Question

Which of the following represents the expression for `(3/4)^"th"` life of 1^st order reaction?

Options

• `"k"/2.303 xx log_10  4/3`

• `2.303/"k" log_10  3/4`

• `2.303/"k" xx log_10 4`

• `2.303/"k" xx log_10 3`

Answer 1

`2.303/"k" xx log_10 4`

Explanation:

For first order reaction, the rate law is

k = `2.303/"t" log_10  (["A"]_0)/(["A"]_"t")` ......(i)

where, k = rate constant

t = time

[A]₀ = initial concentration of reactant A and

[A]_t = concentration of reactant A at time t

At the end of time `("t"_(3//4))` corresponding to `(3/4)^"th"` life,

[A]_t = `(1 - 3/4)` [A]₀ = `1/4` [A]₀

∴ `(["A"]_0)/(["A"]_"t")` = 4

Substituting this in equation (i),

∴ `"t"_(3//4) = 2.303/"k" xx log_10 4`