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Chapter 9: Problem 26

Benzaldehyde is produced from toluene in the catalytic reaction $$\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{3}+\mathrm{O}_{2} \rightarrow \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CHO}+\mathrm{H}_{2} \mathrm{O}$$ Dry air and tolucne vapor are mixed and fed to the reactor at \(350^{\circ} \mathrm{F}\) and 1 atm. Air is supplied in \(100 \%\) excess. Of the toluene fed to the reactor, \(13 \%\) reacts to form benzaldehyde and \(0.5 \%\) reacts with oxygen to form \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). The product gases leave the reactor at \(379^{\circ} \mathrm{F}\) and 1 atm. Water is circulated through a jacket surrounding the reactor, entering at \(80^{\circ} \mathrm{F}\) and leaving at \(105^{\circ} \mathrm{F}\). During a four-hour test period, \(29.3 \mathrm{lb}_{\mathrm{m}}\) of water is condensed from the product gases. (Total condensation may be assumed.) The standard heat of formation of benzaldchyde vapor is -17,200 Btu/lb-mole; the heat capacitics of both toluene and benzaldchyde vapors are approximately \(31 \mathrm{Btu} /\left(\mathrm{lb}-\mathrm{mole} \cdot^{\circ} \mathrm{F}\right) ;\) and that of liquid benzaldehyde is 46 Btu/(lb-mole\cdot"F). (a) Calculate the volumetric flow rates (ft \(^{3} / \mathrm{h}\) ) of the combined feed stream to the reactor and the product gas. (b) Calculate the required rate of heat transfer from the reactor ( \(\mathrm{Btu} / \mathrm{h}\) ) and the flow rate of the cooling water (gal/min). (c) Suppose the process proceeds as designed for several weeks, but one day the product gas and coolant streams emerge at higher temperatures, and the product contains significantly less benzaldchyde. The coolant flow rate is increased, but the product gas temperature cannot be brought down to its prescribed value, so the process must be shut down for troubleshooting. List and briefly explain several possible causes of the problem.

Short Answer

Expert verified
The volumetric flow rates, heat transfer rates, and cooling water flow rates are calculated through a combination of stoichiometric laws, ideal gas law and heat balance equations. Variations in process variables, such as the temperature, significantly impact production. It also brings up the need for troubleshooting potential causes, like cooling system malfunction, catalyst degradation, among others.

Step by step solution

01

Analysis of Reaction Stoichiometry

First, understand the stoichiometry of the reaction. And, identify words used to quantify the stoichiometry like '100 % excess' which signifies unused reactants after completion of the reaction, and '13 %' reacting to form a specific product. Include calculations based on these figures and apply stoichiometric laws.
02

Calculation of Volumetric Flow Rates

Calculate the volumetric flow rates by utilizing the Ideal Gas Law \( PV = nRT \), where \( n \) can be the total moles calculated through the stoichiometry of the reaction. Note that the conditions are standard temperature and pressure. Thus, the calculation is straightforward once the required quantities are known.
03

Calculation of Rate of Heat Transfer and Flow Rate of Cooling Water

This calls for understanding heat transfer in reactors. Account for exothermic or endothermic nature of the reaction. Consider the heat dissipated by cooling water and heat absorbed due to change in temperature of reactor. Make use of heats of formation and heat capacities provided to calculate heat transfer rate and the flow rate of cooling water. Apply the heat balance equation which can take the form \( Q_{rxn} = Q_{cooling water} + Q_{unreacted stream} + Q_{product stream} \).
04

Analyzing Change in Process Variables

This involves applying the theoretical understanding of the process and interpreting how the change in temperature and product formation affects the whole process. This can involve less heat being absorbed by the cooling water, catalyst degradation, insulator malfunction etc.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Stoichiometry Overview
Stoichiometry is a fundamental concept in chemical reaction engineering. It involves calculating the quantitative relationships between reactants and products in a chemical reaction. In this exercise, toluene reacts with oxygen to form benzaldehyde and water. The term '100% excess' in stoichiometry indicates that an additional amount of reactant, twice the stoichiometric requirement, is used to ensure the other reactant gets fully consumed. Similarly, the '13%' figure means only a fraction of toluene is used to produce benzaldehyde, while '0.5%' forms carbon dioxide and water. Understanding these percentages helps in setting up a balanced chemical equation and performing stoichiometric calculations needed to grasp the flow rates of gases involved.
Understanding Heat Transfer in Reactors
In chemical reactors, handling heat transfer is crucial for maintaining appropriate reaction conditions. In this problem, the heat transfer involves water circulating around the reactor to control the temperature. The reaction between toluene and oxygen can either absorb or release heat, known as endothermic and exothermic reactions, respectively.

The data from this exercise, like the heat of formation and heat capacities, are used to determine the heat requirement or release. The cooling water must absorb a significant portion of this heat to maintain reactor efficiency. It's calculated using the heat balance equation which considers all heat entering and leaving the system:
  • Heat from the reaction (Q_rxn)
  • Heat removed by cooling water (Q_cooling water)
  • Heat associated with the exit of unused and product streams (Q_unreacted and Q_product)
Process Troubleshooting Insights
Troubleshooting a chemical process involves identifying issues that deviate from the expected operation. In this scenario, higher temperatures and a drop in benzaldehyde production might occur due to multiple factors:
  • Catalyst Activity: The catalyst might be poisoned or fouling, reducing its effectiveness in driving the reaction.
  • Reactor Insulation: An insulation failure could lead to temperature spikes affecting reaction rates and equilibrium.
  • Cooling Water System: Ineffective heat exchange can arise from fouling in the cooling system or flow rate issues.
Understanding these possibilities allows engineers to systematically resolve the problems by analyzing data and implementing corrective actions.
Role of the Ideal Gas Law in Calculations
The Ideal Gas Law is a highly useful equation in chemical engineering for linking the pressure, volume, temperature, and moles of a gas (PV = nRT). For gas phase reactions, it helps calculate volumetric flow rates, thus assessing how freely gases enter and exit the reactor.

In this exercise, knowing the initial conditions like temperature and pressure lets us determine the flow rates of toluene vapor and air when mixed. Then, we can evaluate how these flow rates contribute to reactor efficiency and product output. The Ideal Gas Law ensures calculations are robust and aligned with physical laws, streamlining complex chemical processes.

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Most popular questions from this chapter

The standard heat of combustion \(\left(\Delta \hat{H}_{c}\right)\) of liquid 2,3,3 -trimethylpentane \(\left[\mathrm{C}_{8} \mathrm{H}_{18}\right]\) is reported in a table of physical properties to be \(-4850 \mathrm{kJ} / \mathrm{mol} .\) A footnote indicates that the reference temperature for the reported value is \(25^{\circ} \mathrm{C}\) and the presumed combustion products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). (a) In your own words, briefly explain what all that means. (b) There is some question about the accuracy of the reported value, and you have been asked to determine the heat of combustion experimentally. You burn 2.010 grams of the hydrocarbon with pure oxygen in a constant-volume calorimeter and find that the net heat released when the reactants and products \(\left[\mathrm{CO}_{2}(\mathrm{g}) \text { and } \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\right]\) are all at \(25^{\circ} \mathrm{C}\) is sufficient to raise the temperature of \(1.00 \mathrm{kg}\) of liquid water by \(21.34^{\circ} \mathrm{C}\). Write an energy balance to show that the heat released in the calorimeter equals \(n_{\mathrm{C}_{3} \mathrm{H}_{18}} \Delta \hat{U}_{\mathrm{c}}^{\mathrm{S}},\) and calculate \(\Delta \tilde{U}_{\mathrm{c}}^{\mathrm{o}}(\mathrm{kJ} / \mathrm{mol}) .\) Then calculate \(\Delta \hat{H}_{c}^{c}\) (See Example 9.1-2.) By what percentage of the measured value does the tabulated value differ from the measured one? (c) Use the result of Part (b) to estimate \(\Delta \hat{H}_{f}\) for 2,3,3 -trimethylpentane. Why would the heat of formation of 2,3,3 -trimethylpentane probably be determined this way rather than directly from the formation reaction?

Hydrogen is produced in the steam reforming of propane: $$\mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow 3 \mathrm{CO}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g})$$ The water-gas shift reaction also takes place in the reactor, leading to the formation of additional hydrogen: $$\mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ The reaction is carried out over a nickel catalyst in the tubes of a shell- and-tube reactor. The feed to the reactor contains steam and propane in a 6: 1 molar ratio at \(125^{\circ} \mathrm{C}\), and the products emerge at \(800^{\circ} \mathrm{C}\). The excess steam in the feed assures essentially complete consumption of the propane. Heat is added to the reaction mixture by passing the exhaust gas from a nearby boiler over the outside of the tubes that contain the catalyst. The gas is fed at \(4.94 \mathrm{m}^{3} / \mathrm{mol} \mathrm{C}_{3} \mathrm{H}_{8}\), entering the unit at \(1400^{\circ} \mathrm{C}\) and 1 atm and leaving at \(900^{\circ} \mathrm{C} .\) The unit may be considered adiabatic. (a) Calculate the molar composition of the product gas, assuming that the heat capacity of the heating gas is \(0.040 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\cdot} \mathrm{C}\right)\) (b) Is the reaction process exothermic or endothermic? Explain how you know. Then explain how running the reaction in a reactor-heat exchanger improves the process economy.

An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen, nitrogen, oxygen, and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Dulong formula: $$H H V(\mathrm{k} J / \mathrm{kg})=33,801(\mathrm{C})+144,158[(\mathrm{H})-0.125(\mathrm{O})]+9413(\mathrm{S})$$ where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125(O) term accounts for the hydrogen bound in the water contained in the coal. (a) Derive an expression for the higher heating value ( \(H H V\) ) of a coal in terms of \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{S},\) and compare your result with the Dulong formula. Suggest a reason for the difference. (b) A coal with an ultimate analysis of \(75.8 \mathrm{wt} \% \mathrm{C}, 5.1 \% \mathrm{H}, 8.2 \% \mathrm{O}, 1.5 \% \mathrm{N}, 1.6 \% \mathrm{S},\) and \(7.8 \%\) ash (noncombustible) is burned in a power-plant boiler fumace. All of the sulfur in the coal forms \(\mathrm{SO}_{2}\) The gas leaving the furnace is fed through a tall stack and discharged to the atmosphere. The ratio \(\phi\) (\(\mathrm{kg} \mathrm{SO}_{2}\) in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate \(\phi\), using the Dulong formula for the heating value of the coal. (c) An earlier version of the EPA regulation specified that the mole fraction of \(\mathrm{SO}_{2}\) in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.

A culture of the fungus aspergillus niger is used industrially in the manufacture of citric acid and other organic species. Cells of the fungus have an ultimate analysis of \(\mathrm{CH}_{1,79} \mathrm{N}_{0.2} \mathrm{O}_{0.5}\), and the heat of formation of this species is necessary to approximate the heat duty for the bioreactor in which citric acid is to be produced. You collect a dried sample of the fungus and determine its heat of combustion to be \(-550 \mathrm{kJ} / \mathrm{mol} .\) Estimate the heat of formation \((\mathrm{kJ} / \mathrm{mol})\) of the dried fungus cells.

A gas stream consisting of \(n\) -hexane in methane is fed to a condenser at \(60^{\circ} \mathrm{C}\) and 1.2 atm. The dew point of the gas (considering hexane as the only condensable component) is \(55^{\circ} \mathrm{C}\). The gas is cooled to \(5^{\circ} \mathrm{C}\) in the condenser, recovering pure hexane as a liquid. The effluent gas leaves the condenser saturated with hexane at \(5^{\circ} \mathrm{C}\) and 1.1 atm and is fed to a boiler furnace at a rate of \(207.4 \mathrm{L} / \mathrm{s}\), where it is burned with \(100 \%\) excess air that enters the furnace at \(200^{\circ} \mathrm{C}\). The stack gas emerges at \(400^{\circ} \mathrm{C}\) and 1 atm and contains no carbon monoxide or unburned hydrocarbons. The heat transferred from the furnace is used to generate saturated steam at 10 bar from liquid water at \(25^{\circ} \mathrm{C}\). (a) Calculate the mole fractions of hexane in the condenser feed and product gas streams and the rate of hexane condensation (liters condensate/s). (b) Calculate the rate at which heat must be transferred from the condenser (kW) and the rate of generation of steam in the boiler ( \(\mathrm{kg} / \mathrm{s}\) ).
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