Consider the two different first order reaction given belowA + B → C (Reaction 1)P → Q (Reaction 2)The ratio of the half life of reaction 1 : Reaction 2 is 5 : 2. If t1 and t2 represent the time taken to complete 2/3rd and 4/5th of Reaction 1 and Reaction 2, respectively, then the value of the ratio t1 : t2 is ____________ × 10–1 (nearest integer).[Given : log10(3) = 0.477 and log10(5) = 0.699]

Engineering

Chemistry

Integrated Rate Law

Question

Consider the two different first order reaction given below

A + B → C (Reaction 1)

P → Q (Reaction 2)

The ratio of the half life of reaction 1 : Reaction 2 is 5 : 2. If t₁ and t₂ represent the time taken to complete 2/3^rd and 4/5^th of Reaction 1 and Reaction 2, respectively, then the value of the ratio t₁ : t₂ is ____________ × 10^–1 (nearest integer).

[Given : log₁₀(3) = 0.477 and log₁₀(5) = 0.699]

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$\frac{{(t_{\frac{1}{2}})}_{I}}{{(t_{\frac{1}{2}}^{2})}_{II}} = \frac{K_{2}}{K_{1}} = \frac{5}{2}$

$K_{1} t_{1} = ℓn \frac{1}{1 - \frac{2}{3}} = ℓn 3$

$K_{2} t_{2} = ℓn \frac{1}{1 - \frac{4}{5}} = ℓn 5$

$\frac{K_{1} t_{1}}{K_{2} t_{2}} = \frac{0.477}{0.699}$

$∴ \frac{t_{1}}{t_{2}} = \frac{0.477}{0.699} \times \frac{5}{2} = 1.7 = 17 \times 10^{- 1}$