Question

Find the three-fourths life, t_3/4 of a first order reaction when for it k = 7.4 × 10⁻⁵ s⁻¹.

Answer 1

For a first-order reaction

`t = 2.303/k log([A]_0/[A])`

At three-fourths life, 75% of the reactant has reacted, so

`[A] = [A]_0/4`

⇒ `[A]_0/[A]`

= 4

By using the formula

`t_(3//4) = 2.303/k log(4)`

log (4) = 0.6021, k = 7.4 ×10⁻⁵ s⁻¹

`t_(3//4) = (2.303 xx 0.6021)/(7.4 xx 10^-5)`

= `1.3874/(7.4 xx 10^-5)`

t_3/4 = 18748.6 seconds

t_3/4 = 1.87 × 10⁴ seconds