Question

At 30°C, the half-life for the decomposition of AB₂ is 200 s and is independent of the initial concentration of AB₂. The time required for 80% of the AB₂ to decompose is ______.

(Given log 2 = 0.30, log 3 = 0.48)

Options

• 200 s

• 323 s

• 467 s

• 532 s

Answer 1

At 30°C, the half-life for the decomposition of AB₂ is 200 s and is independent of the initial concentration of AB₂. The time required for 80% of the AB₂ to decompose is 467 s.

Explanation:

Half-life t_1/2 = 200, independent of concentration ⟹ first-order reaction.

We need time for 80% decomposition, i.e., 20% remains.

For a first-order reaction:

k = `0.693/t_(1//2)`

k = `0.693/200`

= 3.465 × 10⁻³ s⁻¹

The general equation is given as

`ln ([A]_0/([A]))` = kt

For 80% decomposition,

[A] = 0.2 [A]₀

⇒ `[A]_0/([A]) = 1/0.2`

= 5

t = `2.303/k log (5)`

= `2.303/(3.465 xx 10^-3) xx 0.699`

= `1.610/0.003465`

t = 467 s