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An example of an autocatalytic reaction is:
(A) Hydrogenation of oils
(B) Decomposition of nitroglycerine
(C) Oxidation of $N{a_3}As{O_3}$ in presence of $N{a_2}S{O_3}$
(D) Thermal decomposition of $KCl{O_3}$ in presence of $Mn{O_2}$

Answer
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Hint: If one of the reaction products in a reaction can act as a catalyst for the same reaction, then the reaction is said to be autocatalytic. The product formed which will act as a catalyst can be in solid, liquid or gaseous form.

Complete step by step solution:
We will get some information about autocatalytic reactions.
- If one of the reaction products in a reaction can act as a catalyst for the same reaction, then the reaction is said to be autocatalytic.
- If there are more than one reactions occurring at the same time where one of the products is acting as the catalyst for the other reactions, then the set of the reactions are called collectively autocatalytic.
- The decomposition of nitroglycerine can be given as
\[4{C_3}{H_5}{N_3}{O_9} \to 12C{O_2} + 10{H_2}O + {O_2} + 6{N_2}\]
Here, the four products are formed. Out of them, nitrogen gas acts as a catalyst for the decomposition reaction.
- In this way, the nitrogen gas produced as a product acts as a catalyst for the same reaction and hence it is called the auto-catalyst for that particular reaction.
- The catalysis reactions have other two types as well; homogenous and heterogenous catalysis. In homogenous catalysis the catalyst is in the same phase of the reactants. In heterogeneous catalysis, the catalysts are in different phases.
So, we can conclude that decomposition of nitroglycerine is an autocatalytic reaction.

Therefore, the correct answer is (B).

Note: There is another example of autocatalytic reaction in which ethanedioic acid is oxidized in presence of acidified potassium permanganate. This reaction is catalyzed by manganese ions.
\[2Mn{O_4}^{2 - } + 6{H^ + } + 5{C_2}{O_4}{H_2} \to 2M{n^{2 + }} + 10C{O_2} + 8{H_2}O\]