What is this equation balanced: Octane reacts with oxygen to form Carbon dioxide and Water?

Hint: Combustion is a scientific word we can use for burning. It is a reaction in which reactants react with oxygen to produce products along with the release of heat and light. These reactions generally occur at high temperatures. Combustion however requires oxygen as one of the reactants and does not occur in an atmosphere devoid of Oxygen. These are examples of rapid reactions that produce flame.

Complete answer:
Octane is a colorless highly flammable hydrocarbon with the chemical formula ${C_8}{H_{18}}$. It has 18 structural isomers. The molar mass of Octane is 114.23 g/mol. It has a characteristic gasoline odour. It is highly volatile in nature. The combustion of all types of hydrocarbons produces Carbon dioxide and water. This process is useful to obtain energy. The reaction has negative Enthalpy $(\Delta H)$ value.
The general equation for combustion of hydrocarbons is as under-
${C_x}{H_y}(g) + \left( {x + \dfrac{y}{4}} \right){O_2}(g) \to xC{O_2}(g) + \dfrac{y}{2}{H_2}O(l) + heat$
Now we use this equation in case of Octane,
$\begin{gathered}
  {C_8}{H_{18}}(g) + \left( {8 + \dfrac{{18}}{4}} \right){O_2}(g) \to 8C{O_2}(g) + \dfrac{{18}}{2}{H_2}O(l) + heat \\
  {C_8}{H_{18}}(g) + \left( {\dfrac{{25}}{2}} \right){O_2}(g) \to 8C{O_2}(g) + 9{H_2}O(l) + heat \\
\end{gathered} $
To obtain the equation in whole number form we multiply the equation by 2-
$2{C_8}{H_{18}}(g) + 25{O_2}(g) \to 16C{O_2}(g) + 18{H_2}O(l) + heat$
This reaction is a very important reaction in Automobile engines. The Energy of Reactants is more than energy of the products thus we can say reaction is Exothermic. The heat of combustion of octane is -5500 kJ/mol.

Note:
 Octane is an important component of gasoline (petrol). The performance of gasoline depends on its octane rating. Octane rating is called “Anti Knock Rating”. The higher the octane rating the greater the resistance of gasoline to knock. It is the combustion of octane that produces large amount of energy and hence used as a fuel.