What is the ratio of t3/4:t1/2 for a first order reaction?

Asked by lekhakarthikeyan | 26th Aug, 2018, 07:15: PM

Expert Answer:

For first-order reactions:
 
kt equals ln fraction numerator open square brackets straight A close square brackets over denominator open square brackets straight A subscript straight t close square brackets end fraction

For comma space straight t subscript bevelled 1 half end subscript space

open square brackets straight A close square brackets space equals 100 comma space space open square brackets straight A subscript straight t close square brackets space equals space 50

ln fraction numerator open square brackets 100 close square brackets over denominator open square brackets 50 close square brackets end fraction equals kt subscript bevelled 1 half end subscript

straight t subscript bevelled 1 half end subscript space equals space fraction numerator 0.693 over denominator straight k end fraction


For space straight t subscript bevelled 3 over 4 end subscript

open square brackets straight A close square brackets space equals 100 comma space space open square brackets straight A subscript straight t close square brackets space equals space 75

ln fraction numerator open square brackets 100 close square brackets over denominator open square brackets 75 close square brackets end fraction equals kt subscript bevelled 3 over 4 end subscript

straight t subscript bevelled 3 over 4 end subscript space equals fraction numerator space 0.3 over denominator straight k end fraction

therefore fraction numerator straight t subscript bevelled 3 over 4 end subscript space over denominator straight t subscript bevelled 1 half end subscript end fraction equals space fraction numerator space 0.3 over denominator up diagonal strike straight k end fraction cross times fraction numerator up diagonal strike straight k over denominator 0.693 end fraction

fraction numerator straight t subscript bevelled 3 over 4 end subscript space over denominator straight t subscript bevelled 1 half end subscript end fraction equals space 0.4

fraction numerator straight t subscript bevelled 3 over 4 end subscript space over denominator straight t subscript bevelled 1 half end subscript end fraction equals 2 over 5
The ratio of t3/4:t1/2 for a first-order reaction is 2:5 

Answered by Varsha | 27th Aug, 2018, 03:30: PM