Question

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is ______. (Integer answer)

Options

• 1

• 4

• 2

• 0

Answer 1

For a first order reaction, the ratio of the time for 75% completion of a reaction to the time for 50% completion is 2.

Explanation:

k = `2.303/"t" log  "a"/("a - x")`

`therefore 2.303/"t"_(50%) log  100/(100 - 50) = 2.303/"t"_(75%) log  100/(100 - 75)`

`therefore 2.303/"t"_(50%) log 2 = 2.303/"t"_(75%) log 4`

`therefore "t"_(75%) = "t"_(50%) * 2.303/2.303 * (log 4)/(log 2)`

`therefore "t"_(75%) = "t"_(50%) * cancel(2.303)/cancel(2.303) * (cancel(log) cancel(4)^2)/(cancel(log) cancel(2)_1)`

`therefore "t"_(75%) = 2  "t"_(50%)`