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My textbook states that branched alkanes are thermodynamically more stable than straight chain alkanes. Of course, iso-octane has an enthalpy of formation of $\Delta H_\mathrm f$= $\pu{-259.34 kJ mol-1}$ and n-octane has an enthalpy of formation of $\Delta H_\mathrm f$= $\pu{-249.73 kJ mol-1}$ which indicates that iso-octane is relatively more stable than n-octane at room temperature. When they are used as fuels, both produce energy and the enthaply of combustion of iso-octane would be less than enthalpy of combustion of n-octane. So, n-octane should be more efficient fuel than iso-octane. But in petrol, iso-octane has more composition than n-octane. Why?

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Because petrol engines work differently to diesel engines and the property differences matter more than the absolute energy of combustion

Your basic assumption is wrong: diesel engines use mainly straight chain hydrocarbons and it is petrol engines that prefer the unsaturated or branched hydrocarbons.

The absolute amount of energy produced in engines is not the most important factor in the fuel (at least when comparing hydrocarbon fuels). What matters is how they burn and how the particular engine type triggers that combustion.

Petrol engines use a spark and want a volatile fuel that can form a flammable vapour easily. Diesel engines trigger combustion by compressing the fuel-air mixture to the point where it combusts from the heat of compression. These modes of operation have different requirements. If spontaneous combustion happens in a petrol engine (before the spark) it damages the engine and lowers the power. So petrol uses a hydrocarbon mix that doesn't spontaneously ignite at typical engine pressures: this drives the choice to hydrocarbons that are more volatile but less likely to combust from pressure alone. Volatile unsaturated hydrocarbons have those properties. Diesel needs hydrocarbons that can combust without a spark at a given temperature. Saturated hydrocarbons fit this requirement (you can, simplistically, think of this as a product of the higher accessibility of their carbon chains to the oxygen in the air). See How or Why does diesel/kerosene have a much higher 'flash point' but lower auto/self-ignition point than gasoline/petrol? for more details.

Diesel engines tend to be slightly more efficient than petrol engines, partially because of the effect you note (though the situation is really far more complex and many features other than energy output are usually far more important).

But you overall observation that branched chain or unsaturated fuels are more common applies only to petrol engines.

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The main reason for the high quantity of iso-octane is to prevent Engine Knocking. The Wikipedia page for Octane explains this quite well:

The octane rating was originally determined by mixing fuels from only heptane and 2,2,4-trimethylpentane (a highly branched octane), and assigning anti-knock ratings of zero for pure heptane and 100 for pure 2,2,4-trimethylpentane. The anti-knock rating of this mixture would be the same as the percentage of the latter in the mix. Different isomers of octane can contribute to a lower or higher octane rating. For example, n-octane (the straight chain of 8 carbon atoms with no branching) has a -20 (negative) Research Octane Rating, whereas pure 2,2,4-trimethylpentane has an RON rating of 100. Some fuels have an octane rating higher than 100, notably those containing methanol or ethanol.

A fuel made of only octane would have such a high enthalpy of combustion, that it would combust spontaneously in the cylinders, causing knocking, as seen by the RON number of -20 for it. Thus, iso-octane content is high because it reduces knocking and prevents engine wear.

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