To determine the products 'X' and 'Y' formed from the reactions described, we need to analyze two processes involving sodium ethanoate.
The reaction of sodium ethanoate with soda lime (a mixture of sodium hydroxide and calcium oxide) is a decarboxylation reaction. The general reaction for decarboxylation of a carboxylate salt is:
\(RCOONa + \text{NaOH (soda lime)} \rightarrow RH + Na_2CO_3\)
In this case, sodium ethanoate \((\text{CH}_3\text{COONa})\) reacts with soda lime to produce methane \((\text{CH}_4)\) and sodium carbonate \((\text{Na}_2\text{CO}_3)\).
This process involves the Kolbe electrolysis where carboxylate ions are oxidized. The reaction is represented as follows:
The carboxylate ion \((\text{RCOO}^-)\) undergoes electrolysis to form an alkane. In this case:
\(2 \text{CH}_3\text{COO}^- + 2 \text{H}_2\text{O} \rightarrow \text{C}_2\text{H}_6 + 2 \text{CO}_2 + H_2 + 2 \text{OH}^-\text{ (using sodium ethanoate)}\)
This results in the formation of ethane \((\text{C}_2\text{H}_6)\) and other by-products.
From the above analysis, the products 'X' and 'Y' of the respective reactions are:
Thus, the correct option is Methane and Ethane.
Match the following:
In the following, \( [x] \) denotes the greatest integer less than or equal to \( x \). 
Choose the correct answer from the options given below:
For x < 0:
f(x) = ex + ax
For x ≥ 0:
f(x) = b(x - 1)2