Problem $-2($Water$-$gas shift reactor unit of a NG reforming process $-$ mole balance, extent of the reaction at equilibrium and equilibrium conversion calculation$)$

Consider that the equilibrium state of the water$-$gas shift reaction $(CO+H_{2}OharrC{O}_2+H_2)$ approximately described by the following relation

$1$

$\frac{y_{C{O}_2}{y}_{H_2}}{y_{CO}{y}_{H_{2}O}}=K_e(T)=0\mathrm{.}0247$exp$[\frac{4020}{T}(K)]$

where $K_e$ is the reaction equilibrium constant, and $yi$ is the mole fraction of species $i$ in the reactor contents at equilibrium.

The feed to a shift reactor contains $20\mathrm{.}0$mole$\%CO,10\mathrm{.}0\%C{O}_2,40\mathrm{.}0\%$ water, and the balance an inert gas. The reactor is maintained at $T=1123K.$

i$.$ For a basis of $1$mol feed and draw and label a flowchart. Carry out a degree$-$of$-$freedom analysis of the reactor based on extents of reaction and use it to prove that you have enough information to calculate the composition of the reaction mixture at equilibrium. You do not need to do calculation for this part $($i$)$ of this question.

ii$.$ Estimate the total moles of gas in the reactor at equilibrium and then the equilibrium mole fraction of hydrogen in the product.

iii. A gas sample is drawn from the reactor and analyzed shortly after startup and the mole fraction of hydrogen is significantly different from the calculated value. Assuming that no calculation mistakes or measurement errors have been made, what is a likely explanation for the discrepancy between the calculated and measured hydrogen yields?

iv$.$ Construct a spreadsheet to take as input the reactor temperature and the feed component mole fractions $y_{CO}$;$y_{H2O},$ and $y_{CO2}($assume no hydrogen is fed$)$ and to calculate the mole fraction $y_{H2}$ in the product gas when equilibrium is reached. The spreadsheet column headings should be

The columns between $Ke$ and $y(H2)$ may contain intermediate quantities in the calculation of $yH2.$ First test your program for the conditions of Part $($a$)$ and verify that it is correct. Then try a variety of values of the input variables and draw conclusions about the conditions $($reactor temperature and feed composition$)$ that maximize the equilibrium yield of hydrogen.