Radioactive Iodine [131], is frequently used in biochemical studies. The rate of

Question

Radioactive Iodine [131], is frequently used in biochemical studies. The rate of decomposition of radioactive Iodine is shown below. You will determine whether the decomposition is a first order or second order process.

a.) Complete the table with the specified data

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b.) Determine if the decomposition of [131] is first order or second order. Explain why.

c.)What is the half-life for the reaction? Justify answer. (has nothing to do with the value of the rate constant)

d.) How long would it take for a 9.40 M of solution of [131] to decompose to 6.85 M? Justify answer.

Time (days) [131] ln[131] 1/[131] 0 12.00 2.48 .08 4 8.48 2.14 .12 8 6.00 1.79 .17 12 4.24 1.44 .24 16 3.00 1.10

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Explanation / Answer

ln [A] = -kt + ln [Ao]

( ln[Ao] - ln[A] ) / t = k

consider at time= 4

( 2.48- 2.14 ) / 4 = 0.085

consider at time = 8

( 2.48 - 1.79 ) / 8 = 0.08625

consider at time = 12

( 2.48 - 1.44 ) /12 = 0.0866

consider at time = 16

( 2.48 - 1.10 ) /16 = 0.08625

from the above calculations

all are equal to a constant k = 0.08625

so tthe decompostion follows first order reaction

c) half life is the time when half of the reactant is consumed

from the table

[Ao] = 12

so at half life

[A] = [Ao] /2 = 12/2 = 6

from the table it is clear that time = 8 days [A] =6

so the half life is 8 days

d) for first order kinetics

A= Aoe^-kt

6.85 = 9.40 e^-kt

kt =0.316

t = 0.316 / 0.08625

t = 3.67 days

so it takes 3.67 days

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