(a) Define isomerism. Draw all possible isomers of butane.

(b) "A compound 'X' on combustion gives a yellow flame with lots of smoke." What inference would you draw from this statement?

(c) State the role of alkaline $KMnO_4$ in the reaction involving conversion of an alcohol to corresponding carboxylic acid.

(a) Isomerism: The phenomenon in which compounds have the identical molecular formula but different structural arrangements of atoms is called structural isomerism.

Butane ($C_4H_{10}$) has two structural isomers:

1. $n$-Butane (Straight chain):

$$CH_3-CH_2-CH_2-CH_3$$

1. Isobutane (Branched chain, also known as 2-methylpropane):

$$\begin{array}{cccc} CH_3 & - & CH & - & CH_3 \\ & & | & & \\ & & CH_3 & & \end{array}$$

(b) Inference for Compound 'X':

Since compound 'X' burns with a yellow flame and produces a lot of black smoke (soot), it is inferred to be an unsaturated hydrocarbon (an alkene or alkyne). Unsaturated hydrocarbons have a higher carbon-to-hydrogen ratio compared to saturated ones. During combustion in air, the limited oxygen is insufficient to completely oxidize all the carbon, leading to unburnt carbon particles that glow yellow and escape as black smoke.

(c) Role of Alkaline $KMnO_4$:

Alkaline potassium permanganate ($KMnO_4$) acts as an oxidizing agent. It provides nascent oxygen to oxidize alcohols into their corresponding carboxylic acids (for example, converting ethanol to ethanoic acid).