Please answer the question complete and use polymath or excel in case needed.

The irreversible gas$-$phase reaction $2AB+C$ is conducted over a solid catalyst.

The reaction may be considered isothermal. The following reaction mechanism is

proposed, where $S$ represents a surface site:

i$)A+$SharrA$*S$ alscerption

ii$)A*S+A*SB*S+C+S$

iii$)B*SharrB+S$

surtace reaction $$ rake aterermining

It is proposed that step ii is rate determining and irreversible, whereas steps i and iii

are reversible and at equilibrium.

a$)$ Based on the proposed mechanism, derive a rate expression for the reaction.

$(8)$

Experiments in a differential reactor have been used to measure the rate of reaction,

and the results are shown in Table P$2($dat available in Excel template$).$

Table P$2$: Reaction rate as a function of partial pressure of $A,B$ and $C$

b$)$ Are the observed data consistent with the proposed mechanism? Motivate! $(5)$

c$)$ Under the experimental conditions given in Table $P2,$ do you expect that the

surface mainly consists of vacant sites, sites with adsorbed $A,$ sites with

adsorbed $B,$ or sites with adsorbed $C?$ Simplify the reaction rate expression

found under a$),$ based on observations $($Table P$2)$ and combining constants

into new ones?

d$)$ If the mechanism holds, what reaction rate do you predict for $P_A=2\mathrm{.}0$ bar, $P_B$

$=2\mathrm{.}0$ bar and $P_2=2\mathrm{.}0$ bar?