Composite Reactions & the Steady State Approximation

HALOGENATION OF PROPANONE

Hint

To simplify a fraction, look carefully for (multiplier) terms that appear on both the top and bottom of the fraction, and hence can be cancelled.

Examples:

ACDE / BCF = ADE / BF

K(L+M) / 2JK = (L + M) / 2J

(WX - XY) / (ZX + X) = X(W - Y) / X(Z + 1) = (W - Y) / (Z + 1)

(RS)2T / R5S = R2S2T / R5S = S2T / R3S = ST / R3

Note: Only terms which are multipliers may be cancelled in this way, i.e. the following would NOT be valid:
(AB + C) / AD = (B + C) / D

Final Simplification of Rate Expression

Assuming that k-1[H+] << k2[I2], the k-1[H+] term on the bottom of the expression for the overall rate of consumption of iodine can be neglected, resulting in

-d[I2]/dt = + k1k2[H+][I2][Pk] / k2[I2]

This can be further simplified (by cancelling terms that appear top and bottom), giving the final expression (derived from Mechanism A) for the overall rate of consumption of iodine as

-d[I2]/dt = + k1[H+][Pk]

-d[I2]/dt = + k1k2[H+][I2][Pk]

-d[I2]/dt = + k1k2[H+][Pk]

-d[I2]/dt = + k2[I2]