Chemistry · Differential and integral forms of zero and first-order reactions, their characteristics and half-lives
of a first order reaction was completed in 70 min. How much it will take for com
\( 80 \% \) of a first order reaction was completed in 70 min. How much it will take for \( 90 \% \) completion of a reaction?
- A. 114 min
- B. 140 min
- C. \( 100 \mathrm{min} \)
- D. 200 min
Step-by-step solution
For a first-order reaction, the integrated rate law is k = (2.303/t) log([A]₀/[A]). Given 80% completion in 70 min, [A] = 0.2[A]₀, so k = (2.303/70) log(5) ≈ 0.0230 min⁻¹. For 90% completion, [A] = 0.1[A]₀, so t = (2.303/k) log(10) = 2.303/0.0230 ≈ 100 min. Alternatively, t₂/t₁ = log(10)/log(5) = 1/0.699 ≈ 1.43, so t₂ = 70 × 1.43 ≈ 100 min.
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