Calling kinetics experts: rate law from conductivity isnt possible?

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Discussion Overview

The discussion revolves around the feasibility of deriving a rate law from conductivity measurements in the context of the aqueous alkaline hydrolysis of primary halogenoalkanes. Participants explore the relationship between conductivity changes and reaction kinetics, questioning the applicability of certain mathematical models to the observed data.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant describes the reaction RX + OH- --> ROH + X- and notes that the rate law is first order in both RX and OH-. They express frustration that conductivity measurements do not yield a recognizable integrated rate law plot.
  • The same participant suggests that the drop in OH- conductivity can be modeled as an exponential decay, but finds that the actual conductivity data does not fit this model well.
  • Another participant questions the mathematical expression provided, suggesting it does not conform to a simple exponential decay model.
  • Some participants agree that conductivity data from ion exchanges may not be suitable for investigating reaction kinetics, while others argue that it can be used if fitted to the correct equation.
  • A participant raises a question about the significance of the slope in the linear plot of initial rates versus final conductivity, indicating uncertainty about its interpretation.

Areas of Agreement / Disagreement

Participants express differing views on the utility of conductivity data for determining reaction kinetics, with some asserting it cannot be used effectively while others believe it can if approached correctly. The discussion remains unresolved regarding the appropriate mathematical models and interpretations of the data.

Contextual Notes

There are limitations in the assumptions made about the relationship between conductivity and reaction kinetics, as well as potential dependencies on the specific equations used for fitting the data. The discussion highlights unresolved mathematical steps and the need for clarity on the conditions under which conductivity measurements can be applied to kinetics.

Miffymycat
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Calling kinetics experts: rate law from conductivity isn't possible!?

Consider the usual primary halogenoalkane aqueous alkaline hydrolysis reaction

RX + OH- --> ROH + X-

We know the rate law is first order in RX and OH-. We could separately represent the drop in OH- conductivity as an exponential decay with a constant half-life (ΛoOH-e-kt) and the rise of X- conductivity as the inverse function of this (0.5ΛoOH-(1-e-kt), taking the conductivity of X- as 0.5x that of OH-.

In practice, using excess RX, the measured (or modeled) solution conductivity during hydrolysis is obviously the sum of the ion conductivities at any point in time. The mixture conductivity drop-off appears to be an exponential-type decay, but attempts to curve fit (albeit only in Excel) show it is not, nor does it fit a recognisable integrated rate law plot. One can therefore not obtain a rate constant or order from this progress curve, which is frustrating - unless I'm mistaken! {Its not the case for aqueous hydrolysis as this produces ions from neutral molecules rather than an exchange of ions and the graphs work fine}.

Furthermore, taking an initial rates approach and plotting initial (ΔΛ/t) vs Λfinal (over several initial concentrations, rather than a single Λ vs t curve as above) gives a straight line, but whose slope does not appear to be a simple multiple of the calculated k for OH- decay on its own. The stoichiometry is 1:1, so the rate of [OH-] decline = rate of [X-] growth, and I imagined the slope would therefore be k x ratio of ion conductivities ... but it's not. Its a smaller number.

Any thoughts please?
 
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Perhaps I am missing something, but

Ae^{-x} + \frac A 2 (1-e^{-x}) = \frac A 2 (1 + e^{-x})

doesn't look like something that can be fit to just e-x.
 
Agreed, and seems to support the idea that conductivity data from "ion-exchanges" can't be used to investigate reaction kinetics.

Any ideas on the significance of the slope for the linear plot?
 
Miffymycat said:
Agreed, and seems to support the idea that conductivity data from "ion-exchanges" can't be used to investigate reaction kinetics.

I never said that. You can use the conductivity, you just have to fit it to the right equation.
 

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