In the conversion of sugar solution to alcohol, the chemical reaction obeys the law #A=10(1-e^(-0.231t))#, #t>=0# where t is the number of hours after the reaction commences, s is the sugar concentration (%), and A is the alcohol produced in litres.?

Question

Find the speed of reaction at t=5 hours

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Answer 1 · 2018-01-27T17:21:39

#1.37# litres/hour (3s.f.)

finding how much alcohol is produced after #5# hours:

#y(t) = 10(1-e^(-0.231t))#

#y(5) = 10(1-e^(-0.231*5))#

#-0.231*5 = -1.155#

#y(5) = 10(1-e^(-1.155))#

#10(1-e^(-1.155)) = 10 - 10e^(-1.155)#

#10 - 10e^(-1.155) = 10 - 3.15057...#

#=6.85# (3s.f.)

#y(5) = 6.85# (3s.f.)

after #5# hours, #6.85# litres of alcohol are produced.

speed of reaction = amount of alcohol produced / time

speed of reaction = #6.85 / 5# litres/hour

#=1.37# litres/hour (3s.f.)