Yahoo Answers: Answers and Comments for How do you determine the activation energy from temperature and k? [Physics]
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From blahbam
enUS
Thu, 24 Sep 2009 18:27:56 +0000
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Yahoo Answers: Answers and Comments for How do you determine the activation energy from temperature and k? [Physics]
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From mikeya: You're talking about the Arrhenius equatio...
https://answers.yahoo.com/question/index?qid=20090924182756AAlkrcZ
https://answers.yahoo.com/question/index?qid=20090924182756AAlkrcZ
Thu, 24 Sep 2009 18:44:13 +0000
You're talking about the Arrhenius equation as the model, correct?
k = A0 * Exp( Ea / RT )
where
k = reaction rate, sec ^ (1)
A0 = constant
Ea = Activation Energy, J / mol
R = ideal gas constant, 8.314 J / K mol
T = temperature, in Kelvin
* * * * * * * * * * * * * * * * * * * * * * * *
If this is the equation, then let's proceed:
k = A0 * Exp( Ea / RT )
We can attack this in different ways. The best way is to graph it. But first, we need to put the Arrhenius equation in a form that best suits our needs...
Take the natural log of both sides
ln k = ln (A0 * Exp( Ea / RT ))
= ln A0 + ln (Exp(Ea / RT))
= ln A0 + (Ea / RT) * ln e
= ln A0 + Ea / RT * 1
= ln A0 + Ea / RT
We can rewrite the equation as...
ln k = (Ea / R) * (1/T) + ln A0
If we let
y = ln k
b = ln A0
m = Ea / R
x = 1/T
Then
ln k = (Ea / R) * (1/T) + ln A0
can be written as
y = mx + b
Where m is the slope.
If you take your data:
t in celcius: 15.2, 20.3, 24.6, 27.0
k (in sec 1): .043,.067, .095, .150
Convert the T into Kelvins, and then plot the data as
1/T vs. ln k
Draw a best fit line and determine the slope.
Slope = m = Ea / R
So Ea = R * m
Ans. Activation energy, Ea = R * calculated slope.