Question

Radioactive iodine is used in nuclear imaging techniques such as photoemission tomography (PET scans) and X-ray CT scans. It decays according to the nuclear reaction below

I^123 à Te^123 + electron neutrino

The following experiments were run to determine the order of the reaction:

Rate (mol/L hr)    [I^123]

0.00725                     0.137

0.137                       0.275

0.00362                  0.0685

(a)write the generic rate law for this nuclear decay (rate=k[I^123]^n)

(b) what Is the value of k with its correct units?

(c) what is the half-life (t1/2) of I^123?

(d) What concentration of I^123 is left after 1 week if you start with an initial concentration of 0.05M?

Answer 1

rate=k[I¹²⁷]ⁿ

0.00725   = K(0.137)ⁿ

0.00362    = K(0.0685)ⁿ

two eq.are divided

0.00725 /0.00362 = K(0.137)ⁿ / K(0.0685)ⁿ

2                        =( 2)ⁿ

n = 1 first order

rate=k[I¹²⁷]ⁿ

rate=k[I¹²⁷]¹

0.00725   = K(0.137)¹

K = 0.0529hr^-1

C. K = 0.693/t1/2

    0.0529   = 0.693/t1/2

t1/2 = 0.693/0.0529   = 11.8 hr

d. k = 2.303/t log[A0]/[A]

t = 24*7 =168 hr

   0.0529 = 2.303/168 log0.05/[A]

log0.05/[A] =3.8

0.05/[A]    = 10^3.8

[A] =0.05/6309.5   = 0.00000079M