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Question:

The half-life period of a first-order chemical reaction is 6.93 minutes. The time required for the completion of 99% of the reaction is?

460.6 minutes

230.3 minutes

23.03 minutes

46.06 minutes

Solution:

K = 0.693/t1/2
K = 0.693/6.93 = 0.1 min⁻¹
For a first-order reaction,
ln(A₀/A) = Kt
Where,
A₀ = Initial concentration
A = Concentration at time t
K = Rate constant
t = Time
For 99% completion, only 1% of the reactant remains.
Therefore, A = 0.01A₀
ln(A₀/0.01A₀) = 0.1t
ln(100) = 0.1t
4.605 = 0.1t
t = 46.05 minutes ≈ 46.06 minutes