Step 1: Identify compound A.
Sulphur dioxide (\(SO_2\)) reacts with chlorine (\(Cl_2\)) in the presence of charcoal (a catalyst) to form sulfuryl chloride (\(SO_2Cl_2\)).
\( \text{SO}_2 + \text{Cl}_2 \xrightarrow{\text{charcoal}} \text{SO}_2\text{Cl}_2 \).
So, compound A is sulfuryl chloride.
Step 2: Identify compound B.
Sulfuryl chloride (A) reacts with white phosphorus (P\(_4\)). This is a chlorination reaction where SO\(_2\)Cl\(_2\) acts as a chlorinating agent. It chlorinates phosphorus to its higher oxidation state, forming phosphorus pentachloride (PCl\(_5\)).
\( 10\text{SO}_2\text{Cl}_2 + \text{P}_4 \rightarrow 4\text{PCl}_5 + 10\text{SO}_2 \).
So, compound B is phosphorus pentachloride, PCl\(_5\).
Step 3: Analyze the statements about PCl\(_5\).
(A) The shape of 'B' is pyramidal. This is incorrect. In the gaseous and liquid states, PCl\(_5\) has a trigonal bipyramidal shape.
(B) 'B' on hydrolysis gives phosphorus acid. This is incorrect. PCl\(_5\) undergoes complete hydrolysis to give phosphoric acid (H\(_3\)PO\(_4\)) and HCl. Phosphorus acid (H\(_3\)PO\(_3\)) is formed from the hydrolysis of PCl\(_3\).
\( \text{PCl}_5 + 4\text{H}_2\text{O} \rightarrow \text{H}_3\text{PO}_4 + 5\text{HCl} \).
(C) 'B' in solid state exists as an ionic solid. This is correct. In the solid state, PCl\(_5\) exists as an ionic lattice composed of the tetrahedral cation [PCl\(_4\)]\(^+\) and the octahedral anion [PCl\(_6\)]\(^-\).
(D) In 'B' all bonds are equivalent. This is incorrect. In its trigonal bipyramidal molecular form, PCl\(_5\) has two longer axial P-Cl bonds and three shorter equatorial P-Cl bonds. They are not equivalent. In the solid state, the bonds within the [PCl\(_4\)]\(^+\) ion are equivalent, and the bonds within the [PCl\(_6\)]\(^-\) ion are equivalent, but there are two different types of ions with different bond lengths.
Thus, the only correct statement is (C).