Question

Question #d01e3

Answer 1

The time required is 8.499 s.

Explanation:

Whenever you see a kinetics problem that asks something like "What time is needed …", you can be pretty sure that you will have to use an integrated rate law.

The integrated rate law for a first-order reaction is

`color(blue)(|bar(ul(color(white)(a/a)ln(["A"]_0/(["A"]_t)) = ktcolor(white)(a/a)|)))" "`

In this problem,

`["A"]_0 = ["A"]_0`
`["A"]_t = 2/3 ["A"]_0`
`k = "0.047 71 s"^"-1"`

∴ `ln(stackrelcolor(blue)(1)(color(red)(cancel(color(black)(["A"]_0))))/(2/3color(red)(cancel(color(black)(["A"]_0))))) = ln(3/2) = 0.4055 = "0.047 71" t color(white)(l)"s"^"-1"`

`t = 0.4055/"0.047 71 s"^"-1" = "8.499 s"`