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Why do people commonly use octane as a synonym for petrol (gasoline)? Isn't petrol a mixture of hydrocarbon distillates--not a pure substance?

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Octane is a specific molecule with 8 carbons normally found among the many different molecules in gasoline. Pure iso-octane (2,2,4-trimethyl pentane) was chosen as the reference fuel standard for resistance to preignition for gasoline fuels. So the octane number of a fuel is a rating of the preignition potential of that fuel compared to a fuel containing 100 % iso-octane molecules. Since iso-octane is a mouthfull, the "iso" part was dropped and people just call it octane. This is why some vendor calls his product petrol or gasoline or gas or octane or high test, etc...

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Octanes are components of fuel. There is also such concept as "octane number", used to determine quality of gasoline. Higher octane number = higher activation energies, and higher $E_a$ = lower chance of uncontrolled ignition = higher cost per liter. "Gas station numbers" for fuels are octane numbers. You can see (I think) numbers from 87 to 97 (depends on your country), but usually even 92 is considered "premium". As we can see, octane number determines main properties and even gives "name" to types of fuel at gas stations. So, maybe it's okay to call petrol "octane", though I prefer to call it "gasoline" :)

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Octane number is a scale that is used to determine the quality of a fuel. It may be defined the percentage of isooctane by volume in a mixture of isooctane and n heptane that has the same anti knocking properties as fuel under examination.

Petroleum or crude oil is obtained in complex mixture of hydrocarbons (chiefly aliphatic with small amount of aromatic hydrocarbons) along with some trace amount of sulphur and nitrogen.

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Calling gasoline "octane" would be mistake. There are a few widespread misconceptions about this topic. Most importantly, many people think that gasoline contains large amounts of octane, mainly because of the frequent mentioning of the high octane number of gasoline. Accordingly, many textbook chapters about combustion use the reaction of octane as example for a combustion reaction. This is of course wrong or at least misleading.

In order to clear up some of the misconceptions, I have copied the contents from another answer, which fit even better here:

High-octane fuel does not contain a high concentration of octane.

The composition of gasoline varies widely; anyway, typical gasoline contains less than 1 % octane.

The octane number of gasoline does not describe the composition of gasoline. It refers to the measurement of the knock resistance of gasoline, which is usually expressed by their research octane number (RON) or motor octane number (MON). Both parameters are determined in single-cylinder four-stroke test engines with an adjustable compression ratio according to standardized test procedures, e.g. EN 25164 or ASTM D 2699 for RON, and EN 25163 or ASTM D 2700 for MON. During the measurement, the compression ratio is raised until a certain standardized level of knocking is reached. The corresponding octane number is determined by finding a reference mixture of heptane and “octane” that gives the same knock level. The octane number is the fraction of “octane” (in %) in the “octane”-heptane mixture. For example, gasoline with an octane number of 95 has the same knocking performance as a mixture of 95 % “octane” and 5 % heptane; however, this does not mean that the gasoline contains 95 % “octane”.

Nevertheless, the wrong idea that gasoline would contain a high concentration of octane is widespread. For example, in the first relevant Google hit, Ritter, S. Chem. Eng. News 2005, 83 (8), 37:

Octanes are an important component of gasoline because they help provide smoother combustion in the car’s cylinders and prevent knocking.

Also remarkable is the fact that many textbooks and lectures select the combustion reaction of octane of all the possible combustion reactions of gasoline to show the principle of combustion:

$$\ce{2C8H18 + 25 O2 -> 16 CO2 + 18 H2O}$$

The reference substance for the octane number is not octane.

The octane number refers to a mixture of heptane and “octane”. However, the “octane” used for this mixture is not the unbranched alkane octane. It is actually a branched isomer of octane with the traditional name “isooctane”. Thus, gasoline with an octane number of 95 actually has the same knocking performance as a mixture of 95 % “isooctane” and 5 % heptane; however, this also does not mean that the gasoline contains 95 % “isooctane”.

The octane number of pure octane is actually very low. Its knock resistance is worse than the performance of pure heptane, which has a octane number of zero by definition.

The “isooctane” that is used as a reference substance for the octane number is not isooctane.

The name isooctane was in accordance with older nomenclature rules. The corresponding systematic name according to current IUPAC recommendations is 2-methylheptane. However, the “isooctane” that is used for the determination of the octane number is not isooctane, i.e. it is not 2-methylheptane. This “isooctane” actually is 2,2,4-trimethylpentane, which is another isomer of octane. Thus, gasoline with an octane number of 95 actually has the same knocking performance as a mixture of 95 % 2,2,4-trimethylpentane and 5 % heptane; and once again, this does not mean that the gasoline contains 95 % 2,2,4-trimethylpentane.

By way of comparison, the octane number of pure isooctane (2-methylheptane) is only about 23.

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