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Chapter 9: Problem 17

Sulfur dioxide is oxidized to sulfur trioxide in a small pilot-plant reactor. SO \(_{2}\) and \(100 \%\) excess air are fed to the reactor at \(450^{\circ} \mathrm{C}\). The reaction proceeds to a \(65 \% \mathrm{SO}_{2}\) conversion, and the products emerge from the reactor at \(550^{\circ} \mathrm{C}\). The production rate of \(\mathrm{SO}_{3}\) is \(1.00 \times 10^{2} \mathrm{kg} / \mathrm{min}\). The reactor is surrounded by a water jacket into which water at \(25^{\circ} \mathrm{C}\) is fed. (a) Calculate the feed rates (standard cubic meters per second) of the \(\mathrm{SO}_{2}\) and air feed streams and the extent of reaction, \(\xi\) (b) Calculate the standard heat of the SO_ oxidation reaction, \(\Delta H_{\mathrm{t}}^{\mathrm{r}}(\mathrm{kJ}) .\) Then, taking molecular species at \(25^{\circ} \mathrm{C}\) as references, prepare and fill in an inlet-outlet enthalpy table and write an energy balance to calculate the necessary rate of heat transfer ( \(\mathrm{kW}\) ) from the reactor to the cooling water. (c) Calculate the minimum flow rate of the cooling water if its temperature rise is to be kept below \(15^{\circ} \mathrm{C}\) (d) Briefly state what would have been different in your calculations and results if you had taken elemental species as references in Part (b).

Short Answer

Expert verified
The feed rates of \(SO_2\) and air are \(153.85 kmol/min\) and \(307.7 kmol/min\) respectively. The standard heat of reaction, amount of heat transfer and minimum water cooling rate would be determined based on the given feed rate, conversion, and reaction data. The results would have been different if elemental species are considered as reference in the calculation.

Step by step solution

01

Determine the feed rates

Given production rate of \(SO_3\) is \(1.00 \times 10^2 kmol/min\) which means in each minute, \(1.00 \times 10^2 kmol\) of \(SO_2\) are getting converted to \(SO_3\). Since the feed contains 100% excess air, conversion of \(SO_2\) is less than expected. Since conversion rate is 65%, actual feed rate of \(SO_2\) is \(1.00 \times 10^2 kmol/min / 0.65 = 153.85 kmol/min\). Therefore, the feed rates of \(SO_2\) and air are \(153.85 kmol/min\) and \(307.7 kmol/min\) respectively.
02

Calculate the heat of reaction

Heat of reaction \(\Delta H_{t}^r\) for the reaction \(SO_2 + 0.5O_2 鈫� SO_3\) can be obtained from the standard heat of formation of the reactants and products. \(\Delta H_{t}^ {r} = Heat of formation of products 鈥� Heat of formation of reactants\). The standard heat of reaction is now used to determine the energy flow from the reactor to the cooling water by setting up an enthalpy table for the inlet and outlet streams and writing the energy balance around the reactor.
03

Calculate cooling water flow rate

The rate of heat transfer from the reactor to the cooling system can be calculated using \(q=mc\Delta t\), where \(m\) is the cooling water flow rate, \(c\) is the specific heat of water, and \(\Delta t\) is the temperature difference. This equation gives the minimum flow rate of cooling water needed to keep the temperature rise below \(15^{\circ}C\).
04

Analyses of different reference states

If the calculation was using elemental species as reference, the energy of heat transfer would have been calculated based on the heat of formation values which are zero for the elements in their standard states at the reference temperature. This modification would have changed the energy balance equation and therefore the calculated rate of heat transfer. The conversion rate and feed rates would still be same, but the heat of reaction, and therefore the rate of heat transfer and the cooling water flow rate would have been different.

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Key Concepts

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

Sulfur Dioxide Oxidation
Sulfur dioxide oxidation is a crucial reaction in chemical engineering, particularly in the production of sulfuric acid. This reaction involves the conversion of sulfur dioxide (SO\(_2\)) to sulfur trioxide (SO\(_3\)) using oxygen available in excess air. In the described pilot-plant reactor, the conversion efficiency of SO\(_2\) is 65%. This means that 65% of the sulfur dioxide introduced to the reactor is transformed into sulfur trioxide. Oxidation reactions like this one are significant because they determine the effectiveness and efficiency of industrial processes.
One important aspect of this reaction to notice is the excess use of air. This implies that there is more oxygen available than what is necessary to react with the sulfur dioxide. This ensures the reaction goes to completion as much as possible, minimizing leftover reactants.
Conversion percentage is a key parameter that affects the design and operation of chemical reactors, determining the required feed rates and the overall economic feasibility of the process. Thus, understanding and optimizing this aspect is fundamental to chemical reaction engineering.
Heat of Reaction
The heat of reaction is the heat energy absorbed or released during a chemical reaction. For the sulfur dioxide oxidation reaction, it is important to determine this energy change as it directly affects the reactor operation and its thermal management.
To calculate the heat of reaction (\(\Delta H_{rxn}\),for the oxidation of SO\(_2\) to SO\(_3\), start by considering the standard heat of formation for the reactants and products. These values are typically obtained from thermodynamic tables. The formula used is:\[\Delta H_{rxn} = \text{heat of formation of products} - \text{heat of formation of reactants}\]Due to its impact on energy balance calculations, understanding the heat of reaction is crucial. It dictates whether the process is exothermic (releasing heat) or endothermic (absorbing heat). This energy change helps in designing systems to manage the thermal effects generated during the reaction, often requiring the implementation of cooling systems.
Energy Balance
Energy balance is a fundamental concept in chemical reaction engineering, ensuring that all energy inputs and outputs within a process are accounted for. In this context, it deals with achieving a balance between the energy supplied to the system and the energy absorbed or released during the chemical reaction.
Creating an enthalpy table for the inlet and outlet streams is the first step to writing an energy balance for the reactor. This table lists all the thermal energies of each component entering and leaving the system, based on their specific heat capacities and temperatures.
From there, the energy balance equation can be formulated. This includes the sum of all energies entering the system equated to the sum of the energies leaving the system, along with the energy either absorbed or released by the reaction. This helps in calculating the necessary rate of heat transfer to manage the reactor temperature, which is vital for safe and efficient operation.
Cooling Water Flow Rate
The cooling water flow rate is a key operational parameter in chemical reactors, especially those involving exothermic reactions like sulfur dioxide oxidation. The primary function of cooling water is to remove excess heat from the reactor, preventing overheating and ensuring optimal reaction conditions.
This involves applying the principle of heat transfer, where the equation is expressed as:\[q = mc\Delta T\]Here, \(q\) represents the heat removal rate, \(m\) is the flow rate of the cooling water, \(c\) is the specific heat capacity of water, and \(\Delta T\) is the permissible temperature rise of the water.
In this scenario, the goal is to keep the cooling water's temperature change below 15掳C. By substituting known values into the equation, one can solve for the minimum cooling water flow rate necessary. Proper adjustment of this flow rate is essential in maintaining the reactor's stability and preventing any negative impacts on the reaction performance or safety.

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Most popular questions from this chapter

Coke can be converted into \(\mathrm{CO}-\mathrm{a}\) fuel gas- -in the reaction $$\mathrm{CO}_{2}(\mathrm{g})+\mathrm{C}(\mathrm{s}) \rightarrow 2 \mathrm{CO}(\mathrm{g})$$ A coke that contains \(84 \%\) carbon by mass and the balance noncombustible ash is fed to a reactor with a stoichiometric amount of \(\mathrm{CO}_{2}\). The coke is fed at \(77^{\circ} \mathrm{F}\), and the \(\mathrm{CO}_{2}\) enters at \(400^{\circ} \mathrm{F}\). Heat is transferred to the reactor in the amount of \(5859 \mathrm{Btu} / \mathrm{lb}_{\mathrm{m}}\) coke fed. The gascous products and the solid reactor effluent (the ash and unburned carbon) leave the reactor at \(1830^{\circ} \mathrm{F}\). The heat capacity of the solid is \(0.24 \mathrm{Btu} /\left(\mathrm{lb}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\) (a) Calculate the percentage conversion of the carbon in the coke. (b) The carbon monoxide produced in this manner can be used as a fuel for residential home heating, as can the coke. Speculate on the advantages and disadvantages of using the gas. (There are several of each.)

Formaldehyde is produced by decomposing methanol over a silver catalyst: $$\mathrm{CH}_{3} \mathrm{OH} \rightarrow \mathrm{HCHO}+\mathrm{H}_{2}$$ To provide heat for this endothermic reaction, some oxygen is included in the feed to the reactor, leading to the partial combustion of the hydrogen produced in the methanol decomposition. The feed to an adiabatic formaldehyde production reactor is obtained by bubbling a stream of air at 1 atm through liquid methanol. The air leaves the vaporizer saturated with methanol and contains \(42 \%\)methanol by volume. The stream then passes through a heater in which its temperature is raised to \(145^{\circ} \mathrm{C} .\) To avoid deactivating the catalyst, the maximum temperature attained in the reactor must be limited to \(600^{\circ} \mathrm{C}\). For this purpose, saturated steam at \(145^{\circ} \mathrm{C}\) is metered into the air-methanol stream, and the combined stream cnters the reactor. A fractional methanol conversion of \(70.0 \%\) is achicved in the reactor, and the product gas contains 5.00 mole\% hydrogen. The product gas is cooled to \(145^{\circ} \mathrm{C}\) in a waste heat boiler in which saturated steam at 3.1 bar is generated from liquid water at \(30^{\circ} \mathrm{C}\). Several absorption and distillation units follow the waste heat boiler, and formaldehyde is ultimately recovered in an aqueous solution containing 37.0 wt\% HCHO. The plant is designed to produce 36 metric kilotons of this solution per year, operating 350 days/yr. (a) Draw the process flowchart and label it completely. Show the absorption/distillation train as a single unit with the reactor product gas and additional water entering and the formaldehyde solution and a gas stream containing methanol, oxygen, nitrogen, and hydrogen leaving. (b) Calculate the operating temperature of the methanol vaporizer. (c) Calculate the required feed rate of steam to the reactor \((\mathrm{kg} / \mathrm{h})\) and the molar flow rate and composition of the product gas. (d) Calculate the rate ( \(\mathrm{kg} / \mathrm{h}\) ) at which steam is generated in the waste heat boiler. (e) Enough saturated steam was added to the feed to the reactor to keep the reactor outlet temperature at \(600^{\circ} \mathrm{C}\). Explain in your own words (i) why adding steam lowers the outlet temperature, and (ii) the cconomic drawbacks of higher and lower outlet temperatures.

The equilibrium constant for the ethane dehydrogenation reaction, $$\mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g}) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ is defined as $$K_{p}(\mathrm{atm})=\frac{y_{\mathrm{C}_{2} \mathrm{H}_{4}} y_{\mathrm{H}_{2}}}{y_{\mathrm{C}_{2} \mathrm{H}_{6}}} P$$ where \(P(\text { atm })\) is the total pressure and \(y_{i}\) is the mole fraction of the ith substance in an equilibrium mixture. The equilibrium constant has been found experimentally to vary with temperature according to the formula $$K_{p}(T)=7.28 \times 10^{6} \exp [-17,000 / T(\mathrm{K})]$$ The heat of reaction at \(1273 \mathrm{K}\) is \(+145.6 \mathrm{kJ}\), and the heat capacities of the reactive species may be approximated by the formulas $$\left.\begin{array}{rl}\left(C_{p}\right)_{\mathrm{C}_{2} \mathrm{H}_{4}} & =9.419+0.1147 T(\mathrm{K}) \\\\\left(C_{p}\right)_{\mathrm{H}_{2}} & =26.90+4.167 \times 10^{-3} T(\mathrm{K}) \\ \left(C_{p}\right)_{\mathrm{C}_{2} \mathrm{H}_{6}} & =11.35+0.1392 T(\mathrm{K}) \end{array}\right\\}[\mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})]$$ Suppose pure cthane is fed to a continuous constant-pressure adiabatic reactor at \(1273 \mathrm{K}\) and pressure \(P(\text { atm }),\) the products emerge at \(T_{\mathrm{f}}(\mathrm{K})\) and \(P(\mathrm{atm}),\) and the residence time of the reaction mixture in the reactor is large enough for the outlet stream to be considered an equilibrium mixture of ethane, ethylene, and hydrogen. (a) Prove that the fractional conversion of ethane in the reactor is $$f=\left(\frac{K_{p}}{P+K_{p}}\right)^{1 / 2}$$ (b) Write an energy balance on the reactor, and use it to prove that $$f=\frac{1}{1+\phi\left(T_{\mathrm{f}}\right)}$$ where Finally, substitute for \(\Delta H_{\mathrm{r}}\) and the heat capacities in Equation 4 to derive an explicit expression for \(\phi\left(T_{\mathrm{f}}\right)\) (c) We now have two expressions for the fractional conversion \(f\) : Equation 2 and Equation 3 . If these expressions are equated, \(K_{p}\) is replaced by the expression of Equation \(1,\) and \(\phi\left(T_{\mathrm{f}}\right)\) is replaced by the expression derived in Part (b), the result is one equation in one unknown, \(T_{\mathrm{f}}\). Derive this equation, and transpose the right side to obtain an expression of the form $$\psi\left(T_{\mathrm{f}}\right)=0$$ (d) Prepare a spreadsheet to take \(P\) as input, solve Equation 5 for \(T_{\mathrm{f}}\) (use Goal Seek or Solver), and determine the final fractional conversion, \(\left.f \text { . (Suggestion: Set up columns for } P, T_{\mathrm{f}}, f, K_{p}, \phi, \text { and } \psi .\right)\) Run the program for \(P(\text { atm })=0.01,0.05,0.10,0.50,1.0,5.0,\) and \(10.0 .\) Plot \(T_{\mathrm{f}}\) versus \(P\) and \(f\) versus \(P,\) using a logarithmic coordinate scale for \(P\).

In a surface-coating operation, a polymer (plastic) dissolved in liquid acetone is sprayed on a solid surface and a stream of hot air is then blown over the surface, vaporizing the acetone and leaving a residual polymer film of uniform thickness. Because environmental standards do not allow discharging acetone into the atmosphere, a proposal to incinerate the stream is to be evaluated. The proposed process uses two parallel columns containing beds of solid particles. The air-acetone stream, which contains acetone and oxygen in stoichiometric proportion, enters one of the beds at \(1500 \mathrm{mm} \mathrm{Hg}\) absolute at a rate of 1410 standard cubic meters per minute. The particles in the bed have been preheated and transfer heat to the gas. The mixture ignites when its temperature reaches \(562^{\circ} \mathrm{C}\), and combustion takes place rapidly and adiabatically. The combustion products then pass through and heat the particles in the second bed, cooling down to \(350^{\circ} \mathrm{C}\) in the process. Periodically the flow is switched so that the heated outlet bed becomes the feed gas preheater/combustion reactor and vice versa. Use the following average values for \(C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\) in solving the problems to be given: 0.126 for \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}, 0.033\) for \(\mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052\) for \(\mathrm{CO}_{2},\) and 0.040 for \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) (a) If the relative saturation of acetone in the feed stream is \(12.2 \%,\) what is the stream temperature? (b) Determine the composition of the gas after combustion, assuming that all of the acetone is converted to \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O},\) and estimate the temperature of this stream. (c) Estimate the rates ( \(\mathrm{kW}\) ) at which heat is transferred from the inlet bed particles to the feed gas prior to combustion and from the combustion gases to the outlet bed particles. Suggest an alternative to the two-bed feed switching arrangement that would achieve the same purpose.

Methanol vapor is burned with excess air in a catalytic combustion chamber. Liquid methanol initially at \(25^{\circ} \mathrm{C}\) is vaporized at 1.1 atm and heated to \(100^{\circ} \mathrm{C}\); the vapor is mixed with air that has been preheated to \(100^{\circ} \mathrm{C},\) and the combined stream is fed to the reactor at \(100^{\circ} \mathrm{C}\) and 1 atm. The reactor effluent emerges at \(300^{\circ} \mathrm{C}\) and 1 atm. Analysis of the product gas yields a dry-basis composition of \(4.8 \% \mathrm{CO}_{2}\) \(14.3 \% \mathrm{O}_{2},\) and \(80.9 \% \mathrm{N}_{2}\) (a) Calculate the percentage excess air supplied and the dew point of the product gas. (b) Taking a basis of 1 g-mole of methanol burned, calculate the heat ( \(k\) J) needed to vaporize and heat the methanol feed, and the heat (kJ) that must be transferred from the reactor. (c) Suggest how the energy economy of this process could be improved. Then suggest why the company might choose not to implement your redesign.
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