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### Topic: Significant figures of Arrhenius equation  (Read 1046 times)

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#### Aries

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• Mole Snacks: +0/-0 ##### Significant figures of Arrhenius equation
« on: July 05, 2023, 02:14:05 AM »
Hi, I need to determine how many significant figures for k in this expression: . I already got the question wrong by using 4 significant figures. I've concluded it must be temperature because I had originally used 298.15K (5 SF). I believe this is the error because I don't know if 25C (2SF) equals 298.15K (5SF).

The given parameters are:

A = 1
-Ea = -5kcal / mol (-20920 J)
R = 8.314 J / K * mol
T = 25C (? K)

Before we can solve, we need to convert C to K. Using additive SF rules, the temperature in K should be 298.15K = 298. This means the final answer should have 3 SF because it was carried in from a previous operation. However, what if I punch in the entire operation (including the C--->K conversion factor) into my calculator? At first glance, it is not obvious why it wouldn't be 2SF as the temperature was originally taken at 25C and not 25.0C.

If the explanation of my problem is unclear, I can create a better visual. Thanks for the help.

#### Hunter2

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• Gender: • Vena Lausa moris pax drux bis totis ##### Re: Significant figures of Arrhenius equation
« Reply #1 on: July 05, 2023, 02:42:15 AM »
25 ° C correspond to 298,15 K

I think they mean the result

Its 0.00022 or 2.2 * 10^-4

#### Borek ##### Re: Significant figures of Arrhenius equation
« Reply #2 on: July 05, 2023, 03:07:29 AM »
Technically if A is given as 1 and Ea as 5 kcal you have one significant figure only.

In general significant figures are broken and a poor way of expressing accuracy, don't worry too much about them. Whenever you really need to know how accurate is the result you should do a real analysis of the error propagation.
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#### Aries

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• Mole Snacks: +0/-0 ##### Re: Significant figures of Arrhenius equation
« Reply #3 on: July 05, 2023, 03:24:31 AM »
25 ° C correspond to 298,15 K

I think they mean the result

Its 0.00022 or 2.2 * 10^-4

Proof?

Technically if A is given as 1 and Ea as 5 kcal you have one significant figure only.

In general significant figures are broken and a poor way of expressing accuracy, don't worry too much about them. Whenever you really need to know how accurate is the result you should do a real analysis of the error propagation.

I lost marks because of this question.. I need to figure it out. My prof told me to look up the rules which implies he has probably forgotten them himself.

A is actually being divided by itself as this is an excerpt of a more complex operation (K1/K2) where A = A. I used 1 for simplicity but obviously that was a mistake here. However, if I'm starting with 5kcal, isn't that like saying 5000cal where 1 cal = 4.184J?

I usually get SF questions correct but these nested ones confuse me.. It would be great if you could show a proof.

#### Hunter2

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• Gender: • Vena Lausa moris pax drux bis totis ##### Re: Significant figures of Arrhenius equation
« Reply #4 on: July 05, 2023, 03:44:37 AM »
Proof: if you take less then 4 Figures of the result you end up with 0, what means nonsense for further calculations.

And 5 kcal = 20.92 kJ or 5000 cal = 20920 J, what is the same of 20.92 kJ

#### Aries

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• Mole Snacks: +0/-0 ##### Re: Significant figures of Arrhenius equation
« Reply #5 on: July 05, 2023, 03:53:25 AM »
Here is the full operation: k1/k2 = ?

Please include the C -> K conversion factor. The kcal -> cal conversion factor is of course 1 kcal x (1000 cal / 1 kcal).
« Last Edit: July 05, 2023, 04:10:12 AM by Aries »

#### Hunter2

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• Gender: • Vena Lausa moris pax drux bis totis ##### Re: Significant figures of Arrhenius equation
« Reply #6 on: July 05, 2023, 04:14:23 AM »
I would convert the equation using logarithm ĺaws. So Temperature and gas constant  can be erased.

#### Aries

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• Mole Snacks: +0/-0 ##### Re: Significant figures of Arrhenius equation
« Reply #7 on: July 05, 2023, 04:26:09 AM »
I would convert the equation using logarithm ĺaws. So Temperature and gas constant  can be erased.

I'm not sure what you are referring to exactly. I am aware the activation energies can be combined (-5+17=12) but I prefer to keep the expression in this form as I've had a similar problem lose marks. I suspect that error began with how I manipulated C->K significant figures. I'll see what my textbook has to say about SF again but this is the most complex problem in the course that is using several conversion factors.

#### Borek ##### Re: Significant figures of Arrhenius equation
« Reply #8 on: July 05, 2023, 03:10:24 PM »
5 kcal has 1 SF., 5.000 kcal has four.

If something cancels out number of SF it had doesn't matter, as it doesn't affect the final result. What you wrote is just 5/17.
ChemBuddy chemical calculators - stoichiometry, pH, concentration, buffer preparation, titrations.info, pH-meter.info

#### Enthalpy ##### Re: Significant figures of Arrhenius equation
« Reply #9 on: July 21, 2023, 05:29:29 PM »
The exponential in Arrhenius' equation converts an absolute uncertainty into a relative one.

exp(+50±0.1), exp(0±0.1), exp (-50±0.1) carry the same relative uncertainty: exp(±0.1)-1.

Take time to grasp and meditate that, as this leads to mistakes. Sometimes the log or exp are hidden, as in decibels.