Question

For performing a PET scan, a typical patient requires 0.300 g of 18F to allow for proper imaging. If the 18F must be produced off-site from the hospital or radiology lab, and delivery from the source takes 1.50 hours from the time of synthesis, what is the initial mass of 18F that must be produced?

Mass 18 F (g):	Rate (g/min):
21.0	0.133
33.0	0.209
5.00	0.0316
0.200	0.00127

Answer 1

Let the rate expression be given as follows,

Rate = K [18F]^a

where a = order of the reaction wrt 18F

From the data provided,

0.133 = K (21)^a ------------------ (1)

0.209 = K (33)^a ------------------(2)

0.0316 = K (5)^a --------------------(3)

0.00127 = K (0.2)^a ---------------(4)

(2) / (1) gives,

0.209 / 0.133 = (33/21)^a

=> 1.57 = 1.57^a

=> a = 1

Therefore,

Rate = K [18F]

Now from (1)

0.133 = K x 21

=> K = 0.00633

We know that for a first order reaction,

C(t) = Co exp (-Kt)

C(t) = Mass at time t = 0.3 g

Co = initial mass

t = time = 1.5 hours = 90 minutes

K = Rate constant = 0.00633

=> 0.3 = Co exp (-0.00633 x 90)

=> 0.3 = Co x 0.5655

=> Co = 0.53 g = Initial mass of 18F that must be produced