Which one of the following characteristics apply to both ethene and ethyne
A) Explode when mixed with chlorine
B) Decolourise Baeyer’s reagent giving brown precipitate
C) Rapidly absorbed by cold conc. \[{{\rm{H}}_{\rm{2}}}{\rm{S}}{{\rm{O}}_{\rm{4}}}\]
D) Form white precipitate with silver nitrate solution

Hint: Potassium permanganate in the dilute form, which is also cold and acidified is termed Baeyer's reagent. It is used in the determination of alkenes and alkynes. The test of determination of alkenes and alkynes is called Baeyer’s test.

Complete Step by Step Answer:
Let’s understand Baeyer’s test in detail. The appearance of potassium permanganate is purple in colour. In Baeyer’s test, the potassium permanganate becomes colourless. This indicates the presence of an unsaturated compound, that is, alkene and alkyne. So, Baeyer’s test is also termed an unsaturation test.

Let’s write the reactions of ethene and ethyne with Baeyer’s test. The reaction of ethene with Baeyer’s reagent gives ethylene glycol and manganese oxide which appear in a brown colour.
\[{\rm{C}}{{\rm{H}}_{\rm{2}}} = {\rm{C}}{{\rm{H}}_{\rm{2}}} + {\rm{KMn}}{{\rm{O}}_{\rm{4}}} \overset{[O], H_{2}O}{\rightarrow} \mathop {{\rm{OH - C}}{{\rm{H}}_{\rm{2}}}{\rm{ - C}}{{\rm{H}}_{\rm{2}}} - {\rm{OH}}}\limits_{{\rm{Ethylene}}\,{\rm{glycol}}} + \mathop {{\rm{Mn}}{{\rm{O}}_{\rm{2}}}}\limits_{{\rm{Brown}}} \]

Now, we will discuss the reaction of ethyne with Baeyer’s reagent. The reaction of ethyne with Baeyer’s reagent gives oxalic and manganese dioxide. The chemical reaction is,
\[{\rm{C}}{{\rm{H}}_{\rm{2}}} = {\rm{C}}{{\rm{H}}_{\rm{2}}} + {\rm{KMn}}{{\rm{O}}_{\rm{4}}} \overset{[O],H_{2}O}{\rightarrow} \mathop {{\rm{COOH}} - {\rm{COOH}}}\limits_{{\rm{Oxalic}}\,{\rm{acid}}} + \mathop {{\rm{Mn}}{{\rm{O}}_{\rm{2}}}}\limits_{{\rm{Brown}}} \]
Therefore, ethene or ethyne undergoes a reaction with Baeyer’s reagent to give a brown coloured precipitate.
Therefore, option B is right.

Note: It is to be noted that only the acidic nature of potassium permanganate gives the test of unsaturation. If the medium is alkaline, the reaction will change. In such conditions, the purple coloured permanganate (VII) changes to green coloured manganate (VII) ions first and then changes to manganese (IV) oxide which is of dark brown colour.