".
Another useful procedure is to start with what looks like the most complicated formula.
The most complicated formula looks like "C"_8"H"_18. We put a 1 in front of it to remind ourselves that the number is now fixed.
color(red)(1)"C"_8"H"_18 + "O"_2 → "CO"_2 + "H"_2"O"
Balance "C":
We have fixed "8C" on the left, so we need "8 C" on the right. Put an 8 in front of the "CO"_2.
color(red)(1)"C"_8"H"_18 + "O"_2 → color(blue)(8)"CO"_2 + "H"_2"O"
Balance "O":
We can't balance "O" because we have two formulas containing "O" that have no coefficients.
Balance "H":
We have fixed "18 H" on the left, so we need "18 H" on the right. Put a 9 in front of "H"_2"O".
color(red)(1)"C"_8"H"_18 + "O"_2 → color(blue)(8)"CO"_2 + color(orange)(9)"H"_2"O"
Balance "O":
We have fixed "25 O" on the right, so we need 25 "O" on the left.
Oops! That means we would need "12.5 O"_2 on the left.
My instructor never let me use fractions when balancing equations.
The solution: Multiply every coefficient by 2.
color(red)(2)"C"_8"H"_18 + "O"_2 → color(blue)(16)"CO"_2 + color(orange)(18)"H"_2"O"
Now, we have "50 O" on the right, so we can use "25 O"_2 on the left.
color(red)(2)"C"_8"H"_18 + color(purple)(25)"O"_2 → color(blue)(16)"CO"_2 + color(orange)(18)"H"_2"O"
Every formula now has a fixed coefficient. We should have a balanced equation.
Let’s check:
bb("Atom"color(white)(m)"Left hand side"color(white)(m)"Right hand side")
color(white)(m)"C"color(white)(mmmmmm)16color(white)(mmmmmmmm)16
color(white)(m)"H"color(white)(mmmmmm)36color(white)(mmmmmmmm)36
color(white)(m)"O"color(white)(mmmmmm)50color(white)(mmmmmmmm)50
All atoms balance! The balanced equation is
2"C"_8"H"_18 +25"O"_2 → 16"CO"_2 + 18"H"_2"O"
