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Radioactive phosphorus is used in the study of biochemical reaction mechanisms b

ID: 1054159 • Letter: R

Question

Radioactive phosphorus is used in the study of biochemical reaction mechanisms because phosphorus atoms are components of many biochemical molecules. The location of the phosphorus (and the location of the molecule it is bound in) can be detected from the electrons (beta particles) it produces: 32/15P rightarrow 32/16S + e^- The rate constant for this reaction is 4.85 times 10^-2 day^-1. What is the instantaneous rate of production of electrons in a sample with a phosphorus concentration of 0.0033 M? How many hours will it take a sample of a biochemical molecule containing radioactive phosphorus to decay by 25% of the original sample amount. What is the half-life for this reaction? Determine the percent of^32P leftover after 35 days.

Explanation / Answer

9. From the given data

a) Instantaneous rate = k[A] = 4.85 x 10^-2 x 0.0033 = 1.60 x 10^-4 M/d

b) using the first-order kinetics equation,

time (t) = (ln[A]o - ln[A])/k

[A]o = initial concentration

[A] = concentration remaining after time t

k = rate constant

we get,

time taken for 255 sample to decay

t = (ln(0.0033) - ln(0.75 x 0.0033))/4.85 x 10^-2

  = 5.9316 d

= 142.36 h

c) half-life = ln(2)/k

               = 0.693/4.85 x 10^-2

                = 14.292 d-1

d) percent leftover after t = 35 days

ln[A] = ln(0.0033) - 4.85 x 10^-2 x 35

[A] = 0.000604 M