Question #a6570

1 Answer
Ernest Z.
May 2, 2016

The time required is 35 days.

Explanation:

For a third order reaction of the type

"A" → "P"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"

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