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Two different first order reactions, A B and C D , are carried out at the same temperature. The rate constant of the second reaction is 4 times the rate constant of the first reaction ( k₂ = 4k₁ ). If t₁ is the time required for 99.9 % completion of the first reaction and t₂ is the time required for 90 % completion of the second reaction, then the ratio t₁ t₂ is

Correct answer

12

Step-by-step solution

For the first reaction ( A B ), the time for 99.9 % completion is: t₁ = 2.303 k₁ ( 100 100 - 99.9 ) t₁ = 2.303 k₁ ( 100 0.1 ) = 2.303 k₁ (1000) t₁ = 2.303 3 k₁ For the second reaction ( C D ), the time for 90 % completion is: t₂ = 2.303 k₂ ( 100 100 - 90 ) t₂ = 2.303 k₂ (10) = 2.303 1 k₂ Taking the ratio t₁ t₂ : t₁ t₂ = 2.303 3 k₁ 2.303 1 k₂ = 3 k₂ k₁ Given that k₂ = 4k₁ , we substitute k₂ k₁ = 4 : t₁ t₂ = 3 4 = 12 Answer: 12

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