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Half life and activation energy

by Hemolymph
Tags: activation, energy, life
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Hemolymph
#1
Dec16-12, 10:48 AM
P: 30
1. The problem statement, all variables and given/known data
I have two questions that I just dont even know where to start

The activation energy for the reaction CH3CO CH3 + CO is 71 kJ/mol. How many times greater is
the rate constant for this reaction at 170C than at 150C?
A) 0.40 B) 1.1 C) 2.5 D) 4.0 E) 5.0

and
A certain reaction A products is second order in A. If this reaction is 10.% complete after 20. s, how
long would it take for the reaction to be 90.% complete?
A) 180 s B) 1600 s C) 440 s D) 18,000 s E) 540 s

2. Relevant equations

I know the second one is a second order reaction rate which has
1/[A]=1/[A_0]+kt
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Borek
#2
Dec16-12, 11:19 AM
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Have you heard about Arrhenius equation?
Hemolymph
#3
Dec16-12, 11:59 AM
P: 30
Quote Quote by Borek View Post
Have you heard about Arrhenius equation?
I cant see how I can apply the Arrhenius equation if I dont have any activation energies

Pranav-Arora
#4
Dec16-12, 01:55 PM
P: 3,804
Half life and activation energy

Quote Quote by Hemolymph View Post
I cant see how I can apply the Arrhenius equation if I dont have any activation energies
Activation energy is given in the problem statement.

You will have to derive an equation using the Arrhenius equation to relate the rate constants. Take logarithm on both the sides of Arrhenius equation. Let the rate constant at temperature T1 be k1 and at temperature T2, let the rate constant be k2. You get the two equations:
[tex]k_1=Ae^{-E_a/RT_1}[/tex]
[tex]k_2=Ae^{-E_a/RT_2}[/tex]
Take logarithm on both the sides of the equation and subtract the equations you get.
Hemolymph
#5
Dec16-12, 02:01 PM
P: 30
Quote Quote by Pranav-Arora View Post
Activation energy is given in the problem statement.

You will have to derive an equation using the Arrhenius equation to relate the rate constants. Take logarithm on both the sides of Arrhenius equation. Let the rate constant at temperature T1 be k1 and at temperature T2, let the rate constant be k2. You get the two equations:
[tex]k_1=Ae^{-E_a/RT_1}[/tex]
[tex]k_2=Ae^{-E_a/RT_2}[/tex]
Take logarithm on both the sides of the equation and subtract the equations you get.
ln(k1/k2)=Ea/R(1/t_2)-(1/t_1)?
Pranav-Arora
#6
Dec16-12, 02:05 PM
P: 3,804
Quote Quote by Hemolymph View Post
ln(k1/k2)=Ea/R(1/t_2)-(1/t_1)?
Yes, that's right if you mean ln(k1/k2)=Ea/R((1/t_2)-(1/t_1)). (Take care of parentheses. )
Hemolymph
#7
Dec16-12, 02:08 PM
P: 30
ok so I did

ln(Rate 2/rate1)=71/.008314-((1/423)-(1/443))

got .911452

took e^.911452 = 2.5 so 2.5 times greater is rate 2 to rate 1
Pranav-Arora
#8
Dec16-12, 02:10 PM
P: 3,804
Quote Quote by Hemolymph View Post
ok so I did

ln(Rate 2/rate1)=71/.008314-((1/423)-(1/443))

got .911452

took e^.911452 = 2.5 so 2.5 times greater is rate 2 to rate 1
I haven't checked the calculations but your result matches with one of the options so I guess it is correct.
Hemolymph
#9
Dec16-12, 02:14 PM
P: 30
Do you know how i could tackle the second one ?
Pranav-Arora
#10
Dec16-12, 02:18 PM
P: 3,804
Quote Quote by Hemolymph View Post
Do you know how i could tackle the second one ?
You do have posted an equation in the main post. Did you try applying it?
Hemolymph
#11
Dec16-12, 02:22 PM
P: 30
Would I just be able to just substitute the percentages in as if they were concentrations?
Pranav-Arora
#12
Dec16-12, 02:26 PM
P: 3,804
Quote Quote by Hemolymph View Post
Would I just be able to just substitute the percentages in as if they were concentrations?
You can do that but the problem is you are not given the percentage of concentration left.
The percentage left after 20 seconds is 90% of the initial concentration. So substitute [A]=0.9[A0], assuming [A0] to be the initial concentration.
Hemolymph
#13
Dec16-12, 02:37 PM
P: 30
(1/.9)=1/.1+k(20 seconds)

I got k to be .005555

so If I find t i get

(1/.1)=(1/.9)+.005555(t)

9/.0055555=t
t=1600s

that look like the right path to get to the answer?
Pranav-Arora
#14
Dec16-12, 02:41 PM
P: 3,804
Quote Quote by Hemolymph View Post
(1/.9)=1/.1+k(20 seconds)
How you got 0.1? Did you assume the initial concentration [A0] to be 0.1 M? If so, [A] would be equal to 0.09 M, not 0.9 M.
Hemolymph
#15
Dec16-12, 02:45 PM
P: 30
Quote Quote by Pranav-Arora View Post
How you got 0.1? Did you assume the initial concentration [A0] to be 0.1 M? If so, [A] would be equal to 0.09 M, not 0.9 M.
oh i did it wrong then i just assumed it was .1 because 10%=.1
same for 90% being .9
Pranav-Arora
#16
Dec16-12, 10:58 PM
P: 3,804
What's the 10% of 0.1?


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