Match the rate expressions in LIST-I for the decomposition of X with the corresponding profiles provided in LIST-II. \( X_s \) and \( k \) are constants having appropriate units.
\( \mathrm{I} \rightarrow \mathrm{P};\ \mathrm{II} \rightarrow \mathrm{Q};\ \mathrm{III} \rightarrow \mathrm{S};\ \mathrm{IV} \rightarrow \mathrm{T} \)
\( \mathrm{I} \rightarrow \mathrm{R};\ \mathrm{II} \rightarrow \mathrm{S};\ \mathrm{III} \rightarrow \mathrm{S};\ \mathrm{IV} \rightarrow \mathrm{T} \)
\( \mathrm{I} \rightarrow \mathrm{P};\ \mathrm{II} \rightarrow \mathrm{Q};\ \mathrm{III} \rightarrow \mathrm{Q};\ \mathrm{IV} \rightarrow \mathrm{R} \)
\( \mathrm{I} \rightarrow \mathrm{R};\ \mathrm{II} \rightarrow \mathrm{S};\ \mathrm{III} \rightarrow \mathrm{Q};\ \mathrm{IV} \rightarrow \mathrm{R} \)
