For $A k X_{1} B k X_{2} C$ with $k_{1} = 0.30 mi n^{- 1}$ , $k_{2} = 0.10 mi n^{- 1}$ and $[A]_{0} = 0.600 M$ (no B or C initially), find the maximum concentration of B in M (two decimals). Use $3 = 1.732$ .

Numerical answer type, answer in M, tolerance 0.01.

Answer: 0.35 M

Setting

d [B] / d t = 0

in the solution

[B] = \frac{k _{1} [ A ] _{0}}{k _{2} - k _{1}} (e^{- k_{1} t} - e^{- k_{2} t})

gives

[B]_{m a x} = [A]_{0} (k_{2} / k_{1})^{k_{2} / (k_{1} - k_{2})}

. Here the exponent is

0.10/0.20 = 0.5

, so

[B]_{m a x} = 0.600 \times (1/3)^{0.5} = 0.600/1.732 = 0.35 M