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Question:

For a first order reaction A→B, the reaction rate at reactant concentration of 0.01 M is found to be 2.0×10⁻² molL⁻¹s⁻¹. The half-life period of the reaction is:

220 s

30 s

300 s

347 s

Solution:

For first order reaction, A→B
Rate = k × [A]
Given, rate = 2.0 × 10⁻² molL⁻¹s⁻¹
[A] = Conc. of A = 0.01 M
So, 2.0 × 10⁻² = k × 0.01
k = 2.0 × 10⁻²/0.01 s⁻¹ = 2.0 × 10¹ s⁻¹
For first order reaction,
t₁/₂ = 0.693/k = 0.693/2.0 × 10¹ = 346.5 ≈ 347 s