- Derive the form of the Longmuir isotherm for the complete dissociative adsorption of SO2, i.e.: Diagrams included in the Solution
- Take the data at 363 K from problem 5.2. Can you distinguish which of the three isotherms – Langmuir, Freundlich, or Temkin – is the best obeyed? If so, which one?
- Derive the form of the Langmuir isotherm when an adsorbing species occupies two surface sites, i.e: Diagrams included in the Solution
- The following data have been reported by Shen and Smith for benzene (Bz) adsorption on silica gel [16]: a) Do these data better fit a single site or a dual site Langmuir isotherm? Why? b)
- A boron-doped carbon was prepared by adding 0.1 wt % B to a graphitized carbon black (Monarch 700, Cabot Corp.) and then heat treating this material, designated BC-1, at 2773 K under Ar [71,72]. Its
- In a study of iron catalysts, the BET surface areas of a number of materials were determined using N2 or Ar physisorption near 80 K [71–73]. The Po values vary slightly because the bath temperature
- The following H2 chemisorptions results are reported for a 1.5% Rh/Al2O3 catalyst. What is the amount of hydrogen chemisorbed on Rh? What is the dispersion (fraction exposed) of the Rh? H2
- An O2 adsorption isotherm was obtained at 443 K for a 2.43% Ag/SiO2 catalyst and the uptake results are given below. No irreversible adsorption occurs on the silica. What is the dispersion of the
- The following observed rate data have been reported for Pt-catalyzed oxidation of SO2 at 763K obtained in a differential fixed-bed reactor at atmospheric pressure and containing a catalyst with a bed
- A commercial cumene cracking catalyst is in the form of pellets with a diameter of 0.35 cm which have a surface area, Am, of 420m2 g –1and a void volume, Vm, of 0:42 cm3 g–1. The pellet density
- A 1.0% Pd/SiO2 catalyst for SO2 oxidation is being studied using a stoichiometric O2/SO2 feed ratio at a total pressure of 2 atm. At a temperature of 673 K, a rate of 2:0 mole SO2 s-1 L cat-1 occurs.
- Assume that Pt was dispersed throughout the pore structure of the entire pellet in Problem 4.1 and apply the Weisz-Prater criterion to determine if mass transport limitations are expected. Do only
- Vapor-phase benzene (Bz) hydrogenation over carbon-supported Pd catalysts has been studied [65, 66]. A 2.1% Pd/C catalyst prepared with a carbon black cleaned in H2 at 1223 K had a surface-weighted
- The reforming of CH4 with CO2 to produce CO and H2 has been examined over a number of dispersed metal catalysts [67, 68]. At 723K, a CO2 partial pressure of 200 Torr, PCH4 = 200 Torr, and a total
- Utilize the data given in Problem 4.5, assume the benzene hydrogenation reaction is zero order in benzene and first order in H2, and then calculate the Thiele modulus for the largest and smallest
- The rate of formaldehyde (CH2O) oxidation over a Ag=SiO2 catalyst at 493 K and a CH2O pressure of 9 Torr in air was 1:4 x 10 –7 mole CH2Os –1 cm –3. The catalyst particles passed through a
- What is the optimum fractional coverage of a nonuniform catalyst surface if the transfer coefficient a is 2/3 rather than 1/2; in other words, if equation 8.57 utilizes a = 2/3?
- The Temkin rate equation for NH3 synthesis is based on the 2-step sequence provided in Illustration 8.1 and it is given by equation 2 in that Illustration. With the information given there, i.e., m =
- Derive the rate expression for an enzyme-catalyzed unimolecular (single substrate) reaction, such as that shown in steps 9.1 and 9.2, assuming that the decomposition of the reactive intermediate to
- Initial rates of an enzyme-catalyzed reaction for various substrate (reactant) concentrations are listed in the table below. Evaluate rmax and Km by a Lineweaver-Burke plot.
- Derive an expression for the reaction rate, r, in terms of S, E and the constants shown for the following reaction sequence, which includes substrate inhibition:
- Multiple complexes can be involved in some enzyme-catalyzed reactions. For the reaction sequence shown below, develop suitable rate expressions using: (a) The Michaelis equilibrium approach and
- The following first-order rate constants were obtained for the thermal decomposition of ethane: Calculate the activation energy and the pre-exponential factor.
- Using statistical thermodynamics, determine the temperature dependence of the pre-exponential factor for: a) The gas-phase reaction of two N atoms to form N2. b) The bimolecular gas-phase reaction
- Use the steady-state approximation and derive the rate expression for the following sequence of elementary steps describing a chain reaction. Define your rate clearly.
- The series of elementary steps below has been proposed to describe acetaldehyde pyrolysis to methane and CO. Derive the steady-state rate expression making the usual long-chain approximation; i.e.,
- Using the BOC-MP method, calculate the heat of adsorption for the following four species. All the information and values needed are contained in the various tables in section 6.3 of this chapter.
- Based on the BOC-MP method, calculate the heat of adsorption for the following species. All information and values needed are contained in the various tables in Section 6.3 of this chapter. (a) NO
- The kinetics of acetone hydrogenation on Pt catalysts has been studied by Sen and Vannice (See Problem 7.9) [35]. To determine which bonding mode is more probable, the heat of adsorption for an
- Derive Guideline 3 in Table 6.10 for a monatomic species of 30 amu: a) Using collision theory and assuming a 2-dimensional gas. b) Using absolute rate theory and assuming immobile adsorption. c)
- Kircher and Hougen studied NO oxidation, 2NO + O2 → 2NO2, over activated carbon and SiO2 in the presence of water and proposed a Rideal-Eley mechanism between O2 and (N2O2) ad, which gave a
- Derive a rate expression for each of the following single reactions taking place through a sequence of steps as indicated. Define your rate clearly. S represents an active site.
- Derive the form of the rate expression based on the elementary steps below, where S is an active site: a) Assuming [B_S] is the MARI, and b) Assuming [A_S] is the MARI.
- Consider the following sequence of steps to describe the high-temperature kinetics of NO reduction by CH4 on La2O3 and Sr = La2O3 in the absence of O2: (a) Provide any necessary stoichiometric
- A series of elementary steps to describe the water gas shift reaction over copper has been proposed as shown below. Define your reaction rate and derive a rate expression consistent with this model,
- Derive the rate expression in Table 7.10: a) For a bimolecular reaction with nondissociative adsorption as the RDS; b) For a bimolecular reaction with nondissociative adsorption, but now product
- Sinfelt has studied ethane hydrogenolysis, C2H6 + H2 → 2CH4, over the Group VIII metals, and he has proposed the following sequence of steps on cobalt [55]:
- The decomposition of N2O over a 4.56% Cu/ZSM-5 catalyst (ZSM-5 is a zeolite discovered by Socony Mobil, hence the letter designation) has been investigated by Dandekar and Vannice [56]. Temperatures
- N2O decomposition has also been investigated on a 4.9% Cu=ת ─ Al2O3 catalyst in which, after a pretreatment in H2 at 573 K, the Cu was highly dispersed and present almost completely as
- The kinetics of acetone hydrogenation over 5.0% Pt/SiO2 and 1.9% Pt/TiO2 catalysts, previously characterized by H2 chemisorption, were studied by Sen and Vannice [57]. The dispersion of Pt was 0.31
- As an alternative to the model proposed in Illustration 7.3, consider instead the following H-W-type reaction mechanism for NO decomposition, in which unimolecular decomposition occurs with an
- Methane combustion on La2O3-based catalysts has been studied by Toops et al. [46]. With a 4% Sr-promoted La2O3 catalyst (2:5m2g-1) operating between 773 and 973 K, 0:5 -5 Torr CH4 and 3 _ 23 Torr O2
- The reduction of NO by H2 on La2O3 and Sr-promoted La2O3 was examined by Huang et al. [59]. Both N2 and N2O were observed as products. The sequence of elementary steps proposed for the catalytic
- It was mentioned in Chapter 7.1 that if more than one active site is required in a unimolecular decomposition reaction, the denominator must be raised to a power greater than unity. Now, if a RDS
- As stated in this chapter, a reaction sequence need not contain a RDS. A study of N2O reduction with CO over a 4.9% Cu=Al2O3 catalyst provides an example of this [56]. This reaction around 523 K was
- The catalytic reforming of methane with carbon dioxide, i.e., CH4 + CO2 ≡ 2 H2 +2 CO is a complex high-temperature reaction. It has been studied on nickel catalysts between 673 and 823 K by
- As another alternative to the model proposed in Illustration 7.3, consider a sequence with no RDS on the surface and with the formation of an adsorbed (NO) 2 species which then decomposes to give
- Examine the reaction kinetics in Illustration 7.5 again. Focus in particular on steps 10–14. If a H-W-type model is chosen that assumes irreversible toluene desorption as the RDS, is the derived
- In a study of formaldehyde oxidation over Ag catalysts, the power rate law over Ag powder was r = kPo2 and over supported Ag it was r = kP0:3O2 P0:3H2CO [62]. The following sequence of steps was
- Estimation of dense-gas viscosity. Estimate the viscosity of nitrogen at 68oF and 1000 psig by means of Fig. 1.3-1, using the critical viscosity from Table E.1. Give the result in units of lbm/ft ∙
- Estimation of the viscosity of methyl fluoride. Use Figure 1.3-1 to find the viscosity in Pa ∙ s of CH3F at 370oC and 120 atm. Use the following values for the critical constants: Tc = 4.55oC, Pc
- Computation of the viscosities of gases at low density. Predict the viscosities of molecular oxygen, nitrogen, and methane at 20oC and atmospheric pressure, and express the results in mPa. s. Compare
- Gas-mixture viscosities at low density. The following data2 are available for the viscosities of mixtures of hydrogen and Freon-12 (dichlorodifluoromethane) at 25oC and 1 atm: Mole fraction of
- Viscosities of chlorine-air mixtures at low density. Predict the viscosities (in cp) of chlorine-air mixtures at 75oF and 1 atm, for the following mole fractions of chlorine: 0.00, 0.25, 0.50, 0.75,
- Estimation of liquid viscosity. Estimate the viscosity of saturated liquid water at 0oC and at 100oC by means of (a) Eq. 1.5-9, with ∆Uvap = 897.5 Btu/lbm at 100oC, and (b) Eq. 1.5-11.
- Molecular velocity and mean free path. Compute the mean molecular velocity u (in cm/s) and the mean free path λ (in cm) for oxygen at 1 atm and 273.2 K. A reasonable value for d is 3 A. What is the
- Velocity profiles and the stress components τij. For each of the following velocity distributions, draw a meaningful sketch showing the flow pattern. Then find all the components of 'r and pvv for
- A fluid in a state of rigid rotation (a) Verify that the velocity distribution (c) in Problem 1B.1 describes a fluid in a state of pure rotation; that is, the fluid is rotating like a rigid body.
- Viscosity of suspensions, data of V and3 for suspensions of small glass spheres in aqueous glycerol solutions of ZnI2 can be represented up to about ? = 0.5 by the semi empirical expression Compare
- Some consequences of the Maxwell-Boltzmann distribution, in the simplified kinetic theory in S1.4, several statements concerning the equilibrium behavior of a gas were made without proof. In this
- The wall collision frequency, it is desired to find the frequency Z with which the molecules in an ideal gas strike a unit area of a wall from one side only. The gas is at rest and at equilibrium
- Pressure of an ideal gas. It is desired to get the pressure exerted by an ideal gas on a wall by accounting for the rate of momentum transfer from the molecules to the wall.? (a) When a molecule
- Uniform rotation of a fluid(a) Verify that the velocity distribution in a fluid in a state of pure rotation (i.e., rotating as a rigid body) is v = [w x r], where w is the angular velocity (a
- Force on a surface of arbitrary orientation? (Figure 1D.2) Consider the material within an element of volume OABC that is in a state of equilibrium, so that the sum of the forces acting on the
- Thickness of a falling film, water at 20oC is flowing down a vertical wall with Re = 10. Calculate(a) The flow rate, in gallons per hour per foot of wall length, and(b) The film thickness in inches.
- Determination of capillary radius by flow measurement, one method for determining the radius of a capillary tube is by measuring the rate of flow of a Newtonian liquid through the tube. Find the
- Volume flow rate through an annulus, a horizontal annulus, 27 ft in length, has an inner radius of 0.495 in. and an outer radius of 1.1 in. A 60% aqueous solution of sucrose (C12H22O11) is to be
- Loss of catalyst particles in stack gas (a) Estimate the maximum diameter of micro spherical catalyst particles that could be lost in the stack gas of a fluid cracking unit under the following
- Different choice of coordinates for the falling film problem, Re-derive the velocity profile and the average velocity in S2.2, by replacing x by a coordinate x measured away from the wall; that is, x
- Alternate procedure for solving flow problems, in this chapter we have used the following procedure: (i) derive an equation for the momentum flux, (ii) integrate this equation, (iii) insert Newton's
- Laminar flow in a narrow slit (see Fig. 2B.3).? (a) A Newtonian fluid is in laminar flow in a narrow slit formed by two parallel walls a distance 2B apart. It is understood that B p + pgh = p ?
- Laminar slit flow with a moving wall ("plane Couette flow") Extend Problem 2B.3 by allowing the wall at x = B to move in the positive z direction at a steady speed v0. Obtain(a) The shear-stress
- Interrelation of slit and annulus formulas, when an annulus is very thin, it may, to a good approximation, is considered as a thin slit. Then the results of Problem 2B.3 can be taken over with
- Flow of a film on the outside of a circular tube (see Fig. 2B.6), in a gas absorption experiment a viscous fluid flows upward through a small circular tube and then downward in laminar flow on the
- Annular flow with inner cylinder moving axially (see Fig. 2B.7), a cylindrical rod of diameter KR moves axially with velocity v0 along the axis of a cylindrical cavity of radius R as seen in the
- Analysis of a capillary flow meter (see Fig. 2B.8). Determine the rate of flow (in lb/hr) through the capillary flow meter shown in the figure. The fluid flowing in the inclined tube is water at
- Low-density phenomena in compressible tube flow2,3 (Fig. 2B.9). As the pressure is decreased in the system studied in Example 2.3-2, deviations from Eqs. 2.3-28 and 2.3-29 arise. The gas behaves as
- Incompressible flow in a slightly tapered tube, an incompressible fluid flows through a tube of circular cross section, for which the tube radius changes linearly from R0 at the tube entrance to a
- The cone-and-plate viscometer (see Fig. 2B.11). A cone-and-plate viscometer consists of a stationary flat plate and an inverted cone, whose apex just contacts the plate. The liquid whose viscosity is
- Flow of a fluid in a network of tubes (Fig. 2B.12), a fluid is flowing in laminar flow from A to B through a network of tubes, as depicted in the figure. Obtain an expression for the mass flow rate w
- Performance of an electric dust collector (see Fig. 2C.1)5(a) A dust precipitator consists of a pair of oppositely charged plates between which dust-laden gases flow. It is desired to establish a
- Residence time distribution in tube flow, define the residence time function F(t) to be that fraction of the fluid flowing in a conduit which flows completely through the conduit in a time interval
- Velocity distribution in a tube, you have received a manuscript to referee for a technical journal. The paper deals with heat transfer in tube flow. The authors state that, because they are concerned
- Falling-cylinder viscometer (see Fig. 2C.4) A falling-cylinder viscometer consists of a long vertical cylindrical container (radius R), capped at both ends, with a solid cylindrical slug (radius KR).
- Falling film on a conical surface (see Fig. 2C.5)7 a fluid flows upward through a circular tube and then downward on a conical surface. Find the film thickness as a function of the distance s down
- Rotating cone pump (see Fig. 2C.6), find the mass rate of flow through this pump as a function of the gravitational acceleration, the impressed pressure difference, the angular velocity of the cone,
- A simple rate-of-climb indicator (see Fig. 2C.7) under the proper circumstances the simple apparatus shown in the figure can be used to measure the rate of climb of an airplane. The gauge pressure
- Rolling-ball viscometer, an approximate analysis of the rolling-ball experiment has been given, in which the results of Problem 2B.3 are used? Read the original paper and verify the results.
- Drainage of liquids (see Fig. 2D.2) how much liquid clings to the inside surface of a large vessel when it is drained? As shown in the figure there is a thin film of liquid left behind on the wall as
- Torque required to turn a friction bearing (Fig. 3A.1). Calculate the required torque in lbs- ft and power consumption in horsepower to turn the shaft in the friction bearing shown in the figure. The
- Friction loss in bearings) each of two screws on a large motor-ship is driven by a 4000-hp engine. The shaft that connects the motor and the screw is 16 in. in diameter and rests in a series of
- Effect of altitude on air pressure, when standing at the mouth of the Ontonagon River on the south shore of Lake Superior (602 ft above mean sea level), your portable barometer indicates a pressure
- Viscosity determination with a rotating-cylinder viscometer, it is desired to measure the viscosities of sucrose solutions of about 60% concentration by weight at about 20°C with a rotating-cylinder
- Fabrication of a parabolic mirror, it is proposed to make a backing for a parabolic mirror, by rotating a pan of slow-hardening plastic resin at constant speed until it hardens. Calculate the
- Scale-up of an agitated tank, experiments with a small-scale agitated tank are to be used to design a geometrically similar installation with linear dimensions 10 times as large. The fluid in the
- Air entrainment in a draining tank (Figure 3A.7) a molasses storage tank 60 ft in diameter is to be built with a draw-off line 1 ft in diameter, 4 ft from the sidewall of the tank and extending
- Flow between coaxial cylinders and concentric spheres. (a) The space between two coaxial cylinders is filled with an incompressible fluid at constant temperature. The radii of the inner and
- Laminar flow in a triangular duct (Figure 3B.2)2 one type of compact heat exchanger is shown in Figure 3B.2 (a). In order to analyze the performance of such an apparatus, it is necessary to
- Laminar flow in a square duct(a) A straight duct extends in the z direction for a length L and has a square cross section, bordered by the lines x = ± B and y = ± B. A colleague has told you that
- Creeping flow between two concentric spheres (Fig. 3B.4). A very viscous Newtonian fluid flows in the space between two concentric spheres, as shown in the figure. It is desired to find the rate of