**Problem 30-4E: The Spinning Disk Reactor**The "spinning disk" reactor is often utilized for conducting chemical reactions under controlled hydrodynamic conditions. Consider the highly-simplified process shown in **Figure 30-4E** (not provided here). This process involves one spinning disk mounted within a chamber equipped with a single gas inlet and outlet stream. The surface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneous reaction where gaseous reactant **A** is converted into gaseous product **B** (**A → B** on the surface). Given the reaction's presumed instantaneous nature, the reaction rate process is mass transfer limited, and the concentration of **A** at the catalyst surface is essentially zero (**C_AS ≈ 0**). During disk spinning, a hydrodynamic boundary layer forms between the surface and bulk gas, while the spinning motion also creates a well-mixed environment within the chamber. The process is carried out at **600 K** and **2.0 atm**, involving 20 cm³/sec of feed gas (20 cm³/sec at 600 K and 2.0 atm), of which 5.0 mole% is reactant **A** and 95 mole% is inert carrier gas **C** delivered into the chamber. The diameter of the disk is **10 cm**, and the chamber has a volume of 2000 cm³. Potentially relevant properties of gaseous species **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.**| Property | A | B | C ||---------------------------------|-------------------------|--------------------------|---------------------|| molecular diffusion coefficient | D_AC = 0.300 cm²/sec | D_BC = 0.235 cm²/sec | D_AB = 0.219 cm²/sec || kinematic viscosity | ν_A = 0.520 cm²/sec | ν_B = 0.300 cm²/sec | ν_C = 0.520 cm²/sec |### Questions:(a) **Mass Transfer Coefficient Calculation:**Determine the required spinning disk rotation rate, ω, in units of rev/sec, to achieve a mass transfer coefficient of **k_c = 1 ## Spinning Disk Reactor### Mass Transfer PerformanceThe performance of the spinning disk mass transfer is described by the Levich correlation, given by:\[ Sh = 0.62 \text{Re}^{1/2} \text{Sc}^{1/3} \]with \[ \text{Re} = \frac{\omega d^2}{\nu} \]### Characteristic LengthThe "characteristic length" for the spinning disk is its diameter, \( d \). The angular rotation rate \( \omega \) is defined as radians per unit of time. There are \( 2\pi \) radians in one revolution (rev).### Apparatus and Operational DetailsThe diagram depicts a spinning disk reactor, which operates under the following conditions:- Temperature: 600 K- Pressure: 2.0 atm- Gas is well mixed- The system is equipped with a rotating disk### Parameters- **Inlet flow rate (\(v_0\))**: 20 cm\(^3\)/sec- **Mole fractions at inlet**: - \( y_{A,0} = 0.05 \) - \( y_{B,0} = 0.0 \) - \( y_{C,0} = 0.95 \)- Concentration at the inlet \([C_{A,0}]\)The question (\( ? \)) marks the unknown concentration \([C_A]\) at a specific point in the reactor.### Components and Phases- **Rotating Disk**: The disk, with a diameter \( d = 10 \) cm, plays a crucial role in the mixing process.- **Catalytic Surface**: This is where the reaction occurs. The concentration at the catalytic surface is \( C_{As} \approx 0 \), indicating a near-zero concentration due to the reaction consumption.- **Boundary Layer**: Represented on the right side, it indicates a region where concentration changes from \( C_A \) at point B to \( C_{As} \approx 0 \) at the catalytic surface.### Graphical ExplanationThe diagram outlines the movement and reaction of gas on the spinning disk:- With the reactant A concentration \(C_A\) entering the boundary layer at location A and reaching near zero at the catalytic surface.- The angular velocity and rotation are depicted by the arrows

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Problem 30-4E. The "spinning disk" reactor is often used to carry out chemical reactions under controlled 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. The surface of the disk is coated with a non-porous catalyst. The catalyst surface catalyzes an instantaneous reaction where gaseous reactant A goes to gaseous product B (A →B on the surface). Since the reaction is presumed instantaneous, the rate process is mass transfer limited, and the concentration of A at the catalyst surface is essentially zero (CAS≈ 0). As the disk spins, a hydrodynamic boundary layer is created between the surface and the bulk gas, and the spinning motion also mixes the bulk gas to create a well-mixed environment within the chamber. The process is carried out at 600 K and 2.0 atm, where 20 cm³/sec of feed gas (also at conditions of 600 K and 2.0 atm) containing 5.0 mole % of reactant A and 95 mole% of inert carrier gas C are delivered to the chamber. The diameter of the disk is 10 cm, and the volume 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/sec kinematic viscosity VA = 0.520 cm²/sec DBC = 0.235 cm²/sec VB = 0.300 cm2²/sec DAB=0.219 cm²/sec Vc = 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 is the required spinning disk rotation rate, oo, in units of rev/sec? Is the mass-transfer process for reactant 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), to predict the outlet concentration, CA. (c) Determine the outlet concentration, CA, based on kc = 1.345 cm/sec. If the natation of the dial in i which of the fallami