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Chemistry-

General

Easy

Question

60% of a first order reaction was completed in 60 min. The time taken for reactants to decompose to half of their original amount will be

=30 min
=45 min
=20 min
=40 min

The correct answer is: =45 min

$t subscript 1 divided by 2 end subscript equals fraction numerator 0.69 over denominator k end fraction equals fraction numerator 0.3 cross times 2.3 over denominator k end fraction$
$t subscript 60 percent sign end subscript equals fraction numerator 2.3 over denominator k end fraction log invisible function application fraction numerator 100 over denominator 100 minus 60 end fraction equals fraction numerator 2.3 over denominator k end fraction log invisible function application fraction numerator 10 over denominator 4 end fraction$
$k equals fraction numerator 2.3 over denominator 60 end fraction log invisible function application fraction numerator 10 over denominator 4 end fraction$
$fraction numerator 0.3 cross times 2.3 over denominator t subscript 1 divided by 2 end subscript end fraction equals fraction numerator 2.3 over denominator 60 end fraction log invisible function application fraction numerator 10 over denominator 4 end fraction$
$equals fraction numerator 1 over denominator 60 end fraction open square brackets 1 minus 2 log invisible function application 2 close square brackets equals fraction numerator 1 over denominator 60 end fraction left square bracket 1 minus 0.6 right square bracket$
$fraction numerator 0.3 over denominator t subscript 1 divided by 2 end subscript end fraction equals fraction numerator 0.4 over denominator 60 end fraction$
$therefore t subscript 1 divided by 2 end subscript equals fraction numerator 60 cross times 0.3 over denominator 0.4 end fraction equals 45 blank m i n$
Use direct relation
$t subscript 1 divided by 2 end subscript equals 0.3 comma blank t subscript x percent sign end subscript equals open parentheses log invisible function application fraction numerator 100 over denominator 100 minus x end fraction close parentheses$
$t subscript 60 percent sign end subscript equals log invisible function application fraction numerator 10 over denominator 4 end fraction equals left parenthesis 0.4 right parenthesis$
$fraction numerator t subscript 1 divided by 2 end subscript over denominator t subscript 60 percent sign end subscript end fraction equals fraction numerator 0.3 over denominator 0.4 end fraction$
$therefore t subscript 1 divided by 2 end subscript equals t subscript 60 percent sign end subscript cross times fraction numerator 0.3 over denominator 0.4 end fraction equals fraction numerator 60 cross times 3 over denominator 4 end fraction equals 45 blank m i n$

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