Question 12 of 16 In Map A General Chemistry 4th Editi University Science Books

Question

Question 12 of 16 In Map A General Chemistry 4th Editi University Science Books McQuamie Rock Gallogly presented by Sapling Leaming that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the data at t (min) Number of bacteria 100 20.0 200 40.0 400 60.0 800 80.0 1600 How many bacteria will be pre click to ed x 102 min? What is the order of the rate of production of the bacteria? Number O zero order bacteria o first order O second order What is the rate constant for the process? Number units 0 Select answer B There is a hint available! bottom divider bar. Click on the divider bar again to hide the hint. Close A Previous Give Up & View Solution Check Answer Next Ext O H Hint

Explanation / Answer

Given-

t (min)                 Number of bacteria

0                                         100

20                                       200

40                                       400

60                                       800

80                                       1600

1) The order of the rate of production of the bacteria-

Since number of bacteria double every 20 minutes, so order of the rate of production of the bacteria is 1st order. There would be a straight line on a graph, when we draw number of bacteria / t (min)      

2) Bacteria will be present after 10^2 min-

10^2 min = 100min

After 100 min1600 x 2 = 3200 bacteria will be present.

3) The rate constant for the process-

[A]o = 100

[A]t = 200

t = 20 min

Using first order integrated rate law

Ln [A]t = –k(t) + ln[A]o

ln[200] = –k(20) + ln[100]

5.298 = –k(20) + 4.605

5.298 - 4.605 = –k(20)

0.693 = –k(20)

–0.693 = k(20)

–0.693 / 20 = k

k = –0.03465 min^–1

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