Process engineering mass balance in the douglas aproach

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The discussion centers on the mass balance equations for the production of styrene from ethylbenzene. The user is seeking assistance with a specific problem related to mole proportions of various species involved in the reaction. The key components include ethylbenzene (EB), styrene, hydrogen (H2), benzene (Bz), ethylene, toluene, and methane, with their respective mole proportions expressed in terms of variables x, y, and z. The user is instructed to specify values for x (0.3, 0.4, 0.5, 0.6) and derive formulas for y and z as functions of x. The final step involves prorating the calculated moles to determine the correct amount of product and conducting an economic analysis on the products and fuel requirements to evaluate overall feasibility.
latkan
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Hey guys i was hoping for some help with the mass balance of the equations for the production of styrene from ethylbenzene. I have attached my problem sheet and my answer sheet, q 7 is what i am stuck on please help me i am confused
 

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Mole proportions of each species are
EB= 0.98 - x-y-z
Styrene= x
H2= x-z
Bz = y+0.02, ethylene= y
Tol and methane= z
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Specify x= 0.3, 0.4, 0.5, 0.6
Then Figure out y, z as a function of x (two formulas)
Prorate all the moles above to get the right amount of product.
Do economics on the products and fuel requirements, to see where you are.
 

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