SiC is a line compound, with standard free energy of formation at $1900$C of $$f G $=45$ kJ$/$mol$.$ The Si$-$C binary phase diagram is shown below. Clearly, there is very little solubility of C in Si$.$ Assume that the actual solubility of C in Si is $2$ at$.\%$ at $1900$C $($the exact number is not far off$)$ Model the $($C$,$ Si$)$ liquid as a simple regular solution, and estimate the enthalpy of mixing parameter $($called a$0$ in the text$)$ that will produce a solubility limit of $2$ at$.\%$ C in Si at $1900$C