It has been reported that the rate of a batch photopolymerization of an aqueous

Question

It has been reported that the rate of a batch photopolymerization of an aqueous acrylamide solution using a light-sensitive dye is proportional to the square of the monomer concentration, [M]^2, and the square root of the absorbed light intensity, I^(1/2). Note that, although this polymerization is free radical, the apparent kinetics appear not to be typical of usual free-radical polymerization for which the rate of polymerization is proportional to the first power of monomer concentration and to the square root of the initiator concentration (eq. (2.25)). The following polymerization mechanism has been proposed to explain the observed kinetics:

Show that this mechanism appears to be correct by deriving an equation for the rate of propagation in terms of [M], I, and the appropriate rate constants. The following assumptions may be made:

1. Equal reactivity in the propagation steps

3. k_2<<k_5

4. The concentration of dye, [D], that has been activated by light and thereby controbutes to the first initiation step is proportional to the absorbed light intensity.

Explanation / Answer

First process is fee radical mechanishm i.e.its rate determine by intensity of light.

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