
Interpretation:
Show that the second and third virial coefficients implied by the generic cubic equation of state are
Concept Introduction:
Write down the general cubic equation in terms of compressibility factor and for simplicity in terms of density and compare the results with standard expression of compressibility factor in terms of virial coefficients to find relations for both second and third virial coefficients.
Redlich/Kwong equation of state is used to find the values of second and third virial coefficients by formulating the positive constants use in generic cubic equations. So, here we first find the value of
The general cubic equation of state is:
For Redlich/Kwong equation of state,

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Chapter 3 Solutions
EBK INTRODUCTION TO CHEMICAL ENGINEERIN
- chemical engineering Demonstrate how each specific enthalpy was calculated, from the reference state to the process state. Be thorough to the fullest. This is a material-energy balance. The answers are H(1) = 35.7 KJ/kmol, H(2) = 32.0 KJ/kmol, and H(3) = -1.26 KJ/kmol.arrow_forwardheat and mass transfer:arrow_forwardChemical Engineering. Be thorough to the fullest for the three enthalpies. H(1) = 35.7 kj/kmol H(2) =32.0 Kj/kmol H(3)= -1.26 Kj/kmolarrow_forward
- chemical engineering Only solve the specific enthalpies. Be thorough to the fullest for each calculationarrow_forwardDo question 9 please! Question 7 Is just there for reference!!arrow_forward7) You are tasked with separating two proteins by ion exchange chromatography on a 30 cm long column with an inner diameter of 2 cm. The resin has a diameter of 100 μm and a void fraction of 0.3, and your mobile phase flows through the column at a rate of Q = 5 cm³/min. The Van Deemter coefficients A, B, and C have been determined to be 0.0228 cm, 0.0036 cm²/min, and 0.00053 min, respectively, for both proteins. Protein A elutes from the column with an average retention time of 27 min and standard deviation of 0.8 min. Protein B elutes from the column. with an average retention time of 33.8 min and standard deviation of 1.0. a) How many theoretical plates does the column contain? b) What flow rate (Q) will give you the maximum resolution? c) What is the minimum height of a theoretical plate for the system?arrow_forward
- 4) A fixed bed adsorption unit contains rigid (incompressible) silica particles with a diameter of 120 um and porosity of 0.3. The resin bed is 200 cm long and has a diameter of 15 cm. A protein solution is pumped into the column at a rate of 50 L/min, and the mobile phase has a viscosity of 1.2 CP. a) What is the pressure drop for this system (in bar)? b) What would be the pressure drop if the particle diameter were decreased to 30 μm?arrow_forwardYou are part of a team constructing a pipeline to transfer shale gas produced at the oceanfloor to the coastline. The temperature of the pipeline is nearly constant at 2 oC. The pipelineis made of smooth stainless steel and is 0.3 m in diameter and 100 m long. The averagevelocity of shale gas is 10 m/s and the inlet temperature is 20 oC ** Useful shale gas properties at 20 oC (Table A-12 for propane gas):(use these values for calculations and validate them later)• Density (ρ) = 18.13 kg/m3• Cp = 1974 J/kg-K• Viscosity (μ) = 8.54*10-6 kg/m-s• Pr = 0.918• k = 0.01836 W/m-Ka) Is the flow laminar or turbulent? Is the flow hydrodynamically and thermally fully developed?(circle your answer below and provide justification. • Laminar vs. Turbulent• Hydrodynamically developing vs. developed• Thermally developing vs. fully developedJustification: b) Calculate convective heat transfer coefficient (h). c) Calculate the exit temperature of the shale gas. d) Are the shale gas properties…arrow_forward3) A pilot-plant Podbielniak centrifugal extractor operating at 11,400 x g (this is G₁) is capable of processing 500 mL/min of filtered fermentation broth and 125 mL/min organic solvent, giving a recovery of 95%. The rotating cylinder inside the extractor has a diameter of 20 cm and is 2.5 cm wide. You need to scale up this extraction by using a larger Podbielniak extractor that has a diameter of 91 cm and width of 91 cm and delivers 2,300 x g (G2). What flow rates (in L/min) should be used in the larger extractor to achieve the same recovery efficiency?arrow_forward
- 7) You are tasked with separating two proteins by ion exchange chromatography on a 30 cm long column with an inner diameter of 2 cm. The resin has a diameter of 100 μm and a void fraction of 0.3, and your mobile phase flows through the column at a rate of Q = 5 cm³/min. The Van Deemter coefficients A, B, and C have been determined to be 0.0228 cm, 0.0036 cm²/min, and 0.00053 min, respectively, for both proteins. Protein A elutes from the column with an average retention time of 27 min and standard deviation of 0.8 min. Protein B elutes from the column. with an average retention time of 33.8 min and standard deviation of 1.0. a) How many theoretical plates does the column contain? b) What flow rate (Q) will give you the maximum resolution? c) What is the minimum height of a theoretical plate for the system?arrow_forward1 5) You are asked to design a moving bed adsorption process using two columns (see the figure below). Your feed contains 100 mg/L protein and flows through both columns at 4 m³/h. Fresh resin enters the bottom of both columns (resin does not flow from the bottom column to the top column). The maximum resin flow rate that your pumps can comfortably handle is 120 kg resin/h. Experimental data suggest that the adsorption equilibrium can be modeled as qi=4ci where qi is in g protein/kg resin and c; is in g protein/L broth. (Pay attention with units!) a) What is the lowest concentration of proteins that you could get in the effluent from column 1 (indicated by the *) in mg/L? (Hint: set up a mass balance) 0.25 , * 1 2 b) What should be the flow rate of resin (in kg/h) into the second column (B2) if your overall process needs to remove 99% of the protein?arrow_forward6) Instead of moving bed adsorption, you decide to try fixed bed adsorption with a different resin for removal of your protein. Your column is 25 cm long with an inner diameter of 5 cm. The resin packed in the column has a density of 1.5 g/cm³ and a void fraction of 0.25. Equilibrium data suggests that the protein binding to the column follows a Langmuir isotherm with an Stot = 6.25 g protein/kg resin and Keq = 2.58 L broth/g protein. The feed contains 100 mg/L protein and flows through the column at 500 mL/h. The calculated binding capacity of the column under these conditions is 945 mg protein. a) After 17.7 h, you detect an unacceptable level of protein in the column effluent. What is the length of unused bed? b) After deciding that this process will work well for separation, you need to scale up to a 1 m long column with the same diameter. If all else but length of the column is held constant, how long will you be able to run the column before breakthrough?arrow_forward
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