A mixture of methanol, butanol, and ethylene glycol is fed to a flash unit $($Unit $1)$ operating at $165C$ and $7$atm. The liquid from the first flash unit is recompressed, reheated, and sent to a second flash unit $($Unit $2)$ operating at $105C$ and $1$atm. The mixture is fed to the process at a rate of $10,000k\frac{g}{h}.$ Write material balances for each chemical, and solve for the mass flow rate of each product stream $(V_1,V_2,L_2).$ A material balance is simply a mathematical statement that all of the methanol $($for example$)$ going into the process has to come out again. $($This assumes a steady state and no chemical reactions.$)$ The following methanol balance is shown as an example:

methanol in $F=$ methanol in $V_1+$ methanol in $V_2+$ methanol in i

$0\mathrm{.}300*(10,000k\frac{g}{h})=0\mathrm{.}716*V_1+0\mathrm{.}533*V_2+0\mathrm{.}086*L_2$

$57$

The compositions of the feed stream $F$ and of the three product streams are listed here:

$\backslash$table$[[$Component$,$Mass Fraction in Stream$],[,F,V_1,V_2,L_2$