Question

Suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 °C:

t(min) number of bacteria

0 100

20.0 200

40.0 400

60.0 800

80.0 1600

What is the order of the rate of production of the bacteria?

How many bacteria will be present after 1.40 × 102 min?

What is the rate constant for the process?

Answer 1

a)

if you see the data, for every 20 min, number of bacteria doubles. This is the quality of 1st order reaction
Answer: First Order
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c)

Bacteria doubles in 20 minutes
So,
K = 0.693/20
   =0.03465 min-1
Answer: Rate constant = 0.03465 min-1
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b)

t = 1.4*10^2 min = 140 min
use:
[A] = [Ao]*e^(k*t)
       = 100*e^(0.03465*140
       = 12787
Answer: 12787