Using Fick's law for a binary mixture, prove that: (a) Ja + Jb = 0 (b) Dab = Dba

Noting that the Reynolds number (Re) of the reactor is given by equation (2), \mathrm{Re}=\frac{\mathrm{d}_{t} \mathrm{u}}{v} in which u is the mean electrolyte velocity, use the data provided tocalculate, at 293 K, both the Reynolds number and the Schmidtnumber as a function of the volume flow rate. Comment on yourresults.

For Re < 2000, the Sherwood number is predicted to be related to the Reynolds number and the Schmidt number by equation (3) \mathrm{Sh}=\mathrm{aRe}^{\mathrm{b}} \mathrm{Sc}^{1 / 3}

a. (4 pts) Explain conceptually why increasing air flow rate lowers the adiabatic flame temperature. b. (8 pts) Determine the theoretical moles of air necessary to completely combust 1 mol/sof acetylene. c. (28 pts) Determine the unknown inlet and outlet specific enthalpies (and the heat of reaction if using heat of reaction method). To help your calculations, please use the inlet-outlet enthalpy table below and explicitly state your solution method and reference state(s) directly on this sheet!! (60 pts; 3 pages) Energy balance with reaction. Among common liquid fuels, acetylene(C2H2) torches burn at the highest adiabatic flame temperatures. It turns out that for our specific application we desire an outlet temperature of 1500°C, which is much cooler than the adiabatic flame temperature. 1500°C is enforced by using a large quantity of excess air.Assume that acetylene burns completely and clean and with a basis of calculation of 1mol/s, determine the % of excess air by solving an energy balance. The inlet acetylene and air gas streams are at 25°C and 1 atm, and the outlet is set at 1500°C and 1 atm. d. (12 pts) Write the appropriate form of the energy balance needed to solve for n1 – the unknown molar flow rate of air. Your answer should have n1 on the left hand side of the equation and all remaining knowns and unknowns on the process flow diagram on the right hand side.

Rectangular channel flow reactors are a useful basis for the development of electro chemical synthesis as part of a green and sustainable chemical manufacturing involving process electrification. A laboratory-scale electrochemical reactor, developed as a rectangular channel flow cell, had length (L) of 30 cm, a cross-sectional width (B) of3.0 cm and a cross-sectional height (s) of 5.0 mm, and was designed so that the flow would be well-developed before it reached the electrodes embedded in the sides of the reactor. Operation of the cell occurred isothermally at293 K, for a liquid electrolyte (of viscosity 1.002 mPa s and density998.2 kg m) for the electrochemical conversion of a reactant. The diffusion coefficient of the reactant in the liquid electrolyte is 2.67 x 10 cm? s at293 K. (a)Explaining all terms and symbols used, define the following. What are the units of kinematic viscosity (v)?kinematic viscosity of the liquid electrolyte at 293 K, providing your answer in the units you have previously given.(b)Calculate the If the equivalent diameter (de) of the laboratory reactor is given byequation (1),(c) \mathrm{d}_{\mathrm{e}}=4 \times \frac{\text { cross-sectional area }}{\text { cross-sectional perimeter }} calculate the value of the equivalent diameter of the reactor, andgive its units. (d)Noting that the Reynolds number (Re) of the reactor is given byequation (2), \mathrm{Re}=\frac{\mathrm{d}_{e} \mathrm{u}}{\mathrm{v}} in which u is the mean electrolyte velocity, use the data provided tocalculate, at 293 K, both the Reynolds number and the Schmidtnumber as a function of the volume flow rate. Comment on yourresults. (e)Use the data provided to calculate the Sherwood number (Sh) as a function of the volume flow rate at 293 K, and then plot Ig(Sh)against Ig(Re) and comment on your plot. For Re < 2000, the Sherwood number is predicted to be related tothe Reynolds number and the Schmidt number by equation (3)(f) \mathrm{Sh}=\mathrm{aRe}^{\mathrm{b}} \mathrm{Sc}^{/ / 3} where a and b are constants. Use your answers to parts (d) and (e)to calculate the values of a and b. Comment on your findings. For Re > 2000, the Sherwood number is predicted to be related tothe Reynolds number and the Schmidt number by equation (4) S h=c R e^{d} S c where c and d are constants. Use your answers to parts (d) and (e)to calculate the values of c and d. Comment on your findings.

For Re > 2000, the Sherwood number is predicted to be related to the Reynolds number and the Schmidt number by equation (4) \mathbf{S h}=\mathbf{c R e}^{\mathbf{d}} \mathbf{S} \mathbf{c}^{\boldsymbol{A}} where c and d are constants. Use your answers to parts (d) and (e)to calculate the values of c and d. Comment on your findings.

P7.24 A feed mixture F of 5 compounds (A, B, C, D, and E) is fed to an equilibrium stage. The separation requires addition of a material separating agent S. The output from the equilibrium stage is two phases. Phase I con- tains A, B, C, and most of the added S. Phase II con- tains B, C, D, E, and some S. Write down all material balance equations using mole fractions and total molar flows as variables, all phase equilibrium rela- tionships (in the form x₁ =f(x), and equations showing that mole fractions must sum to 1. List all

Consider a packed-bed reactor carrying out an exothermic, first-order reaction that converts A (reactant) into B (product). A enters the reactor through an inlet pipe (diameter 10 cm) with a volumetric flow rate of 0.5 m³/s at a concentration of 0.1 M. The first-order reaction's kinetic constant is k = 10 s¹ and the diffusion coefficient of A in steam is DAB = 5x10³ m²/s at a temperature of 300 °C. Assume that the reaction is irreversible, that there is zero bulk velocity inside the reactor (meaning that convection can be neglected or that there is equimolar counter-diffusion), and that the reactor's temperature is maintained at 300 °C. A. Draw a simple diagram of the packed-bed reactor and label the inlet flow. B. Derive a diffusion equation (in a differential equation form) that describes the concentration profile inside the packed bed reactor. State all assumptions. Do not integrate. C. What is the molar flux of A (in units of mol/m²-s) entering the reactor? D. If full conversion is achieved using 0.3 m of the reactor, determine the concentration profile of A inside the reactor and sketch a plot of concentration of A versus position inside the reactor. Label the concentrations of A at z = 0, 0.1, 0.2, and 0.3 m.

Given: A mixture of O₂ and CO₂ is kept in a container. The molar fraction of the O₂ is 0.4. To find: 1. Molar fraction of the CO₂ 2. Molecular weight of the mixture

Dilute concentrations of toxic organic solutes can be degraded by a "biofilm" attached to an inert, nonporous surface. A biofilm consists of living cell immobilized in a gelatinous matrix.