Why Melt/Vapor and Mineral/Vapor D's =f(mvCl-) are Meaningless

by Phil Candela

Let's say we have a silicate melt with (per kg),

1 mole Na

1mole K

One might find a relationship for the distribution of Na between melt and vapor of the type:

D v/l Na = 0.5mvCl-.

But what does this mean? Should it be reported this way? Well, ONLY if it has some general applicability. Ok, then let's see if it does. let's examine three different magmatic volatile phases.

A. For 0.1 molal Cl in the aq phase, Na aq = 0.05 m,

B. For 1 molal Cl in the aq phase, Na aq = 0.5 m, and

C. For 2 molal Cl in the aq phase, Na aq = 1.0 m.

Now what is balancing the rest of the Cl-? The answer is K: solutions A,B,C are 0.05, 0.5, and 1.0 molal in KCl. (We will ignore HCl and other chlorides for simplicity.)

The relationship seems to hold, you say? Well, don't jump to any conclusions. Let's add another salt; for simplicity, I will add a salt that partitions strongly into the aq phase relative to the melt - this has no effect on the point I want to make, it just makes the calculations simpler. So, let's add an additional 1 molal Cl to the 1 molal solution (solution B), and let's add it as CuCl. Now, solution B' is 2 molal in Cl-. The copper stays in the aq phase, so Cu is 1 molal. The balance of the solution is 0.5 molal Na and 0.5 molal K. Na can't increase beyond 0.5, because it cannot be balanced by Cl if it does, and if it was balanced by anything else, it would not be affected by Cl-! Besides, all studies at mid- to upper-crustal pressures show that the alkalis are balanced dominantly by Cl-.

So, we have, with a different aq phase, D= 0.25mvCl-, demonstrating that the chloride-dependent D formalism has no generality whatsoever! But we could have guessed that. The D cannot be any type of equilibrium constant, because it does not correspond to any possible chemical potential relationship that is expressed among independently variable thermodynamic components of the phases. The increase of Na in the aq phase with increasing mvCl- is a red herring. A closer examination of the data shows that something is constant from one experiment to another: the K-Na exchange constant between vapor and melt. It is easy to see that it is equal to unity (1) in this example (and is ca. 1 +/-0.25 in many melt-vapor studies). Therefore, for a given melt composition, the K/Na ratio of the vapor is fixed (barring significant excursions in P and/or T); once you realize this, you see that, yes, the Na concentration of the aq phase had to increase with increasing chloride (cases A - B - C, above), but that is not the expression of some fundamental principle; rather it is a consequence of the constant K/Na vapor/melt exchange constant, together with "charge balance" in the aqueous phase! Bottom line: pay no attention to chloride dependent D's, but rather, examine balanced chemical reactions and their associated equilibrium (or apparent equilibrium) constants in light of LeChatlier's rule. THIS WILL NOT LEAD YOU ASTRAY.