1. A first order reaction takes 14.3 minutes to be 50.0% complete. How long will
ID: 921618 • Letter: 1
Question
1. A first order reaction takes 14.3 minutes to be 50.0% complete. How long will the reaction take in minutes to be 90.5% complete? Calculate the rate constant for the reaction?
2. Copper-64 is used in studies of Wilson’s disease (the inability to metabolize copper) and in brain scans for tumors. If t1/2 = 12.8 hours for an administered dose of copper-64, calculate the number of days for copper-64 to drop 0.15% of the initial value administered.
anyone could solve these two physical chemistry problems?
Explanation / Answer
1) Given,
Half life ( t 1/2) = 14.3 min.
We know that for a first order reaction,
K = ln (2) / (Half life),
where K = Rate constant
=> K = 0.693 / 14.3 = 0.0485 min^-1
For a first order reaction,
C(t) = Co exp(-Kt)
where,
Co = Initial conc.
C(t) = conc. at time t
since the reaction needs to be 90.5 % complete, conc. of the reactant remaining after time t is = Co - (0.905 Co) = 0.095 Co
=> 0.095 Co = Co exp (-0.0485 t)
=> t = 48.53 min
2)
K = 0.693 / 12.8 = 0.0541 hour^-1
Let initial conc. = Co
=> C(t) = 0.15 Co / 100 = 0.0015 Co
0.0015 Co = Co exp (- 0.0541 t)
=> t = 120.19 hours = 5 days
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