A student investigates the reversible reaction

\[ \text{A(aq)} \rightleftharpoons \text{B(aq)} \]

at \(298\ \text{K}\). The student assigns each catalyzed pathway one of the following labels: homogeneous nonenzymatic, heterogeneous, or enzymatic. The observations and measured activation energies are shown below.

Pathway	Observation	\(E_{a,\mathrm{f}}\) \((\text{kJ mol}^{-1})\)	\(E_{a,\mathrm{r}}\) \((\text{kJ mol}^{-1})\)
\(\text{U}\)	No catalyst is present.	\(80\)	\(50\)
\(\text{P}\)	\(\text{C(aq)}\) forms \(\text{AC(aq)}\) in an elementary step and is regenerated in a later step.	\(55\)	\(25\)
\(\text{Q}\)	\(\text{A(aq)}\) adsorbs onto \(\text{M(s)}\), reacts on its surface, and desorbs as \(\text{B(aq)}\).	\(45\)	\(15\)
\(\text{R}\)	A dissolved protein \(\text{E(aq)}\) binds \(\text{A(aq)}\) at a shape-specific active site, releases \(\text{B(aq)}\), and is regenerated.	\(40\)	\(10\)

Which statement correctly classifies pathways \(\text{P}\), \(\text{Q}\), and \(\text{R}\) and predicts how each catalyst affects the equilibrium ratio \(\dfrac{[\text{B}]}{[\text{A}]}\) relative to pathway \(\text{U}\)?