Chemical Kinetics and Nuclear ChemistryHard

Question

Read the following industrial methods for the preparation of H2SO4 and answer the question at the end. Professor Molina of the Massachusetts Institute of Technology won the 1995 Nobel Prize in Chemistry for his work on atmospheric chemistry. One reaction that he has studied in detail is the acid rain reaction which produces H2SO4 in the atmosphere. He has proposed two possible stoichiometric reactions :
    Proposal A : H2O (g) + SO3(g) → H2SO4(g)
    Proposal B : 2 H2O (g) + SO3(g) → H2SO4 (g) + H2O (g)
Using simple collision theory, what reaction orders would be expected for proposal B ?
Proposal B is thought to proceed by the following two-step process :
SO3 + 2 H2O SO3.2 H2O (fast)
SO3.2 H2O H2SO4 + H2O (slow)    
(SO3.2 H2O is a complex which is stabilized by hydrogen bonds and k2 << k1 or k-1).

Options

A.k [H2O] [SO3]
B.k[H2O]2 [SO3]
C.k [SO3]
D.k[H2O]

Solution

Rate determining step is slow step
Then   Rate = k2 [SO3 . 2 H2O]                    .....(i)
We know by fast equation

[SO3. 2 H2O] = [SO3] [H2O]2                    ....(ii)
put the value of [SO3 . 2 H2O] from (ii) to (i)
Rate = k2 ×   [SO3 ] [ H2O]2
Rate = k  [H2O]2 [SO3]

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