June 04, 2020, 10:53:13 AM
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### Topic: Extrapolating Reaction Rates at Different Temperatures  (Read 1353 times)

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#### bestfishes2048

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##### Extrapolating Reaction Rates at Different Temperatures
« on: February 01, 2019, 07:24:55 PM »
Not sure if this should go here or in the homework forums; it's NOT homework but it might as well be.

I've seen a few publications that measure reactions rates at different temperatures, and then give values for ΔH≠, ΔG≠, TΔS≠, etc. Example:  https://pubs.acs.org/doi/abs/10.1021/bi701480f

Is there a way to use that data to extrapolate reaction rates at other temperatures? I thought I could with the Eyring equation, but when I test it using the temperatures they've given reaction rates for, I'm getting values that are clearly incorrect. Would someone be willing to point me in the right direction?

#### wildfyr

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #1 on: February 01, 2019, 09:00:35 PM »
You're looking for the arrhenius equation.

#### bestfishes2048

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #2 on: February 01, 2019, 10:43:15 PM »
Uuuuuugh. Do you know what I did? I spent TWO HOURS trying to figure out how to apply the arrhenius equation this morning, but when I kept getting wildly different values than what their figure 2 was showing I figured that them not listing Ea as a parameter was a sign that there must be a different way of doing this. I went back after your comment to look again, and finally noticed the x-axis was log10(k), not ln(k).

I am a not a smart man. My values were fine. Thank you so much for your *delete me*

PS: Here they list two values of k, so I can calculate Ea. For studies that only provide k at one temperature, what's the best way to get that? Just Ea= ΔH≠ + RT, or is there a better way to approximate that?

#### Corribus

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #3 on: February 04, 2019, 10:17:20 AM »
You really need the rate data at two temperatures.

Keep in mind, this treatment does require a number of assumptions, namely that the reaction follows Arrhenius kinetics (not always true) and that the pre-exponential factor and other thermochemical parameters are temperature independent. The latter is really only a good approximation over small temperature changes.
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#### Enthalpy

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #4 on: February 04, 2019, 01:14:23 PM »
[...] and finally noticed the x-axis was log10(k), not ln(k). [...]

I suspect this has happened to everyone. Be reassured.

#### Enthalpy

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #5 on: February 04, 2019, 01:21:06 PM »
[...] I've seen a few publications that measure reactions rates at different temperatures, and then give values for ΔH≠, ΔG≠, TΔS≠, etc. [...]
Is there a way to use that data to extrapolate reaction rates at other temperatures? [...]

The answer is no, because all ΔH, ΔG and so on depends only on the initial and final states, while reaction rates depend on the hurdles between the initial and final states. The necessary information is not contained in the ΔH, ΔG... of a synthetic equation. If each step of a reaction were known, maybe all ΔH would give a hint.

#### Babcock_Hall

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #6 on: February 04, 2019, 01:53:42 PM »
[...] I've seen a few publications that measure reactions rates at different temperatures, and then give values for ΔH≠, ΔG≠, TΔS≠, etc. [...]
Is there a way to use that data to extrapolate reaction rates at other temperatures? [...]

The answer is no, because all ΔH, ΔG and so on depends only on the initial and final states, while reaction rates depend on the hurdles between the initial and final states. The necessary information is not contained in the ΔH, ΔG... of a synthetic equation. If each step of a reaction were known, maybe all ΔH would give a hint.
I think that the OP was referring to ΔH-double dagger, etc.  For there to be published values of these quantities, the authors must have performed studies at more than one temperature.

#### bestfishes2048

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #7 on: February 07, 2019, 06:26:48 PM »
[...] I've seen a few publications that measure reactions rates at different temperatures, and then give values for ΔH≠, ΔG≠, TΔS≠, etc. [...]
Is there a way to use that data to extrapolate reaction rates at other temperatures? [...]

The answer is no, because all ΔH, ΔG and so on depends only on the initial and final states, while reaction rates depend on the hurdles between the initial and final states. The necessary information is not contained in the ΔH, ΔG... of a synthetic equation. If each step of a reaction were known, maybe all ΔH would give a hint.
I think that the OP was referring to ΔH-double dagger, etc.  For there to be published values of these quantities, the authors must have performed studies at more than one temperature.

Yes, I was - my apologies for half-assing the notation.

And yes, these studies are performed at multiple temperatures - Here is one example of what I'm talking about : Benchmark Reaction Rates, the Stability of Biological Molecules in Water, and the Evolution of Catalytic Power in Enzymes, in particular table 1. They describe how these values are obtained in the introduction:

Quote
An alternative approach, used in much of the work described here, is to conduct reactions in sealed quartz tubes (which must be encased in steel bombs to avoid explosions when reactions are conducted in aqueous solution above 260°C) for various time intervals at elevated temperatures and, after cooling, to monitor the integrated intensities of the signals arising from the reactants and products by high-field proton NMR. If substrate disintegration and product formation follow simple first-order kinetics at each temperature (with the second substrate in large excess in reactions that involve more than one substrate), and if rate constants obtained over a range of temperatures yield a linear Arrhenius plot when plotted as a logarithmic function of 1/T (kelvin), then the rate constant (k25°C) at 25°C can be extrapolated.

The values I'm interested were among those collected in this way. So they're calculating rate reactions over multiple temperatures and verifying that they follow Arrhenius kinetics, and using that to extrapolate the k25°C. Where I'm getting lost is that it seems bizarre to me that you would go through the effort of collecting enough data to extrapolate the reaction rate at 25°C, but not publish enough of that data to allow readers to extrapolate the reaction rate at other temperatures? Unless I'm overlooking something?

I apologize if these questions are a bit muddled or I'm not providing enough information. This is not my main area of expertise, and I'm feeling a bit muddled now. I really appreciate any guidance you all have.

#### Corribus

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##### Re: Extrapolating Reaction Rates at Different Temperatures
« Reply #8 on: February 08, 2019, 09:58:32 AM »
Well it would be nice if more studies made available their raw data for just this kind of analysis, but sadly it isn't always the case.
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