The ternary system \(A-B-C\) at \(80^{\circ} \mathrm{C}\) and \(100 \mathrm{kPa}\) has the overall composition \(z_{1}=0.40\), \(z_{2}=0.30\), and \(z_{3}=0.30\). Assuming that Raoult's law is appropriate to this system, determine \(L, V, x_{i}\) and \(y_{i}\). The vapour pressure of pure species are given by

\[ \begin{aligned} & P_{1}^{\text {Sat }}=187.32 \mathrm{kPa} \\ & P_{2}^{\text {Sat }}=95.48 \mathrm{kPa} \\ & P_{3}^{\text {Sat }}=50.55 \mathrm{kPa} \end{aligned} \]