What is the balanced equation for heptane (C7H16) burning in oxygen to make carbon dioxide and water?

The balanced equation is ##"C"_7"H"_16 + "11O"_2 → "7CO"_2 + "8H"_2"O##.

You follow a systematic procedure to balance the equation.

Start with the unbalanced equation:

##"C"_7"H"_16 + "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"_7"H"_16##. We put a ##1## in front of it to remind ourselves that the coefficient is now fixed.

We start with

##color(red)(1)"C"_7"H"_16 + "O"_2 → "CO"_2 + "H"_2"O"##

Balance ##"C"##:

We have fixed 7 ##"C"## atoms on the left-hand side, so we need 7 ##"C"## atoms on the right-hand side. We put a ##7## in front of the ##"CO"_2##.

##color(red)(1)"C"_7"H"_16 + "O"_2 → color(blue)(7)"CO"_2 + "H"_2"O"##

Balance ##"O"##:

We can't balance ##"O"## yet because we have two formulas that contain ##"O"## and lack coefficients. So we balance ##"H"## instead.

Balance ##"H"##:

We have fixed 16 ##"H"## atoms on the left-hand side, so we need 16 ##"H"## atoms on the right-hand side. We put an ##8## in front of the ##"H"_2"O"##.

##color(red)(1)"C"_7"H"_16 + "O"_2 → color(blue)(7)"CO"_2 + color(green)(8)"H"_2"O"##

Now we can balance ##"O"##:

We have fixed 22 ##"O"## atoms on the right-hand side: 14 from the ##"CO"_2## and 8 from the ##"H"_2"O"##. We put an ##11## in front of the ##"O"_2##.

##color(red)(1)"C"_7"H"_16 + color(teal)(11)"O"_2 → color(blue)(7)"CO"_2 + color(green)(8)"H"_2"O"##

Every formula now has a fixed coefficient. We should have a balanced equation.

Let’s check:

##color(white)(m)"Element"color(white)(m)"Left-hand side"color(white)(m)"Right-hand side"## ##color(white)(mmll)"C"color(white)(mmmmml)7color(white)(mmmmmmmmll)7## ##color(white)(mmll)"H"color(white)(mmmmll)16color(white)(mmmmmmmm)16## ##color(white)(mmll)"O"color(white)(mmmmll)22color(white)(mmmmmmmm)22##

All atoms balance. The balanced equation is

##"C"_7"H"_16 + 11"O"_2 → 7"CO"_2 + 8"H"_2"O"##