Final answer:
At 2300°C, using Henry's law, the solubility of CaO in MgO is 12.88 mol%, and the solubility of MgO in CaO is 6.23 mol% in a simple eutectic system.
Step-by-step explanation:
To calculate the solubility of CaO in MgO and the solubility of MgO in CaO at 2300°C for a simple eutectic system, we use Henry's law. Henry's law states that the solubility of a solute in a solvent is directly proportional to the partial pressure of that solute above the solvent. In solid solutions, this can be interpreted as the concentration of one component in another being proportional to its activity or 'pressure' in the mixture.
Given the Henry's law constants (r(CaO) in MgO = 12.88 and r(MgO) in CaO = 6.23 at 2300°C), we can make use of the formula for Henry's law solubility: Solubility = k * P, where k is the Henry's law constant and P is the partial pressure of the solute.
In this context, as there's no direct 'pressure', the proportionality constants themselves already represent the concentration limits at the given temperature. Thus, at 2300°C, the solubility of CaO in MgO is 12.88 mol% and of MgO in CaO is 6.23 mol%.