Why dose a fuel with high ocatane number has less tendency to knock, whereas fuel with high centane number has more tendency to knock in an automobile engine ?

Explanation

Octane number is the percentage of isooctane in the mixture of isooctane and n-heptane. Octane number is for gasoline (petrol) fuel. A gasoline with octane number of 80 means `80%` of isooctane and `20%` of n-heptane, i.e., branched-chain alkane is more, so kncking is less. Branched-chain hydrocarbons burn more smoothyl to form more stable, less reactive `3^(@)` radicals, wheres straigth-chain hydrocarbons (e.g., n-heptane) form less stable, more reactive `1^(@)` and `2^(@)` radicals. In contrast, centane number is used for diesel fuel and is defined as the percentage of cetane in a mixture of cetane number 80 means `80%` of cetane `(C_(16)H_(34)` (a straight-chain hydrocarbon) and `20%` of `alpha`-methyl napthalene (aromatic compound). So, ity will not not burn smoothly and produce high knocking. But straight-chain hydrocarbons, e.g., cetane, ignite spontaneously in comparison to aromatic compounds. So, centane number determines the ignition of fuel. Higher cetane number means fuel will ignite faster but will prouduce higher knocking. Lower centane number means fuel will ignite slowly and will produce lesser knocking (rattling sound).