Step 1: Understanding the Question:
The question presents a three-step reaction sequence involving xenon, fluorine, and other reagents to form compounds \(P\), \(Q\), and \(R\). We need to identify the correct statements about these compounds. This question may have multiple correct answers.
Step 2: Key Formula or Approach:
1. Identify compounds \(P\), \(Q\), and \(R\) by analyzing each reaction step.
2. Determine the properties, geometry, and hybridization for each compound using VSEPR theory and known chemical reactions.
Step 3: Detailed Explanation:
Let us identify \(P\), \(Q\), and \(R\).
Reaction 1:
\[
\mathrm{Xe(g) + F_2(g) \xrightarrow[7\,bar]{873\,K} P}
\]
Xenon reacts with fluorine under suitable conditions to form xenon fluorides. Under the given conditions, the major product formed is \(XeF_4\).
Thus,
\[
P = XeF_4
\]
Reaction 2:
\[
P + O_2F_2 \xrightarrow{143\,K} Q + O_2
\]
\(O_2F_2\) acts as a fluorinating agent.
\[
XeF_4 + O_2F_2 \rightarrow XeF_6 + O_2
\]
Thus,
\[
Q = XeF_6
\]
Reaction 3:
\[
Q + H_2O \xrightarrow{\text{complete hydrolysis}} R + HF
\]
Complete hydrolysis of \(XeF_6\) gives:
\[
XeF_6 + 3H_2O \rightarrow XeO_3 + 6HF
\]
Thus,
\[
R = XeO_3
\]
Now evaluate the statements.
(A) \(P\) has two lone pairs of electrons on the central atom.
For \(XeF_4\):
- Xenon has \(8\) valence electrons.
- It forms \(4\) bonds with fluorine atoms.
- Remaining electrons form \(2\) lone pairs.
Hence, the statement is Correct.
(B) \(Q\) has a perfect octahedral geometry.
For \(XeF_6\):
- Xenon forms \(6\) bonds and has \(1\) lone pair.
- Due to the lone pair, the geometry becomes distorted octahedral.
Hence, the statement is Incorrect.
(C) \(Q\) can act as a fluorinating agent.
\(XeF_6\) is a strong fluorinating agent.
Hence, the statement is Correct.
(D) The molecular structure of \(R\) is trigonal pyramidal.
For \(XeO_3\):
- Xenon has \(3\) bonding pairs and \(1\) lone pair.
- Electron geometry is tetrahedral.
- Molecular geometry is trigonal pyramidal.
Hence, the statement is Correct.
Step 4: Final Answer:
Statements
\[
\boxed{(A),\ (C)\ \text{and}\ (D)}
\]
are correct.