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.)