Give the reaction for the following transformations:
$1$. Ethanol from ethane
$2$. Benzene from $2-$hexene

"$P$" is a hydrocarbon with the molecular formula $C_8H_{14}$. On ozonolysis,"$P$" forms "$Q$". "$Q$" on treatment with alkali under reflux conditions produces "$R$",which on treatment with $I_2/NaOH$ gives a yellow precipitate. Acidification of the solution gives "$S$". The structure of "$S$" is given below:
(Structure $S$: $1-$methyl$-2-$oxocyclopentanecarboxylic acid derivative or similar cyclic structure as per common reaction pathways).
The correct structure of "$P$" is:

Compound $A$ $(C_{11}H_{14}O_4)$ is a degradation product of the antibiotic vermiculine. It undergoes the following reactions as shown in the image. Identify the unknown compound $C$ $(C_{11}H_{18}O_2)$.

The major product $'A'$ of the following given reaction has $......\,sp^2$ hybridized carbon atoms.
$2,7-\text{Dimethyl}-2,6-\text{octadiene} \xrightarrow{H^{+}} A \text{ (Major Product)}$

Compound $(X)$ will be:
Compound $(X) \xrightarrow[Pt]{5H_2} \text{Saturated compound}$
Compound $(X) \xrightarrow{AgNO_3} \text{Precipitate}$
Compound $(X) \xrightarrow[Me_2S]{O_3} OHC-CH_2-CH_2-CO-CHO + HOOC-CHO + HCOOH + OHC-CHO$

The octane number is associated with which petroleum product?