- The mean residence time in a tubular reactor is the length L divided by the average velocity v = q/π R2. Using the results from Problems 7.8 and 7.9, what can you say about the relative values of
- Follow the approach in Section 5.7 to derive the equation for the dependence of concentration on spatial position in a tubular reactor of length L operating at steady state, in which the radius is R
- Consider the optimal design problem in Section 7.3, but now suppose that the capital cost of the reactor increases with volume as Vα, α < 1. Derive the algebraic equation for the optimal
- Derive Equation 5.3 directly by doing a steady-state mass balance with a control volume that includes both VR and VP.
- The following data were obtained in a cylindrical vessel of diameter 2.54 cm (1.0 in.) that was allowed to drain through an orifice of diameter 0.109 cm (0.043 in.).a. Fit the equation q = kh to the
- Consider the process in Example 13.4. Can you reduce the required area substantially by changing the coolant flow rate?Example 13.4We must reduce the temperature of a small process steam flowing at 2
- The formation of sugars from biomass is of considerable interest in a variety of applications, including energy alternatives to fossil fuel. Harris and Kline studied the formation of glucose from
- Kinetic data for the reaction between sulfuric acid and diethyl sulfate are given in Examples 6.1 and 6.4. Suppose that V = 25.4 L, qAf = qBf, cAf = 11.0 g-mol/L, cBf = 5.5 g-mol/L, and the required
- An irreversible first-order decomposition reaction A → M is carried out in a CFSTR, with k = 0.005 min−1. The feed composition cAf is 0.2 g-mol/L, and the desired production rate of product is 50
- Select a chemical engineer whose work looks interesting to you, and do a search on his/her publications to get a broader picture. (Your library will have access to several scientific search engines.
- Go to your own chemical engineering department’s home page and see what kind of scholarly work your faculty members are doing.
- Select a topic of interest to you that involves chemical engineering, do some reading, and write a short review of the outstanding issues. Here are a few suggestions of very broad and socially
- A wedge-shaped tank is filled and emptied at constant flow rates qf and qe, respectively. The liquid density is a constant at all times. The liquid height is h0 at t = 0. Find the height at any
- Select a chemical that interests you and learn what you can about its production and uses.
- The system shown in Figure 2P.2 might be used to load ore onto barges for shipment. Let W1 be the constant mass flow rate of ore onto the barge, and letMbe the mass of ore at any time. After the pile
- Select a process that interests you and learn what you can about its creation and subsequent development. (Fluid catalytic cracking is a good choice if you don’t have another.)
- Suppose that we wish to use a combination of feedback and feedforward control in the form qe = q∗ + Kf b(h − h∗) + KffQ(t).a. Show that you obtain perfect control (h = h* at all times) for Kff
- A chemical operator is draining a tank originally full of crude oil. The tank measures 0.91 m (3 ft) in diameter. The operator opens a valve with a 3.18 cm (1–1/4in.) diameter in the tank base. He
- A tank is filled at a constant flow rate qf, while it empties through a valve for which the flow rate is equal to kh1/2. Will this system come to a steady state (dV/dt = 0)? If so, what is the height
- The following population data are available for Iceland and the Faroe Islands (lumped together, because Iceland’s independence from Denmark came only in 1944):Neglecting immigration and emigration,
- The following are population data for theUnited States during the period 1930–1960:Immigration and emigration data are not included. Construct a model of population growth and check against the
- A water clock is a vessel that has a shape such that the liquid level h decreases at a constant rate. In this way, water level markings can be easily calibrated with elapsed time. Water clocks were
- Banks often advertise continuous compounding of interest on savings accounts, by which they mean that interest is added continuously to the account at a rate equal to the product of the current
- The Mediterranean Sea exchanges water with the Atlantic Ocean. Fresh water inflow to theMediterranean is approximately 30,000 m3/s and evaporation occurs at a rate of approximately 80,000 m3/s. The
- A well-stirred process vessel contains 1.7 m3 (450 gallons) of a solution of water and 34 kg of sodium chloride at the time that a pure water feed stream is introduced. Find the salt concentration at
- According to OSHA, a level of chlorine in the air of 3ppmwill cause impairment. Suppose there is a constant source of chlorine of 4 g/hr in a room that is ventilated at a rate of 250 m3/s. What is
- The OSHA recommendation for laboratory ventilation is four to twelve room air changes per hour. Approximately how long does it take to reach a steady-state concentration in a laboratory with a
- A soft drink process requires mixing sugar and water continuously in a 250 m3 tank. We have one measurement of the density of sugar: At a concentration of 207.5 kg/m3 the density is 1,083 kg/m3. The
- Four people enter an empty smoking lounge that has a volume of 50 m3 and is ventilated at a rate of 120 m3/hr. Each person smokes about two cigarettes an hour, and each cigarette produces about 40 mg
- A well-dispersed mixture of solids and liquid is to be concentrated by being pumped through a tank with a porous plate at the bottom through which pure liquid may pass, as shown schematically in
- Suppose that the data in Table 6.1 for the reaction of sulfuric acid with diethyl sulfate in aqueous solution are described by a rate of the form r = kcAn. Investigate the consequences of an error of
- A dialysis system is set up to reduce the concentration of a solute from 100 g/L to 1 g/L. The membrane permeability is 0.001 m/s, and the raffinate flow rate is 0.25 L/min. The permeate stream
- Consider a dialysis system in which the membrane has a permeability of 1/3 cm/min and the total available membrane area is 2,700 cm2. The raffinate feed rate is 300 mL/min and the total permeate flow
- Consider a continuous countercurrent dialysis system that uses a flat membrane with a width of 25 cm and a permeability of 1/3 cm/min. The raffinate and permeate feeds are 300 mL/min and 900 mL/min,
- Data for the decomposition of dibromosuccinic acid (2,3-dibromo-butanedioic acid), C2H2Br2(COOH)2, in a batch reactor are shown in Table 6.P1 as mass of acid remaining as a function of time. Find the
- Reconsider the data in Table 6.1 for the reaction between sulfuric acid and diethyl sulfate, and suppose that you believe that the forward reaction rate is actually of the form r = k′cA. Test this
- The data in Table 6.P3 are for reactant A in the irreversible reaction A + βB → products. The initial concentrations are believed to be in stoichiometric balance. Estimate the reaction order and
- The reaction ClO3− + 3H2SO4 → Cl− + 3SO4= + 6H+ in 0.2N H2SO4 was studied in 1932 by Nixon and Krauskopf, who reported the data in Table 6.P2. Find a rate expression that is consistent with the
- Show that Equation 6.11a for the reaction A + B → μM with equal initial concentrations of A and B (ψ = 0) follows from Equation 6.11b for unequal initial concentrations in the limit ψ →
- The hydrolysis of acetic anhydride in excess water to form acetic acid, (CH3CO)2O + H2O→2CH3COOH, was studied by Elridge and Piret, who found that the rate at 15◦C is first order in anhydride,
- The reaction acetic acid (A) + butanol (B)→ester + water was studied by Leyes and Othmer, who found the data in Table 6.P4 at 100◦C in the presence of 0.03 percent sulfuric acid. The initial
- The saponification of the ester propargyl acetate,with base (B, OH–) was studied by Myers, Collett, and Lazzell using a conductivity technique to follow the course of the reaction. Conductivity,
- Consider the full data set in Table 6.5 for the reversible reaction between sulfuric acid and diethyl sulfate and test the applicability of each of the following rate expressions:Table
- The reaction A → products is believed to follow a rate expressionHow will the concentration in a batch reactor change with time? Discuss the limits k2cA0 ≫ 1 and k2cA0 ≪ 1. TA- ICA = 1+k₂CA
- The chemical reaction sequence A→M→S takes place in a CFSTR. You may assume that the reactions are irreversible and first order, with rate constants k1 for the reaction A→M and k2 for the
- The irreversible reaction A → products is believed to be nth order in the concentration of A. Devise a strategy for obtaining the order and rate constant by carrying out steady-state experiments in
- The decomposition of the carcinogen N-nitrosodiethylamine (NDEA) in water was shown in Example 6.3 to be first order when exposed to ultraviolet radiation at an intensity of 1 mW/cm2, with a rate
- Generalize your result to Problem 7.7 as follows: A first-order reaction is to be carried out in a batch reactor and in a CFSTR to achieve a relative reduction RR in concentration. (In Problem 7.7,
- In Equation 9.2, show that ∂(cA/cAf )/∂k2 > 0.Equation 9.2 СА C Af || 1 + k20 1+ (ki + kz)0
- Derive Equation 10.29 by carrying out a mass balance for species A on a control volume that encompasses both Phase I and Phase II. Then assume that A is in equilibrium between the two phases and
- In analogy to the treatment in Section 5.7, derive the equations describing a countercurrent membrane reactor in which the reversible first-order reaction A⇄ M is carried out.Section 5.7:The staged
- One step in the preparation of nicotine sulfate from tobacco is the extraction of nicotine from aqueous solution by kerosene. Table 10.P1 shows equilibrium data for the distribution of nicotine
- The data in Table 10.P2 are from a batch experiment measuring the distribution of octanoic acid between an aqueous phase consisting of a solution of corn syrup in water and an organic xylene phase.
- A useful model of interfacial mass transfer makes three assumptions:(i) There is a difference between the concentrations of A at the interface, denotedcI∗A and cII∗A in Phases I and II,
- Trace amounts of phenol are to be extracted from an aqueous stream (Phase I) using pure xylene as a solvent. From data in the Chemical Engineers’ Handbook we have M = 1.4.a. What xylene/water flow
- a. What is the minimum solvent flow rate that can be used in countercurrent operation to remove 75 percent of the acetic acid in the process stream described in Problem 11.1?b. How many
- Repeat Problem 11.1 without the assumption of negligible solute transfer.Problem 11.1It is necessary to process 100 kg/min of a water stream containing 15 percent acetic acid by weight. How much acid
- In an experiment carried out by one of our undergraduate students, a water stream and a chloroform stream** were fed continuously to a 1,000 cm3 cylindrical tank with a cross-sectional area of 81
- Data for the distribution of picric acid in a benzene-water system at 15◦C are shown in Table 10.P3. (Note that the concentrations are in molar units, and that Nerst’s “law” clearly does not
- It is necessary to process 100 kg/min of a water stream containing 15 percent acetic acid by weight. How much acid can be extracted in a single equilibrium stage with pure isopropyl ether using(a)
- 10 kg of water is heated to raise the temperature by 7◦C. How high would the liquid have to be lifted to change the total energy by the same amount? To what velocity must we accelerate the liquid
- Repeat the calculation in Problem 10.3 with the assumption that the heat capacity of liquid toluene is constant, using the values at(a) 10◦C;(b) 35◦C;(c) 60◦C. How large is the error in each
- The heat capacity of liquid toluene at atmospheric pressure is well represented in the range 280 K to 360 K by the empirical equation cp = -1.17 + 9.61 × 10−3T, where T is in K and cp is in J/g
- What is the change in enthalpy of 1 kg of water when the temperature is changed from 25◦C to 10◦C?
- The data in Table 11.P2 were obtained for the recovery of methyl ethyl ketone from water by solvent extraction. 500 kg/hr of an aqueous 18 percent by weight ketone solution is to be processed, with
- Trace amounts of phenol are to be extracted from an aqueous stream using pure xylene, for which M = 1.4 . What is the minimum amount of xylene required to remove 90 percent of the phenol from the
- a. A separation is to be carried out in an N-stage cross-flow configuration using the same feed/solvent ratio in each stage. The total feed/solvent ratio is therefore ∧/N. Compute the minimum
- Show that Equations 13.32 and 13.33 apply to an exchanger in which there are N parallel tubes of identical diameter if D is simply replaced by ND.Equations 13.32Equations 13.33 Qs hтл
- Liquids are contained in concentric cylinders of height L, where the radius of the inner cylinder is R and the radius of the outer cylinder is R. If the temperatures T1 (inner) and T2 (outer) are
- A cylindrical preheat tank with a length-to-diameter ratio of 1 and a capacity of 100 m3 is used in a semi batch operation. The tank is completely jacketed, and the temperature of the heating
- Derive Equations 13.34a and b.Equations 13.34a.Equations 13.34b. Qs = Piqic pt (Tio TiL).
- You are required to design a jacketed system to heat a continuous flow of 1m3/min of a liquid with the physical properties of water from 20◦C to 80◦C. You may assume that the heating medium is
- a. 10 L each of ethanol at –1.1◦C (30◦F), ethylene glycol at –6.67◦C (20◦F), and water at 26.7◦C (80◦F) are poured into a tank and mixed. What is the final temperature? Relevant
- A crude oil stream available at 209◦C is to be used to cool a heavy gas oil stream from 319◦C to 269◦C in a shell-and-tube heat exchanger. The crude oil is on the shell side and the gas oil on
- An insulated tank contains 10 kg of water at 20◦C. A stream of 100 percent sulfuric acid at 20◦C is added by accident at a rate of 1 kg/min. How long will it take for the temperature to rise to
- A continuous mixing operation is carried out by adding 0.3 kg/hr of calcium chloride crystals to a pure water stream flowing at 1 kg/hour.a. If both streams are at 25◦C when they enter the mixer,
- Find the heat of reaction ΔHR for each of the following reactions using both heat of formation and heat of combustion data, as available. (1) C6H6+ HNO3 → C6H5NO₂ + H₂O (ii) C₂H5OH +
- a. 5 kg/hr of sodium hydroxide and 10 kg/hr of water are to be mixed in an insulated tank. Both feed streams are to be put into the mixer at the same temperature. What is a safe inlet temperature at
- a. Derive an equation for the heat of reaction at any temperature if you are given the heat of reaction ΔHR R(To) at a standard temperature To. You may assume an ideal solution.b. Find the
- For the formation of glucose from cellulose discussed in Problem 6.12, the rate constant k1 shows the following temperature dependence at an HCl concentration of 0.055 mol/L:Check the validity of the
- The following specific reaction rate constant data were reported by Smith [J. Phys. & Coll. Chem., 59, 367 (1947)] for the reaction urea + formaldehyde → monomethylolurea:Check the validity of
- A common rule of thumb states that the reaction rate doubles for each 10◦C rise in temperature. Under what conditions is this rule of thumb valid?
- The catalytic gas phase oxidation of naphthalene to form phthalic anhydride is thought to take place as follows:The reaction has been studied by DeMaria, Longfield, and Butler [Ind. Eng. Chem., 53,
- The irreversible exothermic reaction A + B → nD is to be carried out isothermally in a batch reactor. The rate is described by mass action kinetics.a. What is the rate at which heat must be removed
- The irreversible first-order reaction A→R is to be carried out in an adiabatic continuous flow stirred-tank reactor. The molecular weight of A is 18, and you may take all physical properties to be
- Do a search to find an original research paper in which the heat capacity of some liquid was measured. Carefully read the paper and describe the experimental procedure in your own words. Show clearly