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### Topic: Calculating first order kinetic Ea in temperature programmed desorption  (Read 357 times)

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#### tonnager

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• Mole Snacks: +0/-0 ##### Calculating first order kinetic Ea in temperature programmed desorption
« on: July 31, 2019, 08:54:54 PM »
Hi all,

I'm new in the forum and I am not actually an undergrad (doing postgrad in analytical chem) so if my question is not suitable to this subforum please feel free to let me know.

I have a repeat exam relating to to the topic of surface science, with question on temperature programmed desorption, in two days and my lecturer hasn't replied since I emailed him days ago when I asked for help. I have uploaded the question for reference: https://imgur.com/a/cw9A7AS

The question is to find the activation energy (Ea) assuming that the reaction is first order kinetics. But I could not get the correct answer, which I have underlined, as shown in the image. So my question is: how do I find the equation of the line? I am trying to do the m=(y2-y1)/(x2-x1) formula but I could not get the value as shown in the screenshot. The slope says it is 9172.8 which is the Ea/R but the Ea says 76.27. I could not get value on my calculation.

Thank you and I would greatly appreciate it if I get prompt response please.

tonnager,

#### Corribus

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• Gender: • A lover of spectroscopy and chocolate. ##### Re: Calculating first order kinetic Ea in temperature programmed desorption
« Reply #1 on: July 31, 2019, 10:50:14 PM »
Not sure what a lot of your units are, but the gas constant has units of J/k mol (typically). This gives Ea/R units of temperature because Ea has units equivalent to, say, J/mol. So if the slope is equal to 9172.8 K, and R = 8.3145 J/mol K, this means Ea is equal to 9172.8*8.3145 = 76503 J/mol, or 76.27 kJ/mol. Not far from the Ea listed. What am I missing?
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman

#### tonnager

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• Mole Snacks: +0/-0 ##### Re: Calculating first order kinetic Ea in temperature programmed desorption
« Reply #2 on: August 01, 2019, 04:27:19 AM »
R = 8.3145 J/mol K

Apologies if it may sound stupid but R is a constant value then?

Also, I need to make a clarification that I could not get the slope of the line is essentially my question, not finding the equation of the line, since I could not arrive at the value of 9172.8 K. I should have edited my first post for corrections but it doesn't seem to allow me.
« Last Edit: August 01, 2019, 08:25:30 AM by tonnager »

#### mjc123

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• Mole Snacks: +236/-11 ##### Re: Calculating first order kinetic Ea in temperature programmed desorption
« Reply #3 on: August 01, 2019, 06:54:58 AM »
What did you think R was? How much chemistry have you studied?

Using m = (y2-y1)/(x2-x1) is not a good idea because you will get quite different results depending on which 2 points you use, due to the scatter. You should do a least-squares regression. Are you familiar with this? You can do it, for example, by clicking "Add Trendline" on a graph in Excel, as appears to have been done in the given answer. Are you allowed to do this in an exam?

#### tonnager

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• Mole Snacks: +0/-0 ##### Re: Calculating first order kinetic Ea in temperature programmed desorption
« Reply #4 on: August 01, 2019, 08:24:24 AM »
Hi mjc123,

I should have said earlier but my background is actually in biotechnology so I have little chemistry knowledge and I didn't know R is a given. I am doing analytical chemistry course to put my foot on the door in an analytical laboratory since my course has industry placement.

In the exam we are meant to draw the graph after calculating the values. How could I calculate the slope of a line on a drawn graph?

#### Corribus

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• Gender: • A lover of spectroscopy and chocolate. ##### Re: Calculating first order kinetic Ea in temperature programmed desorption
« Reply #5 on: August 01, 2019, 10:02:25 AM »
Yes, R is a universal constant: https://en.wikipedia.org/wiki/Gas_constant

This value, which obviously depends on the unit set you are using, would normally be given to you.

It sounds like a general chemistry course should be a prerequisite to your class if this was not explained to you.

If you are asked to solve a problem like this and you have access to a computer during the (exam, excercise) you will want to find the best linear fit using computer software like excel. Doing a linear regression "by hand" isn't easy, so on a test without a computer I guess the best way to estimate the slope would be as you outlined, although this will as mjc123 pointed out introduce significant error. A better approximation could be achieved by performing the same analysis with every combination of two points in the dataset and averaging all the slopes. But a good test writer wouldn't ask you to do something like this - most likely you'll just be given the slope and asked to do something with it.
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?  - Richard P. Feynman