Question

Question #a6570

Answer 1

The time required is 35 days.

Explanation:

For a third order reaction of the type

`"A" → "P"`

the rate law is

`color(blue)(|bar(ul(color(white)(a/a)-(d[A])/dt = k[A]^3color(white)(a/a)|)))" "`

and the integrated rate law is

`color(blue)(|bar(ul(color(white)(a/a)1/[A]^2 = 1/[A]_0^2 + 2kt color(white)(a/a)|)))" "`

The time `t` required for the concentration of `"A"` to decrease from `"[A]"_0` to `"[A]"` is

`t = 1/(2k)(1/[A]^2 - 1/[A]_0^2)`

∴ `t = 1/(2× 3.50×10^"-4"color(red)(cancel(color(black)("L"^2"mol"^"-2")))"s"^"-1")(1/(0.021 color(red)(cancel(color(black)("mol·L"^"-1"))))^2 - 1/(0.077 color(red)(cancel(color(black)("mol·L"^"-1"))))^2) = 1429×2099 = 3.00 × 10^6color(white)(l) "s" = 5.00 × 10^4 color(white)(l)"min" = "833 h" = "35 days"`