[CHIP]

Isomers have almost the same solubility coefficients so would Henry's law apply to them separately or not?

For example, 14CO2, 13CO3 and 12CO2 are almost the same molecules, so would Henry's law apply to them all separately?

[sjb]

Isomers have almost the same solubility coefficients so would Henry's law apply to them separately or not?

For example, ¹⁴CO₂, ¹³CO₂ and ¹²CO₂ are almost the same molecules, so would Henry's law apply to them all separately?

Strictly, these are isotopologues, rather than just isomers (the latter are more like e.g. diethyl ether and methyl propyl ether, or 1-butanol). But yes, they will all probably have different physical properties. Why limit yourself to isotopes of carbon, why not e.g. ¹²C¹⁶O₂, or ¹³C¹⁷O¹⁸O, or...?

Look into e.g. kinetic isotope effects as well.

[CHIP]

Why limit myself to isotopes of carbon? Well, lately I've been doing some research into anthropogenic global warming and the adjustment time of atmospheric CO2 and based on measurements of anthropogenic C14CO2 the half-life of this molecule in the atmosphere is around 12 years. These measurements were taken after the 1963 test-ban treating after we almost doubled the cocentration of 14CO2 in the atmosphere. Given Henry's law would apply to 14CO2 separately as you suggest then isn't the fast removal of C14CO2 from the atmosphere a measurement of the equilibrium partitioning coefficient of Henry's law between the atmosphere and oceans for the C14CO2 molecule?

EDIT: When arguing against the idea that the removal of 14CO2 from the atmosphere is a result of the partitioning coefficient of Henry's law for C14CO2 someone on another website states that: "As C14CO2 is chemically the same as C12C02 (the molecular ratio being about 1 to 10^12) 14CO2 is not taken up according to its individual partial pressure difference, but according to the total one, i.e. the difference for C12CO2. Thus C14CO2 can only be considered as 'tagged' C12CO2". Intuitively this seems false to me as they are different molecules (despite being very similar) and what they are suggesting would constitute a non-linear modification to Henry's law.

[mjc123]

I think it amounts to the same thing, just stated in different terms. It is the same thing, if the Henry's law constants for the different isotopomers are the same, and I can't see them being significantly different.
In a system in equilibrium (which of course the Earth isn't, but let that pass), all relevant equilibria must be satisfied simultaneously. So atmospheric and oceanic CO₂ are in equilibrium, as are, separately, atmospheric and oceanic ¹²CO₂, atmospheric and oceanic ¹³CO₂ etc. Suppose you inject a large quantity of ¹⁴CO₂ into the atmosphere. You can say that you will get equilibration between atmospheric and oceanic ¹⁴CO₂, so the former will decrease and the latter increase. Or you can say that the equilibrium between atmospheric and oceanic CO₂ is dynamic, with molecules continually entering and leaving the ocean, and if there is a difference between the isotopic composition in the two phases this will be evened out as gas lower in ¹⁴C leaves the ocean and gas richer in ¹⁴C enters it.

[Intanjir]

Henry's Law is about the equilibrium of a dilute solution of a gas which does not react with its solvent.
We do not have anything resembling an equilibrium, CO2 does react with water, and furthermore the ocean isn't just a solvent- it is an active chemical soup. Henry's law is not at all applicable. I'm not even sure how you were intending to apply it given that there is no term in it representing the rate of anything.

Even if we did have an equilibrium of the carbon cycle it would not be applicable. The equilibrium for Henry's law assumes that the solution is in equilibrium so in particular that it is homogeneously mixed whereas an equilibrium of the carbon cycle is going to have concentration gradients as carbon is taken up and released by the various actors.

I don't know what 'equilibrium partition coefficient' would even mean in this context, but if it would be given by Henry's law then we would have to stop the carbon cycle completely.

You are looking at an equilibrium law when you should be looking at a rate law. What governs the rate at which a gas will dissolve? The gradient of concentration near the surface for one and how much the surface is being perturbed(ie waves) for another. These are the parameters that C14CO2 data is telling you something about.

[Intanjir]

Anyways C14 CO2 will be net taken up faster than C12 CO2 as long as the ratio of C14 to C12 in the air is greater than that in the ocean. And yes you should be able to treat it as its own gas with essentially identical properties as C12 CO2 so long as you keep in mind that it does compete with C12 CO2 for solvation in the same way that NaCl would compete with KCl. Which brings up the point here that Henry's Law is about dilute solutions. This assumption is added for precisely the reason that a sufficiently dilute solute won't compete with itself or other solutes. This assumption is a big part of what makes the solubility come out to be linear.

So you see the linearity of Henry's Law isn't some given that cannot be violated, it is simply assumed. The assumption is valid most of the time, ie things are 'sufficiently dilute' because gas molecules barely interact with each other so that it isn't until you start packing them in tightly enough into solution that either the ideal gas law would start to break down or more often for typical gases until they make up enough of the solution to perturb the properties of the solvent as a whole. It takes a lot of pressure to dissolve enough gas that the gas becomes a significant mole fraction. Of course it takes a lot less pressure for your gas to perturb the solvent if it reacts and makes things acidic....