In $A k X_{1} k X_{- 1} I k X_{2} P$ with $k_{1} = 0.010 s^{- 1}$ , $k_{- 1} = 0.002 s^{- 1}$ , $k_{2} = 0.200 s^{- 1}$ , use the steady-state approximation for I. Select the correct statement(s).

AIf $k_{- 1}$ is raised to $2.0 s^{- 1}$ , the apparent rate constant falls to about $9.1 \times 1 0^{- 4} s^{- 1}$ .
BThe apparent first-order rate constant for the loss of A through P is $9.90 \times 1 0^{- 3} s^{- 1}$ .
CThe apparent rate constant can exceed $k_{1}$ if $k_{2}$ is made large enough.
DThe apparent rate constant exceeds $k_{2}$ .

Answer: A, B

Steady state:

k_{eff} = k_{1} k_{2} / (k_{- 1} + k_{2}) = (0.010) (0.200) / (0.002 + 0.200) = 9.90 \times 1 0^{- 3} s^{- 1}

. Since

k_{2} / (k_{- 1} + k_{2}) < 1

k_{eff} < k_{1}

always, and here it is far below

k_{2} = 0.200

. With

k_{- 1} = 2.0

k_{eff} = 0.0020/2.2 = 9.1 \times 1 0^{- 4} s^{- 1}