Question

?t (min) Number of bacteria 0.00.0 100100 20.020.0 200200 40.040.0 400400 60.060.0 800800 80.080.0 16001600 Suppose...

?t (min) Number of bacteria
0.00.0 100100
20.020.0 200200
40.040.0 400400
60.060.0 800800
80.080.0 16001600

Suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria. At 37 °C, you collect the data summarized in the table.

How many bacteria will be present after 1.40×10^2 min?

What is the rate constant for the process?

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Answer #1

from the table rate of production of bacteria is proportional to time.

so this is first order process.

here for every 20 min , bacteria is double .

so half - life = 20 min

rate constant k = 0.693 / half - life

                        = 0.693 / 20

                       = 0.03465 min-1

time = 140 min

number of bacteria present = 100 x 2^(140 / 20)

                                            = 12800 bacteria

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