Question

The rate equation for a reaction,
N₂O → N₂ + 1/2O₂
is Rate = k[N₂O]⁰ = k. If the initial concentration of the reactant
is a mol Lit⁻¹, the half-life period of the reaction is
(a) t₁/₂ = a/2k
(b) -t₁/₂ = ka
(c) t₁/₂ = a/k
(d) t₁/₂ = k/a

Answer 1

answer : option (a) t½ = a/2k

The rate equation for a reaction,

N₂O → N₂ + 1/2O₂ is Rate = k[N₂O]⁰ = k. it shows rate of reaction is in zero order.

so, rate = k

⇒-d[N₂O]/dt = k

⇒∫d[N₂O] = -k∫dt

⇒[N₂O]_f - [N₂O]_i = -kt

in half life period, t = t½ and [N₂O] = [N₂O]_i/2

so, [N₂O]_i/2 - [N₂O]_i = -kt½

⇒-[N₂O]_i/2 = -kt½

given, [N₂O]_i = a mol/L

so, -a/2 = -kt½ ⇒a/2 = kt½

⇒t½ = a/2k

hence option (a) is correct choice.

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