[msk034]

Hello, In gas phase, what is the rate of the exchange reaction D2 + H2 --> 2HD ?

[Corribus]

The rate depends on the partial pressures (i.e., concentrations) of the two reactants.

[Enthalpy]

As gas at room temperature, it must be essentially zero.
H and D are known to swap in water because of the H⁺ and OH^- dissociation. That won't happen in a gas.

[Corribus]

I don't know about at room temperature, but the gas phase reaction has been observed experimentally.

Bauer and Ossa, J. Chem. Phys, 1966, 45, 434.

It's also been studied theoretically.

E.g., Gimarc, J. Chem. Phys., 1970, 53, 1623.; Wilson and Goddard, ibid. 1969, 51, 716.

Based on thermochemical data I predicted here that the reaction would be spontaneous at room temperature, and estimated an equilibrium constant, but I haven't looked through the literature to see if that prediction is borne out in practice.

[Enthalpy]

Nicely done, the zero-point energy from the spectrum...

As for an exchange speed between H and D in the gas at room temperature, it depends fundamentally on the energy barrier to intermediate steps, which must be high. The Gibbs calculation tells that H and D would mix (better than indifferent according to your computation) provided they have a path.

Thinking to a different path... A bit of UV light could split few H₂ or D₂ molecules, and in pure hydrogenS, the rearrangement game could go pretty far - until two lone atoms meet and find a way to recombine in a molecule. Or radioactivity or cosmic rays, if no light is available. Or the boxe's walls, if it thermalizes adsorbed atomic hydrogen, thus providing an easier path to gaseous atomic hydrogen. That would lead to a mix having the "indifferent" proportions for being a very dynamic process, far from thermo equilibrium.

Such processes must completely overshadow the thermal ones in the gas at room temperature.

[Corribus]

Just for full disclosure, this article is also relevant, in which shock-tube studies in the 50s and 60s were alleged to be contaminated by H atom impurities, which catalyze the exchange reaction in the gas phase.

http://scitation.aip.org/content/aip/journal/jcp/79/6/10.1063/1.446178

These authors conclude that when measures are taken to eliminate such free radical generation, a direct H2 + D2 to 2HD exchange convesion is "highly doubtful", even at relatively high temperatures.

So, I think we can agree that while the (concerted) reaction might be thermodynamically favorable, it is likely pretty slow... and the rate also difficult to measure. I put forward that this may be the case because any transition state in a concerted reaction would have to be a very highly unfavorable 4-center structure, so the probability of a successful reaction is quite low.  Of course, any mechanism which can give rise to cleavage or otherwise generate free hydrogen/deuterium radicals - such as photolytic cleavage, as you suggest - would provide a more convenient route to completion of the reaction. So, I would agree with you that, based on this cursory examination of the literature, the rate of a concerted reaction at room temperature is practically zero, but that other, possibly non-thermal mechanisms will still give rise to isotope exchange.

To the thread's main question, I think putting an actual number on a rate constant will be rather difficult. It'll depend on factors other than just the temperature and pressure of the gasses.  This is not atypical of gas-phase reactions, which can often end up being far more complicated than they would appear based on a simple balanced equation.