The reaction between chloroethane (C2H5Cl) and water to form ethanol and HCl in aqueous solution proceeds very slowly at 298 K. Addition of a trace amount of silver ion, Ag+, greatly accelerates the reaction. A simplified mechanism is proposed:
(1) C2H5Cl + Ag+ ⇌ [C2H5Cl·Ag+] fast equilibrium, K1
(2) [C2H5Cl·Ag+] → C2H5+ AgCl(s) slow, k2
(3) C2H5+ + H2O → C2H5OH + H+ very fast
Assume the AgCl formed in step (2) precipitates immediately and does not redissolve, and that Ag+ is regenerated via an independent rapid process involving another species present in large excess.
(a) Derive an expression for the overall rate of ethanol formation in terms of k2, K1, [C2H5Cl], and the total dissolved concentration of silver species, [Ag+]total. Clearly state any steady-state or other kinetic assumptions you invoke.
(b) Using your derived rate law, predict quantitatively how the observed initial rate will change if [Ag+]total is doubled while all other conditions remain the same.
(c) Discuss two experimental observations you would expect if the regeneration of Ag+ were incomplete, leading to a gradual net decrease in dissolved Ag+ concentration over time.