Acetic acid can be produced through the given balanced reaction and with the process shown in the image.

$Ca(C_2{H}_3{O}_2{)}_2+H_{2}S{O}_{4}CaS{O}_4+2C_2{H}_4{O}_2$

In the process, $535l\frac{b}{h}$ of fresh $Ca(C_2{H}_3{O}_2{)}_2$ and enough $H_{2}S{O}_4$ to be in $10\mathrm{.}0\%$ excess for converting the fresh $Ca(C_2{H}_3{O}_2{)}_2$ is fed into the reactor. The single pass conversion of $Ca(C_2{H}_3{O}_2{)}_2$ in the reactor is $90\mathrm{.}0\%.$ Determine the amount of $Ca(C_2{H}_3{O}_2{)}_2$ recycled and the production rate of $C_2{H}_4{O}_2$ by performing the given steps.

What is an expression for the amount of $Ca(C_2{H}_3{O}_2{)}_2.$ entering the reactor, $m_3,$ in terms of the recycled flow of $Ca(C_2{H}_3{O}_2{)}_2,m_8,$ and the fresh feed of $Ca(C_2{H}_3{O}_2{)}_2,m_2?$

$m_3=$

What is an expression for the amount of unreacted $Ca(C_2{H}_3{O}_2{)}_2$ leaving the reactor, $m_4,$ in terms of the amount of $Ca(C_2{H}_3{O}_2{)}_2$ in the recycle stream, $m_8?$

$m_4=$

What is an expression for the amount of unreacted $Ca(C_2{H}_3{O}_2{)}_2$ leaving the reactor, $m_4,$ in terms of $m_3?$

$m_4=$

Substitute the first two expressions into the last expression to eliminate the $m_4$ and $m_3$ terms. Plug in known values and solve for the amount of $Ca(C_2{H}_3{O}_2{)}_2$ in the recycle stream, $m_8=$ Ib $Ca\frac{(C_2{H}_3{O}_2{)}_2}{h}{m}_8.$

To find the production rate of $C_2{H}_4{O}_2,$ first calculate the flow rate of fresh $Ca(C_2{H}_3{O}_2{)}_2$ in $lb-mo\frac{l}{h}.$

flow rate:

Ib$-$ molCa$\frac{(C_2{H}_3{O}_2{)}_2}{h}$

For every pound$-$mole $($Ib$-$mol$)$ of fresh $Ca(C_2{H}_3{O}_2{)}_2$ that enters the process, how many pound$-$moles of $C_2{H}_4{O}_2$ leave the process?

amount leaving:

$lb-mol{C}_2{H}_4{O}_2$

What is the flow rate of $C_2{H}_4{O}_2$ in the product streum in $lb-mo\frac{l}{h}?$

flow rate:

$b-molC{l}_2{H}_4{O}_{2}h$

What is the flow rute of $C_2{H}_4{O}_2$ in the product stream in pounds per hour $(l\frac{b}{h})?$

$m_3=$

$ib{C}_2{H}_4{O}_{2}m$