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Chapter 9: Problem 51

A dilute aqueous solution of sulfuric acid at \(25^{\circ} \mathrm{C}\) is used to absorb ammonia in a continuous reactor, thereby producing ammonium sulfate, a fertilizer: $$2 \mathrm{NH}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq}) \rightarrow\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}(\mathrm{aq})$$ (a) If the ammonia enters the absorber at \(75^{\circ} \mathrm{C}\), the sulfuric acid enters at \(25^{\circ} \mathrm{C}\), and the product solution emerges at \(25^{\circ} \mathrm{C}\), how much heat must be withdrawn from the unit per mol of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) produced? (All needed physical property data may be found in Appendix B.) (b) Estimate the final temperature if the reactor of Part (a) is adiabatic and the product of the solution contains 1.00 mole \(\%\) ammonium sulfate. Take the heat capacity of the solution to be that of pure liquid water [4.184 kJ/(kg.'C)]. (c) In a real (imperfectly insulated) reactor, would the final solution temperature be less than, equal to, or greater than the value calculated in Part (b), or is there no way to tell without more information? Briefly explain your answer.

Short Answer

Expert verified
In Part a, the heat to be withdrawn per mol of product was calculated using the enthalpy of reaction and heat capacities of substances. In Part b, the final temperature of the adiabatic reactor was calculated based on energy produced by the reaction and heat capacity of the solution. For Part c, it was inferred that a real (imperfectly insulated) reactor would have lower final solution temperature than the adiabatic due to heat loss.

Step by step solution

01

Part a: Calculation of heat withdrawn

To determine the heat to be withdrawn, differential heat balances will be performed. During the absorption process, 1 mol of sulfuric acid reacts with 2 mol of ammonia to form 1 mol of ammonium sulfate. From Appendix B, we get values for enthalpy of reaction, heat capacities of all substances. We use \(\Delta H = \Delta H_{rxn} + \Delta H_{cooling}\), where \(\Delta H_{rxn}\) is heat due to reaction and \(\Delta H_{cooling}\) is heat of cooling to bring ammonia from 75掳C to 25掳C. Heat of cooling \(\Delta H_{cooling} = 2 * Cp_{NH_3} * (T_{initial} - T_{final})\). Plug in values to get the amount of heat withdrawn.
02

Part b: Final Temperature Calculation

An adiabatic reactor does not exchange heat with its surroundings. So, the heat produced in the reactor because of the reaction must be accounted for the increase in temperature. Initial temperature will be taken as 25掳C (temperature of the entering sulfuric acid). Use the equation \(q_{absorption} = q_{reaction} + q_{heating}\) where \(q_{absorption}\) is enthalpy absorbed by absorber and \(q_{heating}\) is energy required to increase temperature from 25掳C to T_final. As this is adiabatic conditions, \(q_{absorption} = 0\), so \(-\Delta H_{reaction} = Cp_{solution} * (T_{final} - T_{initial})\). Here \(\Delta H_{reaction}\) is enthalpy change due to reaction and \(Cp_{solution}\) is heat capacity of solution. Solve this to find \(T_{final}\).
03

Part c: Final solution temperature in real reactor

In an imperfectly insulated reactor, some heat will escape due to heat loss. As a result, not all heat generated by a reaction will be available to increase the temperature of the solution. Therefore, the temperature of the final solution in a real reactor would be lower than in an adiabatic reactor.

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Key Concepts

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

Heat Balances
When dealing with chemical processes, it's essential to consider the heat balances of reactions. This involves calculating the heat produced or absorbed during a chemical process. In the context of sulfuric acid absorbing ammonia to form ammonium sulfate, we perform a heat balance to find out how much heat needs to be withdrawn to maintain the product temperature at a desired level.

The heat balance equation often breaks down as follows:
  • \(\Delta H = \Delta H_{rxn} + \Delta H_{cooling}\)
Here, \(\Delta H_{rxn}\) is the enthalpy change from the chemical reaction, and \(\Delta H_{cooling}\) is the heat removed to cool the substances to a desired final temperature. In this problem, to ensure that the final product temperature is 25掳C, we subtract the heat generated in the reaction and cool the entering ammonia from 75掳C to 25掳C.

Understanding heat balances helps maintain control over reactions, both for safety and efficiency reasons.
Adiabatic Reactors
Adiabatic reactors are a type of reactor where no heat is exchanged with the environment. In these reactors, all heat generated by the reaction is used to change the temperature of the system.

In the case of our sulfuric acid and ammonia reaction, an adiabatic process means that the heat produced by the conversion to ammonium sulfate directly increases the temperature of the reaction mixture. We use the equation:
  • \(-\Delta H_{reaction} = Cp_{solution} \times (T_{final} - T_{initial})\)
This equation implies that any heat from the reaction raises the temperature of the solution from the initial 25掳C. Understanding adiabatic reactions is crucial because they give insight into how much the temperature will change without outside heat transfer.

Such knowledge is useful for designing reactors and predicting behavior under various conditions.
Enthalpy of Reaction
The enthalpy of reaction, \(\Delta H_{rxn}\), is a measure of the heat absorbed or released during a chemical reaction at constant pressure. In our exercise, the enthalpy of reaction tells us how much heat is generated or consumed when ammonia reacts with sulfuric acid.

This value is crucial for calculating overall heat balance. For example, if \(\Delta H_{rxn}\) is negative, the reaction is exothermic, releasing heat. Conversely, if it's positive, the reaction is endothermic, absorbing heat. Knowing \(\Delta H_{rxn}\) helps determine how much external heat or cooling is required to achieve desired product conditions.

Understanding this concept allows engineers and scientists to safely and effectively design and operate chemical processes, ensuring the desired outcomes and maintaining safety standards.

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Most popular questions from this chapter

Methane at \(25^{\circ} \mathrm{C}\) is burned in a boiler furnace with \(10.0 \%\) excess air preheated to \(100^{\circ} \mathrm{C}\). Ninety percent of the methane fed is consumed, the product gas contains \(10.0 \mathrm{mol} \mathrm{CO}_{2} / \mathrm{mol} \mathrm{CO},\) and the combustion products leave the furnace at \(400^{\circ} \mathrm{C}\). (a) Calculate the heat transferred from the furnace, \(-\dot{Q}(\mathrm{kW}),\) for a basis of \(100 \mathrm{mol} \mathrm{CH}_{4}\) fed/s. (The greater the value of \(-\dot{Q}\), the more steam is produced in the boiler.) (b) Would the following changes increase or decrease the rate of steam production? (Assume the fuel feed rate and fractional conversion of methane remain constant.) Briefly explain your answers. (i) Increasing the temperature of the inlet air; (ii) increasing the percent excess air for a given stack gas temperature; (iii) increasing the selcctivity of \(\mathrm{CO}_{2}\) to \(\mathrm{CO}\) formation in the furnace; and (iv) increasing the stack gas temperature.

Methane and \(30 \%\) excess air are to be fed to a combustion reactor. An inexperienced technician mistakes his instructions and charges the gases together in the required proportion into an evacuated closed tank. (The gases were supposed to be fed directly into the reactor.) The contents of the charged tank are at \(25^{\circ} \mathrm{C}\) and 4.00 atm absolute. (a) Calculate the standard internal energy of combustion of the methane combustion reaction. \(\Delta \hat{U}_{c}^{\circ}(\mathrm{kJ} / \mathrm{mol}),\) taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v})\) as the presumed products. Then prove that if the constant-pressure heat capacity of an ideal-gas species is independent of temperature, the specific internal energy of that species at temperature \(T\left(^{\circ} \mathrm{C}\right)\) relative to the same species at \(25^{\circ} \mathrm{C}\) is given by the expression $$\hat{U}=\left(C_{p}-R\right)\left(T-25^{\circ} \mathrm{C}\right)$$ where \(R\) is the gas constant. Use this formula in the next part of the problem. (b) You wish to calculate the maximum temperature, \(T_{\max }\left(^{\circ} \mathrm{C}\right),\) and corresponding pressure, \(P_{\max }(\text { atm }),\) that the tank would have to withstand if the mixture it contains were to be accidentally ignited. Taking molecular species at \(25^{\circ} \mathrm{C}\) as references and treating all species as ideal gases, prepare an inlet-outlet internal energy table for the closed system combustion process. In deriving expressions for each \(\dot{U}_{i}\) at the final reactor condition \(\left(T_{\max }, P_{\max }\right),\) use the following approximate values for \(C_{p_{i}}\left[\mathrm{k} J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]: 0.033 \mathrm{for} \mathrm{O}_{2}, 0.032\) for \(\mathrm{N}_{2}, 0.052 \mathrm{for} \mathrm{CO}_{2},\) and \(0.040 \mathrm{for} \mathrm{H}_{2} \mathrm{O}(\mathrm{v}) .\) Then use an energy balance and the ideal-gas equation of state to perform the required calculations. (c) Why would the actual temperature and pressure attained in a real tank be less than the values calculated in Part (a)? (State several reasons.) (d) Think of ways that the tank contents might be accidentally ignited. The list should suggest why accepted plant safety regulations prohibit the storage of combustible vapor mixtures.

Ethylene oxide is produced by the catalytic oxidation of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(\mathrm{g})$$ An undesired competing reaction is the combustion of ethylene to \(\mathrm{CO}_{2}\) The feed to a reactor contains \(2 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} / \mathrm{mol} \mathrm{O}_{2} .\) The conversion and yield in the reactor are respectively \(25 \%\) and \(0.70 \mathrm{mol} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) produced/mol \(\mathrm{C}_{2} \mathrm{H}_{4}\) consumed. A multiple- unit process separates the reactor outlet stream components: \(\mathrm{C}_{2} \mathrm{H}_{4}\) and \(\mathrm{O}_{2}\) are recycled to the reactor, \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}\) is sold, and \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) are discarded. The reactor inlet and outlet streams are each at \(450^{\circ} \mathrm{C}\), and the fresh feed and all species leaving the separation process are at \(25^{\circ} \mathrm{C}\). The combined fresh feedrecycle stream is preheated to \(450^{\circ} \mathrm{C}\). (a) Taking a basis of 2 mol of ethylene entering the reactor, draw and label a flowchart of the complete process (show the separation process as a single unit) and calculate the molar amounts and compositions of all process streams. (b) Calculate the heat requirement ( \(k J\) ) for the entire process and that for the reactor alone. Data for gaseous ethylene oxide $$\begin{aligned}\Delta \hat{H}_{\mathrm{f}}^{\prime} &=-51.00 \mathrm{kJ} / \mathrm{mol} \\ C_{p}[\mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})] &=-4.69+0.2061 T-9.995 \times 10^{-5} T^{2} \end{aligned}$$ where \(T\) is in kelvins. (c) Calculate the flow rate \((\mathrm{kg} / \mathrm{h})\) and composition of the fresh feed, the overall conversion of ethylene, and the overall process and reactor heat requirements (kW) for a production rate of \(1500 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O} /\) day. Briefly explain the reasons for separating and recycling the ethylene-oxygen stream. (d) One of the attributes of this process defined in the problem statement is extremely unrealistic. What is it?

In the preliminary design of a furnace for industrial boiler, methane at \(25^{\circ} \mathrm{C}\) is burned completely with \(20 \%\) excess air, also at \(25^{\circ} \mathrm{C} .\) The feed rate of methane is \(450 \mathrm{kmol} / \mathrm{h}\). The hot combustion gases leave the furnace at \(300^{\circ} \mathrm{C}\) and are discharged to the atmosphere. The heat transferred from the furnace \((\dot{Q})\) is used to convert boiler feedwater at \(25^{\circ} \mathrm{C}\) into superheated steam at 17 bar and \(250^{\circ} \mathrm{C}\). (a) Draw and label a flowchart of this process [the chart should look like the one shown in Part (b) without the preheater] and calculate the composition of the gas leaving the furnace. Then, calculate \(\dot{Q}(\mathrm{kJ} / \mathrm{h})\) and the rate of steam production in the boiler \((\mathrm{kg} / \mathrm{h})\). (b) In the actual boiler design, the air feed at \(25^{\circ} \mathrm{C}\) and the combustion gas leaving the furnace at \(300^{\circ} \mathrm{C}\) pass through a heat exchanger (the air preheater). The combustion (flue) gas is cooled to \(150^{\circ} \mathrm{C}\) in the preheater and is then discharged to the atmosphere, and the heated air is fed to the furnace. Calculate the temperature of the air entering the furnace (a computer solution is required) and the rate of steam production (kg/h). (c) Explain why preheating the air increases the rate of steam production. (Suggestion: Use the energy balance on the furnace in your explanation.) Why does it make sense economically to use the combustion gas as the heating medium?

In a coal gasification process, carbon (the primary constituent of coal) reacts with steam to produce carbon monoxide and hydrogen (synthesis gas). The gas may either be burned or subjected to further processing to produce any of a variety of chemicals. A coal contains 10.5 wt\% moisture (water) and 22.6 wt\% noncombustible ash. The remaining fraction of the coal contains 81.2 wife \(\mathrm{C}, 13.4 \%\) O, and \(5.4 \%\) H. A coal slurry containing \(2.00 \mathrm{kg}\) coal/kg water is fed at \(25^{\circ} \mathrm{C}\) to an adiabatic gasification reactor along with a stream of pure oxygen at the same temperature. The following reactions take place in the reactor: $$\begin{array}{l}\mathrm{C}(\mathrm{s})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightarrow \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=+131.3 \mathrm{kJ} \\\\\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}): \quad \Delta H_{\mathrm{r}}^{\circ}=-393.5 \mathrm{kJ} \\ 2 \mathrm{H}(\mathrm{in} \mathrm{coal})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{v}): \quad \Delta H_{\mathrm{r}}^{\circ} \approx-242 \mathrm{kJ}\end{array}$$ Gas and slag (molten ash) leave the reactor at \(2500^{\circ} \mathrm{C}\). The gas contains \(\mathrm{CO}, \mathrm{H}_{2}, \mathrm{CO}_{2},\) and \(\mathrm{H}_{2} \mathrm{O}^{14}\) (a) Feeding oxygen to the reactor lowers the yield of synthesis gas, but no gasifier ever operates without supplementary oxygen. Why does the oxygen lower the yield? Why it is nevertheless always supplied. (Hint: All the necessary information is contained in the first two stoichiometric equations and associated heats of reaction shown above.) (b) Suppose the oxygen gas fed to the reactor and the oxygen in the coal combine with all the hydrogen in the coal (Reaction 3) and with some of the carbon (Reaction 2), and the remainder of the carbon is consumed in Reaction 1. Taking a basis of 1.00 kg coal fed to the reactor and letting \(n_{0}\) equal the moles of \(\mathrm{O}_{2}\) fed, draw and label a flowchart. Then derive expressions for the molar flow rates of the four outlet gas species in terms of \(n_{0}\). [Partial solution: \(n_{\mathrm{H}_{2}}=\left(51.3-n_{0}\right)\) mol \(\mathrm{H}_{2} . \mathrm{J}\) (c) The standard heat of combustion of the coal has been determined to be -21,400 kJ/kg, taking \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) to be the combustion products. Use this value and the given clemental composition of the coal to prove that the standard heat of formation of the coal is \(-1510 \mathrm{kJ} / \mathrm{kg}\). Then use an energy balance to calculate \(n_{0},\) using the following approximate heat capacities in your calculation: Take the heat of fusion of ash (the heat required to convert ash to slag) to be \(710 \mathrm{kJ} / \mathrm{kg}\).
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