A reactant decomposes with a half-life of 125 s when its initial concentration i

Question

A reactant decomposes with a half-life of 125 s when its initial concentration is 0.343 M. When the initial concentration is 0.568 M, this same reactant decomposes with the same half-life of 125 s. What is the order of the reaction? What is the value and unit of the rate constant for this reaction? Suppose that you place exactly 100 bacteria into a flask containing nutrients for the bacteria and that you find the following data at 37 degreeC: What is the order of the rate of production of the bacteria? What is the rate constant for the process? How many bacteria will be present after 135 min?

Explanation / Answer

1) in this case

the half life is independent of the initial concentration

so

the order of the reaction is 1

now

for 1st order reaction

half life (t1/2) = ln 2 / rate constant (k)

so

t1/2 = ln2 / k

125 = ln2 / k

k = 5.545 x 10-3

so

the rate constant is 5.545 x 10-3 s-1

2)

the reaction is first order

for 1st reaction

ln N = -kt + ln No

so

after t = 15 min

ln 200 = -15k + ln 100

k = -0.0462

so

the rate constant is -0.0462 min-1

now

t = 135 min

so

ln N = ( 0.0462 x 135) + ln 100

N = 51200

so

there will be 51200 bacteria after 135 min

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