# Calling kinetics experts: rate law from conductivity isnt possible?

Calling kinetics experts: rate law from conductivity isnt 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 modelled) 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.

Borek
Mentor
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" cant be used to investigate reaction kinetics.

Any ideas on the significance of the slope for the linear plot?

Borek
Mentor
Agreed, and seems to support the idea that conductivity data from "ion-exchanges" cant 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.