Fan et al$.$ studied the excess molar volume of a binary mixture containing methanol$-$methyl

metacrylate at atmospheric pressure and developed the corresponding mathematical

correlations, which is reported in the Journal of Chemical and Engineering Data $2008,$ vol.

$53,$ pp$\mathrm{.}18361840.$

By using equations in the paper, determine:

a$.$ the volumes of methanol and methyl$-$metacrylate that need to be mixed to make $1$L solution

containing $60$ mol$\%$ methanol at $50$ oC$.$

b$.$ The partial molar volumes of methanol and methyl$-$metacrylate at the condition in part a$.$

above.

c$.$ Plot the volume change of mixing against temperature, and briefly justify the trends.

State clearly the equations you use and the methods to solve the question.