An organic compound undergoes firstorder decomposition If

Question

An organic compound undergoes first-order decomposition. If the time taken for the

60 \%

decomposition is

540 \mathrm{~s}

, then the time required for

90 \%

decomposition will be ________ s. (Nearest integer).

Given:

\ln 10=2.3 ; \log 2=0.3

DivineJEE · Accepted Answer

For the first order reaction, k=(1 / t) ln (a / a-x) => t=(1 / k) ln (a / a-x) When reaction is 60 \% completed, x=(60 / 100) a=0.6 a, t=540 seconds ; k= (1 / t_1) ln (a / a-0.6 a) Therefore t_1=(1 / k) ln (a / 0.4 a) When reaction is 90 \% completed, i.e., x=0.9 a k= (1 / t_2) ln (a / a-0.9 a) \ => t_2=(1 / k) ln (a / 0.1 a) \ Therefore (t_1 / t_2) =frac(1 / k) ln (a / 0.4 a)(1 / k) ln (a / 0.1 a) \ => (540 / t_2) =fracln (10 / 4)ln 10 => (540 / t_2) =(2.3log 10-2.3log 4 / 2.3log 10) => (540 / t_2) =(2.3-2.3(0.6) / 2.3) => (540 / t_2) =0.4 => t_2=(540 / 0.4)=1350 sec

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