Extra Credit $(20$ points$)$

A local restaurant holds a contest challenging contestants to mix equal volumes of ethanol and water to get a total volume of $100c{m}^3.$ The partial molar volumes of water and ethanol are shown in Figure $1.$

Figure $1.$ The partial molar volumes $(V_m)$ of water and ethanol in a water$-$ethanol mixture.

EC$\mathrm{.}1.$ Your friend proposes to mix$50c{m}^3$ of water and $50c{m}^3$ ethanol. Explain in $10$ words or less why he will lose the contest. $(5$ points$)$

EC$\mathrm{.}2.$ Dr$.$ K $($unsurprisingly$)$ wins the contest through by calculating the correct amounts to mix through an understanding of thermodynamics. Calculate the amount of water $(V_w)$ and ethanol $(V_e)$ that was mixed. $(15$ points$)$