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### Topic: Kinetics data  (Read 6679 times)

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##### Kinetics data
« on: August 25, 2013, 12:54:10 PM »
t (/ms); [HCl] (/mol·dm-3)
2; 0.57
4; 1.05
8; 1.74
12; 2.19
16; 2.46
∞; 3.00

Given this experimental data, and the function for k1 in terms of [HCl] and [HCl]t=∞, how can I calculate a best possible value for k1? Obviously just choosing any of the numbers and plugging them in gives me one value, but that value doesn't correspond exactly to producing the other numbers.

#### Corribus

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##### Re: Kinetics data
« Reply #1 on: August 25, 2013, 05:35:14 PM »
Probably some sort of linear regression or function fitting algorithm. Origin will do this without breaking a sweat. Or you can always do it by hand.
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

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##### Re: Kinetics data
« Reply #2 on: August 25, 2013, 05:45:41 PM »
How accurate would it be just to get all the k_1 values (at each t) and then take the average?

#### Babcock_Hall

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##### Re: Kinetics data
« Reply #3 on: August 26, 2013, 10:15:15 AM »
Does the problem specify what the rate law is?

Averaging would probably be better than nothing, but I suspect that it would be inferior to linear or nonlinear regression.  For one thing, not all of the data points are likely to be equally well determined, and using statistical weights can counteract this problem (although the issue of weighting the data is probably beyond what you need to worry about for right now).  Here are two reviews on the subject of nonlinear regression:
http://www.cell.com/trends/biochemical-sciences/abstract/0968-0004(90)90295-M
http://www.fasebj.org/content/1/5/365.abstract

#### curiouscat

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##### Re: Kinetics data
« Reply #4 on: August 26, 2013, 11:20:01 AM »
Why don't you at least write down the "function for k1 in terms of [HCl] and [HCl]t=∞" part for us?

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##### Re: Kinetics data
« Reply #5 on: August 26, 2013, 02:42:14 PM »
Because, as always with me, this is a more general problem than that. I'm not worried about the actual calculation of k1, just the fact that I'd end up with a different one for each data reading.

Anyway for your interest here goes:

$$c_{HCl} = c_{HCl,t = \inf} \cdot (1 - e^{-k \cdot t \cdot c_{CH4}})$$

[CH4] was given. And now solving for k1 is almost painfully easy, just rearrange. But getting a good average is the problem.

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##### Re: Kinetics data
« Reply #6 on: August 26, 2013, 02:44:54 PM »
Does the problem specify what the rate law is?

Averaging would probably be better than nothing, but I suspect that it would be inferior to linear or nonlinear regression.  For one thing, not all of the data points are likely to be equally well determined, and using statistical weights can counteract this problem (although the issue of weighting the data is probably beyond what you need to worry about for right now).  Here are two reviews on the subject of nonlinear regression:
http://www.cell.com/trends/biochemical-sciences/abstract/0968-0004(90)90295-M
http://www.fasebj.org/content/1/5/365.abstract

Thanks for the advice. I'm guessing linear regression would have been ok for this problem and that's what I'll have a look at. (I studied it a few months ago but forgot after my exams, I'm not that keen on statistics  )

#### Babcock_Hall

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##### Re: Kinetics data
« Reply #7 on: August 26, 2013, 03:55:07 PM »
Do you know how to write your equation in a linear form?

#### curiouscat

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##### Re: Kinetics data
« Reply #8 on: August 26, 2013, 04:02:38 PM »

Because, as always with me, this is a more general problem than that. I'm not worried about the actual calculation of k1, just the fact that I'd end up with a different one for each data reading.

Anyway for your interest here goes:

$$c_{HCl} = c_{HCl,t = \inf} \cdot (1 - e^{-k \cdot t \cdot c_{CH4}})$$

[CH4] was given. And now solving for k1 is almost painfully easy, just rearrange. But getting a good average is the problem.

If I were setting the problem I'd insert an outlier  point to make a brute force average blow up and totally mess your answer.

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##### Re: Kinetics data
« Reply #9 on: August 26, 2013, 08:22:42 PM »
If I were setting the problem I'd insert an outlier  point to make a brute force average blow up and totally mess your answer.

I don't think this is actually in the problem, but there'd be no point anyway - my calculator cannot handle the entire expression being put in 6 times, so I'd be calculating k1 values one-by-one and taking the average. Obviously I'd eliminate clear anomalies. But it's a matter of principle really. Given the rest of the question was so easy (rearrangement) and it's worth more marks than the part that asks you to actually derive this equation from the reaction mechanism, I'm guessing they want regression of some form.

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##### Re: Kinetics data
« Reply #10 on: August 26, 2013, 08:23:53 PM »
Do you know how to write your equation in a linear form?

What do you mean? I might give the rearrangement a go but what are you suggesting I rearrange for exactly?

#### Corribus

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##### Re: Kinetics data
« Reply #11 on: August 26, 2013, 09:48:56 PM »
@BD.

Just for your own benefit: this is why just calculating k's from single points and averaging is not a good way to do things.

Using your data I calculate k*[CH4] of 0.108 using your "averaging method" and 1.0979 using a basic linear regression with partial least squares. Not too bad, right?

Ok, well change your first point (t = 2) from 0.57 to 0.17. Using the averaging method now I get a value of 0.09328, a drop of about 9% or so. Using the PLS regression, I get a value for k*[CH4] of 1.0917, a deviation of <1%.

Even a simple regression can tolerate an anomalous outlier point, whereas just averaging the values cannot, because it weights each point evenly.
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

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##### Re: Kinetics data
« Reply #12 on: August 27, 2013, 06:58:44 AM »
Ok, thanks for the outline.

#### curiouscat

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##### Re: Kinetics data
« Reply #13 on: August 27, 2013, 07:00:21 AM »
Do you know how to write your equation in a linear form?

What do you mean? I might give the rearrangement a go but what are you suggesting I rearrange for exactly?

For linearity. y=kx+c