What is the balanced equation for combustions of propane gas that yields carbon dioxide and water?

A combustion reaction is a reaction between a hydrocarbon burned in oxygen to form carbon dioxide and water.

A hydrocarbon is a molecule composed of carbon and hydrogen in this case propane. The pro- prefix tells us we have 3 carbon.
For hydrocarbons that end in the suffix -ane the formula is #C_nH_(2n+2)#. This means we need 8 hydrogen, making the formula #C_3H_8#.

Now we can format the basic reaction.

#C_3H_8 + O_2 -> CO_2 + H_2O#

A reminder that oxygen is a diatomic molecule as a gas, #O_2#.

Begin by balancing the hydrogen by adding a coefficient of 4 in from of the water.

#C_3H_8 + O_2 -> CO_2 + 4H_2O#

This balances the hydrogen at 8. Now add a a coefficient of 3 in from of the carbon dioxide.

#C_3H_8 + O_2 -> 3CO_2 + 4H_2O#

This balances the carbon at 3. We now have 10 oxygen on the on the product side, 6 from #CO_2# and 4 from #H_2O#. We need to add a coefficient of 5 in front of the oxygen to balance the oxygen at 10.

#C_3H_8 + 5O_2 -> 3CO_2 + 4H_2O#

The combustion reaction is now balanced.

I hope this was helpful.
SMARTERTEACHER