Write a balanced chemical equation for the complete combustion of pentane.

First it is important to know the molecular formula for pentane and the products of the combustion reaction so that we can write the unbalanced equation. From the prefix 'pent' we know that the hydrocarbon contains 5 carbons and because this is an alkane we can use the C_nH_2n+2 general formula to work out the molecular formula of pentane as C₅H₁₂. Because the question asks for complete combustion, the products are water (H₂O) and carbon dioxide (CO₂).

Therefore:

C₅H₁₂ + O₂ → CO₂ + H₂O

Now we need to balance this equation by ensuring the same number of each atom is on both sides. Starting with carbon, there are 5 on the left hand side but only one on the right hand side so we need to add a 5 in front of the CO₂. 

C₅H₁₂ + O₂ → 5CO₂ + H₂O

Next we need to balance the hydrogens. As there are 12 on the left but only 2 on the right we need to add a 6 in front of the H₂O to produce 12 in total (2 x 6 = 12).

C₅H₁₂ + O₂ → 5CO₂ + 6H₂O

Finally we need to balance the oxygens. There are 2 on the left but 16 on the right so we need to add an 8 in front of the O₂ on the left to produce 16 in total (2 x 8 = 16).

C₅H₁₂ + 8O₂ → 5CO₂ + 6H₂O