12 from Masterton Radioactive decay is firstorder in the con

12) (from Masterton) Radioactive decay is first-order in the concentration of the unstable (reactant) species. Suppose that you have a sample containing 4% by weight 14C, which has a half-life of 5700 years. What will the decay rate d[ \"C]/dt be 600 years from now? (Hint, use the integrated rate law to find [14C] at t-600, then use the instantaneous rate expression to find d[ \"C]/dt.) 14 14

Solution

Apply:

dC/dt = k*[C]

find k.

from 1st order:

t 1/2 = ln(2)/k

k = ln(2) / t1/2

k = ln(2) / (5700) = 1.2160*10^-4

now

Rate = k*[C]

[C] 4% --> 0.04

so

Rate = (1.2160*10^-4) ( 0.04) = -0.000004864 M/s