What would be the concentration of products in this calcium producing system?
T l, Dr:  despite what you see from the aqueous electromotive series, potassium does not reduce calcium oxide in this setting.

You may be assuming that potassium, which lies above calcium in the electromotive series for aqueous solutions, therefore lies above calcium in all other settings regardless of chemical environment or temperature.  It doesn't.  The electromotive series we see can change in different environments and at different temperatures.

For instance, in this Ellingham-Richardson diagram you see calcium oxidation at a very low oxygen potential, corresponding to a great tendency towards oxidation and thus a very high position for calcium in the "electromotive series" for anhydrous oxide formation.  Where is potassium?  Much higher up in free energy (starting around -650 on the free energy scale), corresponding to a less stable oxide and thus a lower tendency for potassium oxidation.  In the absence of water solvent and at elevated temperatures (or even without elevated temperature but still in the absence of water), potassium does not displace calcium, or even manganese, from oxide formation.  The order is very different from the aqueous one.

Apart from lithium, all of the alkali metals are notoriously poor at oxide formation, compared with what we expect from aqueous solutions.  Look again at the diagram; sodium isn't so hot compared with calcium, magnesium or aluminum either.



Calcium is made industrially by either electrolysis or reduction of calcium oxide with aluminum.  In the latter reaction aluminum still forms a less stable oxide than calcium, but unlike potassium it can form ternary calcium-aluminum oxides that are still more stable than just calcium oxide.  Thus part of the calcium from the lime is converted to these ternary compounds while the rest, not fitting in the ternary compounds, comes off as vapor.