Calling kinetics experts: rate law from conductivity isnt possible?

[Miffymycat]

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 (Λ_oOH^-e^-kt) and the rise of X- conductivity as the inverse function of this (0.5Λ_oOH^-(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 Λ_final (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?

 

[Borek]

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.

 

[Miffymycat]

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?

 

[Borek]

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.

 

[LudusRex]

I understand your frustration with trying to obtain a rate law from conductivity data in the hydrolysis reaction you described. However, it is important to keep in mind that conductivity is just one piece of information in a complex reaction system. It is not always possible to obtain a rate law solely from conductivity measurements.

In this case, the hydrolysis reaction involves multiple steps and intermediates, and the conductivity data may not accurately reflect the rate of the overall reaction. Additionally, the presence of excess RX and the stoichiometry of the reaction can also affect the conductivity measurements.

It may be helpful to consider other methods for obtaining a rate law, such as measuring the concentration of reactants and products over time using techniques like titration or spectroscopy. These methods can provide more accurate data for determining the rate law.

Overall, it is important to approach scientific problems with an open mind and consider multiple factors before drawing conclusions. I encourage you to continue exploring different methods and seeking input from other experts in the field to better understand the kinetics of this reaction.