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${ C }_{ 10 }{ H }_{ 22 }\rightarrow { C }_{ 5 }{ H }_{ 12 }{ +x }$
If this equation is considered as an experiment of cracking, the compound in the place of x is:
a.) ${ C }_{ 5 }{ H }_{ 10 }$
b.) ${ C }_{ 5 }{ H }_{ 12 }$
c.) ${ C }_{ 5 }{ H }_{ 8 }$
d.) ${ C }_{ 5 }{ H }_{ 5 }$

Answer
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Hint: Cracking is the process in which complex organic molecules such as kerogens (a mixture of organic compounds) or heavy hydrocarbons are broken down into simpler molecules such as light hydrocarbons, by the breaking of covalent carbon-carbon bonds in the precursors.

Complete step by step solution:
The balancing of ${ C }_{ 10 }{ H }_{ 22 }\rightarrow { C }_{ 5 }{ H }_{ 12 }{ +x }$ suggests that a number of a particular atom must be the same in the reactant and the product formed. Hence, the number of a carbon atom and the hydrogen atom in x is 5 and 10 respectively.
Therefore, the balanced chemical equation will be:
${ C }_{ 10 }{ H }_{ 22 }\rightarrow { C }_{ 5 }{ H }_{ 12 }{ +C }_{ 5 }{ H }_{ 10 }$

So, the correct answer is “Option A”.

Additional Information:
In thermal cracking, high temperatures in the range of ${ 450 }^{ \circ }{ C }$ to ${ 750 }^{ \circ }{ C }$ and pressures up to about 70 atmospheres are used.
The source of the large hydrocarbon molecules is the naphtha fraction of the gas oil fraction from the fractional distillation of crude oil (petroleum). Thermal cracking gives blends of products containing high extents of hydrocarbons with double bonds - alkenes.
 It is one of several cracking methods used in the petroleum industry to process crude oil and other petroleum products for commercial use.
Catalytic cracking is also being widely used. One of the examples that is used is zeolite which contains aluminium oxide and silicon oxide.

Note: The possibility to make a mistake is that you may choose option B. In cracking, a thermal decomposition reaction takes place, not a thermal dissociation reaction. Don’t confuse between two as dissociation reactions are usually reversible whereas decomposition reactions are usually irreversible.