A decomposes by two parallel first-order paths, A -> B (k_1 = 3.0x10^-3 s^-1) and A -> C (k_2 = 2.0x10^-3 s^-1). The overall rate constant for the disappearance of A, in s^-1, is

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A decomposes by two parallel first-order paths, $A B$ ( $k_{1} = 3.0 \times 1 0^{- 3} s^{- 1}$ ) and $A C$ ( $k_{2} = 2.0 \times 1 0^{- 3} s^{- 1}$ ). The overall rate constant for the disappearance of A, in $s^{- 1}$ , is

In parallel reactions the rates add:

- d [A] / d t = (k_{1} + k_{2}) [A]

. So

k = 3.0 \times 1 0^{- 3} + 2.0 \times 1 0^{- 3} = 5.0 \times 1 0^{- 3} s^{- 1}