If pressure and temperature are known constants, how can I determine the solubility of a known amount of gas in a mixture of molten salts?

Assume the mixture of salts is homogeneous and the composition (as well as amount of said compounds) is known.

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    $\begingroup$ Long story short, you can't. $\endgroup$ – Ivan Neretin Aug 30 '19 at 15:13
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    $\begingroup$ Arbitrary gas and salt mixture? Why even think there's non-negligable solubility? $\endgroup$ – Mithoron Aug 30 '19 at 15:13
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    $\begingroup$ @IvanNeretin of course it is possible. Geologists and volcanologists have spent decades experimentally measuring the solubility of various gases in various molten liquids (some of which are not too different from molten salts). $\endgroup$ – Gimelist Aug 31 '19 at 14:04
  • $\begingroup$ @Mithoron once you increase pressure above atmospheric, you can dissolve pretty much any gas in any liquid. $\endgroup$ – Gimelist Aug 31 '19 at 14:05
  • $\begingroup$ Pumice illustrates this solubility of gases in lava. $\endgroup$ – Ed V Aug 31 '19 at 16:12

If you know the phase diagram of the gas, and can calculate the exact pressure the gas should have given the volume outside of the molten salt, you can use the measured pressure/temperature to determine any difference in pressure. Then you can calculate the number of moles of gas that must be absorbed to generate the pressure difference. If the gas is relatively inert (which it probably needs to be if it wont react with molten salt), you can probably use the ideal gas equation: $$P_0V = NRT$$ If you compare to the actual pressure, you can determine the number of moles absorbed by the salt: $$\delta N = (P_0-P_\mathrm{exp})V/(RT)$$

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    $\begingroup$ This answer is incorrect. The solubility does not depend (at least directly) on volumes. The solubility can be parameterised experimentally for any liquid-has pair, and then calculated using that. $\endgroup$ – Gimelist Aug 31 '19 at 14:08
  • $\begingroup$ I don't think you understood why I used the ideal gas law here. The solubility is directly related to how much gas is absorbed at a specific pressure/temperature. You can use the ideal gas law to calculate an estimate on how much gas has been absorbed by the molten salt. If the amount of salt is known, then the solubility can be calculated trivially. $\endgroup$ – jakerz Sep 4 '19 at 17:10
  • $\begingroup$ "You can use the ideal gas law to calculate an estimate on how much gas has been absorbed by the molten salt." - No, you cannot. $\endgroup$ – Gimelist Sep 4 '19 at 22:38
  • $\begingroup$ Can you explain your logic? Why would a pressure loss not be due to absorbance? It is not helpful to simply say "you're wrong". $\endgroup$ – jakerz Sep 5 '19 at 5:10
  • $\begingroup$ Because once you're a bit higher than atmospheric pressure, things do not act as ideal gases any more. For example, oxygen fugacity can be an order of magnitude higher than oxygen partial pressure. As solubility is determined by fugacity, not partial pressure. Furthermore, the composition of the molten salt has a very strong influence on the solubility of gases in it. Furthermore, at temperatures high enough to melt salts, you will get salt vapour as well and your atmosphere is not the pure gas any more. And let's remember that you have an unknown molar volume of the gas component in the salt. $\endgroup$ – Gimelist Sep 5 '19 at 5:16

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