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# how do you determine the activation energy from temperature and k?

The question is: determine the activation energy of this reaction.

t in celcius: 15.2, 20.3, 24.6, 27.0

k (in sec -1): .043,.067, .095, .150

### 1 Answer

- 1 decade agoFavorite Answer
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.

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