5. The half-life of a radioactive (follows first order rate law) isotope is 10 d
ID: 636615 • Letter: 5
Question
5. The half-life of a radioactive (follows first order rate law) isotope is 10 days. How many days would be required for the isotope to degrade to one eighth of its original radioactivity? 6. The following data were obtained for the reaction A + B C. AM [B] M Rate M/ 2.0 6.0 6.0 3.0 3.0 6.0 0.10 0.90 0.90 (a) Determine the differential rate law for this equation. Justify your answer (b) Experiment 1 was monitored until completion. How long did it take for the concentration of A to decrease by ? (c) What was the concentration of B at this same time? (d) Write down the process you went through to determine the answers to (a), (b), and (c). Explain how this problem helps to relate multiple types of rate laws.Explanation / Answer
Ques 5 : 1/2n =1/8
n=3
So it takes 3 half lives to dagrade to 1/8th
Half life = 10 days
Therefore it takes 30 days to degrade to 1/8th
Ques 6 :
a) rate = k [A]2
b) kt = ( 1/[A]t - 1/[A]0)
Kt = 1/[A]0
0.1=k × 4
k =1/40
t =40/2
t=20 sec
c) concentration of B is 2M
d) in a we just compared the change in change in rate by keeping the concentration of one reactant constant.
in b we just used the integrated rate laws.
in c we just calculated the change in concentration of A that same change was done for B.
ques 1:
In zero order reaction rate is independent of concentration.
in first order reaction rate is directly proportional to the concentration of reactant. RATE = K [concentration of reactant]
in second order reaction rate is directly proportional to the 2 power of concentration of reactant .
RATE = K [ concentration of reactant]2
it gives a parabola in graph btw rate and concentration of reactant.
ques 2:
differential rate law specifically based on law of mass action.it give the order of reaction.
integrated law give the integrated relation. Using integrated law we can find concentration of reactant at any instant of time.
ques 4:
t= 1/k ln ( [A]0/[A]t)
t= 1/k ln (4/3)
t= 0.13 hours
Ques 3:
kt = ln [A]0 --ln [A]t
ln [A]t = kt + ln [A]0
graph between time and natural log of concentration of reactant at time t. Time on x axis and ln [A]t on y axis.
Slope will give the rate constant and intersection on y axis give the initial concentration.
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