Gilly: gasoline is a mixture of many different hydrocarbons (different "n" and different isomers), and I'm sure octane (n=8: C8H18) is one of them. Analyzing and expanding the generic formula C8H18 of octane will show that as many as 18 octane isomers may exist. Among them, only n-octane is a straight-chain octane isomer, the remaining ones are branched-chain ones.

Octane (or n-octane): straight chain octane
2-Methylheptane
3-Methylheptane
4-Methylheptane
2,2-Dimethylhexane
2,3-Dimethylhexane
2,4-Dimethylhexane
2,5-Dimethylhexane
3,3-Dimethylhexane
3,4-Dimethylhexane
3-Ethylhexane
2,2,3-Trimethylpentane
2,2,4-Trimethylpentane (or isooctane)
2,3,3-Trimethylpentane
2,3,4-Trimethylpentane
2-Methyl-3-ethylpentane
3-Methyl-3-ethylpentane
Tetramethylbutane

As I said in my previous post, one of the current ways to increase the OCTANE rating of gasoline is to increase the amount of BRANCHED hydrocarbons such as isooctane (2,2,4-trimethylpentane) or many other branched hydrocarbons in gasoline. The reason why branched hydrocarbons burn smoothly with little knock can be explained based on the conceps of Standard Enthalpy (H), Entropy of Formation (S), Free Energy (G), and Activation Energy (E). I don't want to delve into explaining what these concepts are, because our purpose is to find out why OCTANE rating (anti-knock or no early combustion) of a specific type of gasoline will increase if there are more branched hydrocarbons in it.

Change in (G) = Change in (H) - T * Change in (S)

For a chemical process to occur spontaneously, the resulting change in Free Energy must be NEGATIVE. From the above formula, you can see that the change in Free Energy depends on the temperature (T in Kelvin), and becomes negative if T is large enough. However, it also requires that the Activation Energy (E)
supply is enough to bring the reactants (hydrocarbons and oxygen) into various transition states before they actually come into contact and react with each other. But we can temporarily ignore (E) for now, even though it's quite important to include it in some cases. For an internal engine combustion process, the Activation Energy (E) comes from piston compression heat and sparks.

The above formula implies that an early combustion (causing knocking) process may never occur if the temperature is low enough, but will occur spontaneously if the temperature is high enough to render the change in Free Energy NEGATIVE. Piston compression of the gasoline/air mixture produces heat (and higher temperature) in addition to sparks from spark plugs. Higher compression ratio is MB gas engines (such as 10:1) produces more heat (thermal energy -> activation energy), and higher temperature (change in (G)), thus gasoline with high octane rating is needed to prevent knocking in all MB gas engines.

It has been found that the changes in Standard Enthalpy and Entropy of Formation for most branched hydrocarbons during combustion process (and at a certain temperature) are in such a range of values that help keep the change in Free Energy POSITIVE (not occurring spontaneously), while straight-chain hydrocarbons with similar generic formulas more easily cause the change in Free Energy to be NEGATIVE (occurring spontaneously). Of course, when the temperature is high enough (thanks to high compression, sparks), the change in (G) for branched hydrocarbons will also become NEGATIVE (and Activation Energy (E) is high enough), and these hydrocarbons will burn right away (but delayed enough to prevent knocking).

BTW, T(in Kelvin) = 273.15 + T(in Celcius)

There are some other ways to increase the OCTANE rating via altering the change in (G) and activation energy (E) by adding Tetraethyl Lead Pb(C2H5)4 or Ethanol C2H5(OH) etc... in gasoline. Pb(C2H5)4 was banned from US gasoline for more than 20 years ago because lead is too poisonous and highly detrimental to the environment (BTW, I'm a "tree hugger" .) There are quite a few countries which are still using leaded gasoline.

I'm sorry if my explanations are confusing and ambiguous. English is my ESL. I wish I could explain it to you guys in Vietnamese

Best regards,

Eric