Question

Question #ae9bf

Answer 1

It will take 17.5 days for the reaction to go to 95 % completion.

Explanation:

To solve this problem, we can use the second-order integrated rate law:

`color(blue)(bar(ul(|color(white)(a/a)1/(["A"]_t ) - 1/(["A"]_0) = ktcolor(white)(a/a)|)))" "`

Here,

`["A"]_0 = "0.45 mol/L"`
`["A"]_t = "0.05 × 0.45 mol/L = 0.0225 mol/L"`
`k = 2.8 × 10^"-5"color(white)(l) "L·mol"^"-1""s"^"-1"`

∴ `1/(0.0225 color(red)(cancel(color(black)("mol·L"^"-1")))) - 1/(0.45 color(red)(cancel(color(black)("mol·L"^"-1")))) = 2.8 × 10^"-5"color(white)(l) color(red)(cancel(color(black)("L·mol"^"-1")))"s"^"-1" × t`

`44.44 - 2.22 = 2.8 × 10^"-5"color(white)(l)"s"^"-1" × t`

`t = 42.22/(2.8 × 10^"-5"color(white)(l)"s"^"-1") = 1.51 × 10^6 "s" = "419 h" = "17.5 days"`