Bonus Problem (+15 points). Consider the following two-feed distillation column, in which the specifications of all feed and product streams are known to us and labeled: -DX0 Section 1 H V3.12 Section 2 F1.2.97 pav. Section 3 cy In the following exercises, we will show that, as long as the liquid and vapor flow rates in one of the column sections are given, one can derive the operating line equation for any other column section. (a) Starting from mass balance equations by drawing a control volume around the top of the column and somewhere in Section 2 (between stage n and stage n+1), show that the operating line equation for Section 2 can be expressed using Section I liquid and vapor flow information as: L: +9F DxD-Fi? Xin + V-(1-1){ V -(1-4) where the quantity Dxi - FZ., is simply component i's net material upward flow in Section 2. (b) Starting from mass balance equations by drawing a control volume around the bottom of the column and somewhere in Section 2 (between stage n and stage n + 1), show that the operating line equation for Section 2 can also be expressed using Section 3 liquid and vapor flow information as: Ly - -BX, +% Yint = V+ (1 -9.) V: +(1-4) where the quantity Bxus + Fyzir, is equal to component t's net material upward flow in Section 2. And of course, -BX+F2 = DX-F2, which can be seen by performing a component mass balance around the column -Xint