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1) In the reaction A-->2B, the rate law was determined to be rate=k[A] 2 (k=0.1

ID: 871961 • Letter: 1

Question

1) In the reaction A-->2B, the rate law was determined to be rate=k[A]2 (k=0.1 M-1min-1). When the initial [A]=0.5M, what is the concentration of A after one hour?   

2) The half life of 131I is 8 days. How long will it take for 99.9% of a sample containing 131I to decay?

3) reaction A-->2B is first order in A. At time=0s, [A] was 1.0M and [B] was 0M. After 100s, [B] increased to 0.5M. What is the half life of A in this reaction?

4) The first order reaction A-->B+C has a half life (t1/2) of 30 min at 300K and 3min at 400K. What is the activation energy of the reaction? Can somebody show me how to do it step by steps!

Explanation / Answer

1)The rate constant units suggest the reaction to be second order

The rate of reaction -dCa/dt= 2KCa2 ( assuming constant volume and liquid phase reaction)

UPon integration

1/Ca-1/Cao= 2kt

K=0.1 , t= 60minutes= 3600sec

1/Ca-1/0.5= 2*0.1*60*60

1/ca =1/0.5+3600

Ca=0.000278M

2) half life is given by =0.693/ K =where K is rate constant

K =0.693/ half life =0.693/8=0.086625/days

for first order reaction

ln(Cao/Ca)= Kt (1)

Ca=concentration at time t

Percent decayed X=0.999

X=1-Ca/Cao= Ca/Cao=1-0.999=0.001

Cao/Ca=1000

Substituting in (1)

ln1000= 0.08625t

t=ln1000/0.08625=79.74 days

3) As per stoichiometry, for every 1 moles of A reacted, 2 moles of B is formed

Since concentraton ogf B is 0.5M, 0.25M of A must have reacted in 100 seconds

Cao=1M

Ca=0.75M

t=100second

For first order reaction

ln(Cao/Ca)=kt

ln(1/0.75)=1000K

K=0.00287/sec

Half life= 0.693/K= 0.693/0.00287=240 sec

4) For first order reaction

K=0.693/half life

at 300K

K300=0.693/30=0.0231/min

at 400K

K400 =0.693/3 =0.231/min

From Arhenius equation

ln(K400/K300)= (Ea/R)*(1/300-1/400)

ln(0.231/0.0231)= (Ea/R) *0.000833

2.3= (Ea/R)*0.000833

Ea/R= 2/0.000833=2400

Ea=2400*8.314 J/molK=19953.6 J/mol

ln(1000)