To prepare the feed for a polymerization process, a selective hydrogenation of phenyl acetylene (P) to styrene (S) is performed over a supported Pd catalyst in the liquid phase, in order to eliminate traces of this component that may poison the polymerization catalyst. The applied hydrogen pressure is 10 bar, sufficient to be in excess in the liquid phase. However, styrene can be further hydrogenated in a consecutive reaction to the undesired ethylbenzene (EB), resulting in a loss of monomer. a) Derive an LHHW-type rate expression for the conversion of phenyl acety- lene, assuming an irreversible overall reaction, based on the following four "elementary processes." Steps 1, 2, and 4 are in quasi-equilibrium. 1. H, +* *H, 2. P+ *P 3. 'P+ 'H, s+: 4. S+' S b) Propose, in analogy to the rate expression derived (do not derive), a rate expression for the styrene reaction to ethylbenzene. Moderators (M) are often added to suppress the consecutive reaction. Some people interpret this in terms of competitive adsorption of this moderator on the active sites, increasing the selectivity (= ratio of P and S conversion rates). c) Use your rate expressions as a basis to show whether this interpretation is correct or not. Comment on your conclusion.