Photodissociation of Cr(CO)6 in the Presence of the Compound M

Question:
The photodissociation of Cr(CO)6 in the presence of the compound M is taking place according to the following mechanism:
Cr(CO)6 + hν → Cr(CO)5 + CO, with intensity I;
Cr(CO)5 + CO → Cr(CO)6 , with rate constant k2 ;
Cr(CO)5 + M → Cr(CO)5 M, with rate constant k3 ;
Cr(CO)5 M → Cr(CO)5 + M, with rate constant k4 .
The rate in the first reaction of the mechanism is equal to the intensity of absorbed light I. Assume also that the intensity is weak, i.e., I<< k4 [Cr(CO)5 M].
a) Determine the coefficient f in the rate equation

b) What is the value of f at M → 0.
c) What is the value of f when [CO] >> 1.

Solution:
a) According to the mechanism of the photodissociation, we have,

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