The half life for a first order reaction is 10 mins .What percentage of reactant will be left behind after 60mins. 

Asked by dhruvrana348 | 28th Jun, 2020, 08:58: AM

Expert Answer:

Given:
 
 
 
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


50% reactant will be left behind after 60 min.

Answered by Ramandeep | 29th Jun, 2020, 12:28: PM