Problem 30-4E. The "spinning disk" reactor is often used to carry out chemical reactions undercontrolled hydrodynamic conditions. Consider the highly-simplified process shown in Figure 30-4E,where one spinning disk is mounted within a chamber equipped a single gas inlet and outlet stream. Thesurface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneousreaction where gaseous reactant A goes to gaseous product B (A →B on the surface). Since the reactionis presumed instantaneous, the rate process is mass transfer limited, and the concentration of A at thecatalyst surface is essentially zero (CAS≈ 0). As the disk spins, a hydrodynamic boundary layer iscreated between the surface and the bulk gas, and the spinning motion also mixes the bulk gas to create awell-mixed environment within the chamber. The process is carried out at 600 K and 2.0 atm, where 20cm³/sec of feed gas (also at conditions of 600 K and 2.0 atm) containing 5.0 mole% of reactant A and 95mole% of inert carrier gas C are delivered to the chamber. The diameter of the disk is 10 cm, and thevolume of the chamber is 2000 cm³. Potentially relevant properties for A, B, and C are provided below:Selected properties of gaseous species A, B, and C at T = 600 K and P = 2.0 atm.molecular diffusion coefficient DAC = 0.300 cm²/seckinematic viscosityVA = 0.520 cm²/secDBC = 0.235 cm²/secVB = 0.300 cm²/secDAB = 0.219 cm²/secVc = 0.520 cm²/sec(a) A mass transfer coefficient of ke = 1.345 cm/sec for reactant A in the gas mixture is desired. What isthe required spinning disk rotation rate, co, in units of rev/sec? Is the mass-transfer process forreactant A within the boundary layer best described as a dilute unimolecular diffusion process (UMD)process, or an equimolar counter-diffusion (EMCD) process? Justify your reasoning.(b) Develop a steady-state process material balance model, in fully algebraic form (no numbers), topredict the outlet concentration, CA.(c) Determine the outlet concentration, CA, based on kc = 1.345 cm/sec.(d) If the rotation rate (o) of the disk is increased, which of the following process variables will alsoincrease in value? Select all that apply, and justify your choice for each.(1) ke(2) CA at outlet (3) NA(e) If the volumetric flowrate Vo is increased, which of the following process variables will also increasein value? Select all that apply, and justify your choice for each(1) ke(2) CA at outlet(3) NA The spinning disk mass transfer performance is described by the Levich correlation, given by@d²Sh = 0.62 Re¹/2 Sc¹/3 with Re=VThe "characteristic length" for the spinning disk is its diameter, d. The angular rotation rate o is definedas radians/time. There are 2 radians in one revolution (rev).V₁ = = 20 cm³/secYA,O = 0.05Ув,0 = 0.0Yc,o= 0.95CAO600 K, 2.0 atmwell mixed gasrotatingdisk(d = 10 cm)Figure 30-4E. Spinning disk reactor.(radian/sec)2л (rev/sec)V₁ = 20 cm³/secCA = ?АA BCAI loveCA 0catalytic surfaceboundarylayer

Question

Problem 30-4E. The &#34;spinning disk&#34; reactor is often used to carry out chemical reactions undercontrolled hydrodynamic conditions. Consider the highly-simplified process shown in Figure 30-4E,where one spinning disk is mounted within a chamber equipped a single gas inlet and outlet stream. Thesurface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneousreaction where gaseous reactant A goes to gaseous product B (A →B on the surface). Since the reactionis presumed instantaneous, the rate process is mass transfer limited, and the concentration of A at thecatalyst surface is essentially zero (CAS≈ 0). As the disk spins, a hydrodynamic boundary layer iscreated between the surface and the bulk gas, and the spinning motion also mixes the bulk gas to create awell-mixed environment within the chamber. The process is carried out at 600 K and 2.0 atm, where 20cm³/sec of feed gas (also at conditions of 600 K and 2.0 atm) containing 5.0 mole% of reactant A and 95mole% of inert carrier gas C are delivered to the chamber. The diameter of the disk is 10 cm, and thevolume of the chamber is 2000 cm³. Potentially relevant properties for A, B, and C are provided below:Selected properties of gaseous species A, B, and C at T = 600 K and P = 2.0 atm.molecular diffusion coefficient DAC = 0.300 cm²/seckinematic viscosityVA = 0.520 cm²/secDBC = 0.235 cm²/secVB = 0.300 cm²/secDAB = 0.219 cm²/secVc = 0.520 cm²/sec(a) A mass transfer coefficient of ke = 1.345 cm/sec for reactant A in the gas mixture is desired. What isthe required spinning disk rotation rate, co, in units of rev/sec? Is the mass-transfer process forreactant A within the boundary layer best described as a dilute unimolecular diffusion process (UMD)process, or an equimolar counter-diffusion (EMCD) process? Justify your reasoning.(b) Develop a steady-state process material balance model, in fully algebraic form (no numbers), topredict the outlet concentration, CA.(c) Determine the outlet concentration, CA, based on kc = 1.345 cm/sec.(d) If the rotation rate (o) of the disk is increased, which of the following process variables will alsoincrease in value? Select all that apply, and justify your choice for each.(1) ke(2) CA at outlet (3) NA(e) If the volumetric flowrate Vo is increased, which of the following process variables will also increasein value? Select all that apply, and justify your choice for each(1) ke(2) CA at outlet(3) NA The spinning disk mass transfer performance is described by the Levich correlation, given by@d²Sh = 0.62 Re¹/2 Sc¹/3 with Re=VThe &#34;characteristic length&#34; for the spinning disk is its diameter, d. The angular rotation rate o is definedas radians/time. There are 2 radians in one revolution (rev).V₁ = = 20 cm³/secYA,O = 0.05Ув,0 = 0.0Yc,o= 0.95CAO600 K, 2.0 atmwell mixed gasrotatingdisk(d = 10 cm)Figure 30-4E. Spinning disk reactor.(radian/sec)2л (rev/sec)V₁ = 20 cm³/secCA = ?АA BCAI loveCA 0catalytic surfaceboundarylayer

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