Ethanol is produced commercially by the hydration of ethylene:C2H4(g)+H2O(v) =CH5OH(v)Some of the product is converted to diethyl ether in the undesired side reaction2C2H5OH (v) = (C2H5)20(v)+H2O(v)The combined feed to the reactor contains 53.7 mol% C2H4 , 36.7% H2O and the balance nitrogenwhich enters the reactor at 310°C. The reactor operates isothermally at 310°C. An ethylene conver-sion of 5% is achieved, and the yield of ethanol (moles ethanol produced/mol ethylene consumed)is 0.900.Data for Diethyl EtherAH = -272.8 kJ /mol for the liquidAH, = 26.05 kJ /mol assume independent of TCkJ/mol - °C]= 0.08945 +40.33 × 10-°T(°C) – 2.244 x 10-7T2(a) Calculate the reactor heating or cooling requirement in kllmol feed.(b) Why would the reactor be designed to yield such a low conversion of ethylene? Whatprocess- ing step (or steps) would probably follow the reactor in a commercial implementa-tion of this process?

Given: The reaction for the production of industrial ethanol by the hydrolysis of ethylene is: C2H4g+H2Ov⇌C2H5OHv Some of the desired product is converted to diethyl ether by the side reaction, 2C2H5OHv⇌C2H52Ov+H2Ov The composition of the combined feed to the reactor: 53.7mol% C2H4, 36.7 mol% H2O and rest nitrogen. The feed temperature, TF = 310°C The reactor is isothermal. The conversion of ethylene is 5% and the ethanol yield is 0.900 mol ethanol/mol ethylene consumed. For diethyl ether, the enthalpy data given are: ΔH^f∘=−271.2 kJ/mol for liquidΔH^v=26.05 kJ/mol independent of TCpkJ/mol⋅∘C=0.08945+40.33×10−5T−2.244×10−7T2(a) The basis of the calculations is taken as 1 mol feed. The flowchart of the given process is shown below:Calculate the number of unreacted moles of ethylene present in the product stream from the given 5% conversion of ethylene as: f=moles reactedmoles fed0.05=10.537−n10.537n1=0.510 mol C2H4v Now, from the given yield of ethanol, calculated the moles of ethanol produced as: 0.900=n310.537−n10.900=n310.537−0.510n3=0.0243 mol C2H5OHvSince, there are reactions taking place in the reactor, apply material balance on elemental species, carbon (C) as: 20.537=2n1+2n3+4n420.537=20.510+20.0243+4n4n4=0.00135 mol C2H52Ovn4=1.35×10−3 mol C2H52Ov Apply material balance on elemental species, oxygen (O) as: 40.537+20.367=4n1+2n2+6n3+10n440.537+20.367=40.510+2n2+60.0243+100.00135n2=0.3414 mol H2OvFor energy balance, take the reference as O2(g), H2(g), C(s) at 25°C, and N2(g) at 310°C The inlet-outlet table for enthalpy is:From the standard table, the specific enthalpy of C2H4(v) at 310°C is the sum of its enthalpy of formation at 25°C and its enthalpy at 310°C: H^1=ΔH^∘fC2H4v+∫25310CpC2H4vdT=52.28+16.41 kJ/mol=68.69 kJ/mol From the standard table, the specific enthalpy of H2O(v) at 310°C is the sum of its enthalpy of formation at 25°C and its enthalpy at 310°C: H^2=ΔH^∘fH2Ov+H^H2Ov310∘C=−241.83+9.93 kJ/mol=−231.90 kJ/mol From the standard table, the specific enthalpy of C2H5OH(v) at 310°C is the sum of its enthalpy of formation at 25°C and its enthalpy at 310°C: H^3=ΔH^∘fC2H5OHv+∫25310CpC2H5OHvdT=−235.31+24.16 kJ/mol=−211.15 kJ/mol From the given enthalpy information of diethyl ether, the specific enthalpy of (C2H5)2O (v) at 310°C is the sum of its enthalpy of formation at 25°C and its enthalpy at 310°C: H^4=ΔH^∘fC2H52Ov+ΔH^vC2H52Ov+∫25310CpC2H52OvdT=−272.8+26.05+42.52 kJ/mol=−204.2 kJ/mol The enthalpy table now becomes:The potential energy of the system is zero and any kinetic change in the system is assumed to be zero. Also, there is no shaft work done on the system. Thus, the energy balance equation reduces to: Q=ΔH Thus, Q=∑outniH^i−∑inniH^i=0.51068.69+0.3414−231.90+0.0243−211.15+0.00135−204.2−0.53768.69+0.367−231.90=−1.32 kJ Since there is a negative sign, it means that the heat is withdrawn from the reactor. Also, the calculations are done on the basis of 1 mol of feed. Therefore, the rate of cooling of the reactor is, Q = 1.32 kJ/mol feed.(b) The yield of ethanol is kept low to minimize the undesirable side reaction that would take place. If the concentration of ethanol is low, then it is less likely that the molecules will come in contact with each other and react to produce undesired diethyl ether. If the reactor is to be implemented commercially for the given process, then, first the reactor contents should be sent to the separation processes to remove the desired product and unreacted ethylene from the reaction mixture of the product stream. Second, the unreacted ethylene separated from the product stream should be sent back to the reactor through the recycle stream to achieve the higher conversion of ethylene and higher yield of the ethanol.