CBSE Class 12-science Answered
The half life for a first order reaction is 10 mins .What percentage of reactant will be left behind after 60mins.
Asked by dhruvrana348 | 28 Jun, 2020, 08:58: AM
Given:
50% reactant will be left behind after 60 min.
![straight t subscript bevelled 1 half end subscript space equals space 60 space min
Order space of space reaction space equals space first space order
So comma space for space first space order space reaction comma space
we space have
straight t subscript bevelled 1 half end subscript space equals space fraction numerator 0.693 over denominator straight k end fraction
straight k equals space fraction numerator 0.693 over denominator straight t subscript bevelled 1 half end subscript end fraction
space space equals fraction numerator 0.693 over denominator 60 end fraction
straight k space equals space 0.0115 space straight s to the power of negative 1 end exponent
For space time space 60 space min
straight k space equals fraction numerator 2.303 over denominator straight t end fraction log fraction numerator open square brackets straight a subscript 0 close square brackets over denominator open square brackets straight a close square brackets end fraction
therefore 0.0115 space equals fraction numerator 2.303 over denominator 60 end fraction log fraction numerator open square brackets straight a subscript 0 close square brackets over denominator open square brackets straight a close square brackets end fraction
log fraction numerator open square brackets straight a subscript 0 close square brackets over denominator open square brackets straight a close square brackets end fraction equals space 0.2996
fraction numerator open square brackets straight a subscript 0 close square brackets over denominator open square brackets straight a close square brackets end fraction space equals space antilog space left parenthesis 0.2996 right parenthesis
fraction numerator open square brackets straight a subscript 0 close square brackets over denominator open square brackets straight a close square brackets end fraction space equals space 1.99
space space space space space space space space space space space space almost equal to space 2
percent sign space of space the space reactant space left space after space 120 min space
fraction numerator open square brackets straight a close square brackets over denominator open square brackets straight a subscript 0 close square brackets end fraction cross times 100 space equals 1 half
space space space space space space space space space space space space space space space space space space space equals 50 percent sign](https://images.topperlearning.com/topper/tinymce/cache/3555ac23213c5d4e30bd4615667f3c36.png)
50% reactant will be left behind after 60 min.
Answered by Ramandeep | 29 Jun, 2020, 12:28: PM
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