Must a sample of a deuterated compound be isotopically pure for kinetic isotope experiments?

Question

I'm trying to do a project on the primary kinetic isotope effect on the dehydroxylation of $\alpha-FeOOH$, goethite. The goethite consists of edge-sharing double octahedra of 3 oxyanions and 3 hydroxyanide. The double octahedra are joined at corners by the oxyanion or hydroxide, leaving empty channels across which hyroxides and oxyanions form hydrogen bonds.

The dehydroxylation mechanism is believed to consist of proton diffusion from the bulk of the material to the surface (likely facilitated by a series of protonations down the hydrogen-bonding channels), then binding of hydrogens to surface hydroxyl group, forming water desorbing. The proton diffusion is believed to be the rate-determining step.

I thought I could lend more evidence to whether this is the case by performing the dehydroxylation on a deuterated compound and a compound of natural isotopic abundance. However, I cannot find the deuterated compound for sale and will have to synthesize it. The most facile synthetic method given time constraints involves potassium hydroxide. We could use deuterated hydroxide, but that would be more expensive. Grey et. al.** were able to do this synthesis with the undeuterated hydroxide, but they didn't report an H/D ratio.

All the papers I've come across on kinetic isotope effect experiments work under the assumption that their deuterated compounds are isotopically pure. It may just be a matter of convention, but would I actually need to do this experiment on an isotopically pure sample? Could I use a sample with, say, an isotope ratio halfway between pure deuterated and natural abundance? Would the calculated kinetic isotope effect (defined as hydrogen rate constant/deuterium rate constant) then be twice what I measure with this partially-enriched sample?

*Surface and Bulk Reactivity of Iron Oxyhydroxides - A Molecular Perspective Xiaowie Song Umea University

**2H MAS NMR Studies of Deuterated Goethite (α-FeOOD) Kathryn E. Cole,†,§, Younkee Paik,†,§, Richard J. Reeder,‡,§, Martin Schoonen,‡,§ and, and Clare P. Grey*,†,§ The Journal of Physical Chemistry B 2004 108 (22), 6938-6940 DOI: 10.1021/jp0486090

Answer 1

There are two approaches to measuring kinetic isotope effects.

One is to have two completely separate, isotopically pure systems, one heavy, and one light. In each system you can measure the rate of the reaction however you want. You don't have to be able to measure the rate in an "isotopically resolved" way, just measure the bulk rate. Each of your systems is isotopically pure, so the rate of each system is 100% reflective of the isotope composition of that system.

The other way is to have a single system with variable/unknown isotopic composition. You measure the rate of your reaction, but you have to be able to measure (e.g.) the rate of depletion of each substrate isotopomer separately. (Or the rate of formation of each product isotopomer, but that sounds very difficult in your system.) For example, if you had a mixture of $\ce{CH4}$ and $\ce{CD4}$ and you were interested in the kinetic isotope effect of some kind of combustion reaction of those gases with oxygen, you could measure the ratio of $\ce{CD4}$ to $\ce{CH4}$ over time, e.g. using mass spectrometry. It would increase as the $\ce{CH4}$ is preferentially depleted by the combustion reaction. You could also measure the rates of formation of $\ce{H2O}$ and $\ce{D2O}$. The rate of formation of $\ce{H2O}$ would be much higher than that of $\ce{D2O}$. (The exact numerical values here would depend strongly on the nature of your combustion system, e.g. temperature, catalysts used, etc.)

So iff you can measure $\ce{FeOOH}$ and $\ce{FeOOD}$ separately in the same system, then you don't need an isotopically pure material. I'm not an expert in these types of measurements, but it sounds very hard to me. Probably if you don't already know how to do it, it will be cheaper just to buy $\ce{KOD}$ and get on with the synthesis of an isotopically pure material so you can use the first approach.