[ctp123]

Hello all,

New here. I am a graduate student and I am trying to determine the decomposition kinetics of a particular compound. I have found that it is not so straight forward because the decomposition appears more 2nd order in the beginning and as more of the compound decomposes, it is best described as first order.

How would I determine the rate constant(s) and the half-life for this system?

Also, how would I make a kinetics plot? I know it's typically Ln([a]) vs t for first order, and 1/[a] vs time for second order.

I've looked into this online but I am a synthetic inorganic chemist and am no expert in mathematics.

You don't have to give me the answer but any direction would be beneficial because it's been so long since I've derived equations.

Thanks!

[Borek]

You may have more than one path.

[ctp123]

I do not know the reaction mechanism for this so it is difficult to give a path. The reaction is not in equilibrium by any means. The decomposition should look something like A²⁺ ---> A³⁺ + e^-. I assume the compound decomposes by reaction with the solvent (associative mechanism for rate determining step) since there are no other compounds present in solution.

It just seems that at higher concentrations, the observed absorbance is is determined by the square of the concentration. I do not know why this would happen.

[ctp123]

I'm actually observing the disappearance of a metal to ligand charge transfer band by UV-Visible spectroscopy. An absorption that only occurs in the A²⁺ species

[ctp123]

You may have more than one path.

I should still be able to represent it linearly even if there are multiple paths.

[Borek]

No, if each path has a different order as you described.

I am not saying that's what is happening, that's just the first explanation I could think of. When the concentration is high enough system is dominated by a second order reaction, once the concentration goes down, first order starts to dominate. That's what you said you see on the plot.

I would try to fit the data to a×ln([A])+b/[A] and see if it works (can be completely off).

[Irlanur]

To be honest, these discussion would be a whole lot easier if you would just be concrete. what do you have?

A2+ ---> A3+ + e-

I guess not... or do you have free electrons in the solution? Do you have no idea at all what the product is? can you use NMR or EPR if not?

[curiouscat]

Can you post your raw data here? Or provide a link?

[ctp123]

To be honest, these discussion would be a whole lot easier if you would just be concrete. what do you have?

A2+ ---> A3+ + e-

I guess not... or do you have free electrons in the solution? Do you have no idea at all what the product is? can you use NMR or EPR if not?

So this compound is of the formula, [K(2.2.2.-cryptand][Cp''₂YCp], where Cp'' = C₅H₃(TMS)₂ and Cp = C₅H₅. It contains an Yttrium center in the +2 oxidation state which is super unstable at room temperature. I'm not in a mechanistic lab but I have isolated K(2.2.2.-cryptand)Cp from a vial containing decomposed product. It's hard to say what else is formed. An NMR of solids from the decomposed solution show peaks for the cryptand and both Cp ligands so it's not all that conclusive.

A screenshot of the data is attached. I've calculated the rate constants for first and second order.

The constant is not constant at all but it appears to be more constant as second order in the beginning and more constant as first order towards the end.

BTW I cannot use NMR because Y2+ is paramagnetic. I've used EPR and I just see a doublet from the Y S=1/2 nucleus. This just disappears since Y3+ is diamagnetic. I could maybe watch the spectrum grow in by NMR since Y3+ is diamagnetic but I'm not sure if this is the best way to do it.

[ctp123]

No, if each path has a different order as you described.

I am not saying that's what is happening, that's just the first explanation I could think of. When the concentration is high enough system is dominated by a second order reaction, once the concentration goes down, first order starts to dominate. That's what you said you see on the plot.

I would try to fit the data to a×ln([A])+b/[A] and see if it works (can be completely off).

That's what I was thinking but I don't have any software to determine a and b values that give me a linear plot.

[Irlanur]

It's not absolutely necessary to use linear regression. you can also try to just fit the data directly (maybe that's possible with excel, but would do it with R/matlab/whatever).

Probably won't help you much, but because I am interested: any pulse EPR spectrometer for ENDOR/HYSCORE/ESEEM?

[curiouscat]

Tried replicating? I hope you aren't chasing a red herring.

[ctp123]

Tried replicating? I hope you aren't chasing a red herring.

I haven't tried replicating but I have 3 other compounds that show similar behavior.

[mjc123]

If you have two parallel processes, such that
d[A]/dt = -k₁[A]² - k₂[A]
then you get
[A] = rαe^-k₂t/(1-αe^-k₂t) where r = k₂/k₁ and α = [A]₀/([A]₀+r)
We can rearrange this to give
ln([A]/([A]+r)) = lnα - k₂t
So plot ln([A]/([A]+r)) vs. t, and vary r till you get a straight line. This is simple in Excel.
(Hint: r is of the order of 0.001. You will find the later points deviate from the model somewhat - [A] decreases faster than first order predicts - so try to maximise the function RSQ using the points for t < 10000.)