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Chapter 9: Problem 41

Carbon disulfide, a key component in the manufacture of rayon fibers, is produced in the reaction between methane and sulfur vapor over a metal oxide catalyst: $$\begin{array}{c}\mathrm{CH}_{4}(\mathrm{g})+4 \mathrm{S}(\mathrm{v}) \rightarrow \mathrm{CS}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{S}(\mathrm{g}) \\ \Delta H_{\mathrm{r}}\left(700^{\circ} \mathrm{C}\right)=-274 \mathrm{kJ} \end{array}$$ Methane and molten sulfur, each at \(150^{\circ} \mathrm{C}\), are fed to a heat exchanger in stoichiometric proportion. Heat is exchanged between the reactor feed and product streams, and the sulfur in the feed is vaporized. The gascous methane and sulfur leave the exchanger and pass through a second preheater in which they are heated to \(700^{\circ} \mathrm{C}\), the temperature at which they enter the reactor. Heat is transferred from the reactor at a rate of \(41.0 \mathrm{kJ} / \mathrm{mol}\) of feed. The reaction products emerge from the reactor at \(800^{\circ} \mathrm{C}\), pass through the heat exchanger, and emerge at \(200^{\circ} \mathrm{C}\) with sulfur as a liquid. Use the following heat capacity data to perform the requested calculations: \(C_{p}\left[J /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \approx 29.4\) for \(\mathrm{S}(1), 36.4\) for \(\mathrm{S}(\mathrm{v}), 71.4\) for \(\mathrm{CH}_{4}(\mathrm{g}), 31.8\) for \(\mathrm{CS}_{2}(\mathrm{v}),\) and 44.8 for \(\mathrm{H}_{2} \mathrm{S}(\mathrm{g})\) (a) Estimate the fractional conversion achieved in the reactor. In enthalpy calculations, take the feed and product species at \(700^{\circ} \mathrm{C}\) as references. (b) Suppose the heat of reaction at \(700^{\circ} \mathrm{C}\) had not been given. What would be different in your solution to Part (a)? (Be thorough in your explanation.) Sketch the process paths from the feed to the products built into both the calculation of Part (a) and your alternative calculation. Explain why the result would be the same regardless of which method you used. (c) Suggest a method to improve the energy economy of the process.

Short Answer

Expert verified
In summary, this process has a certain fractional conversion efficiency determined by the stoichiometry of the reaction and the interplay between heat exchange and heat capacity. Without the given heat of reaction, the calculation would require the careful assessment of heat capacities and temperature changes, and would likely achieve the same results due to the energy balance of the process. Several methods to improve energy economy could include optimizing the operation temperatures or improving the catalyst.

Step by step solution

01

Calculate the change in Enthalpy for Reactants

The change in enthalpy for reactants is calculated by applying the formula for calculating enthalpy, which is \(\Delta H = \sum C_{p}*\Delta T\). The Cp values and the temperature difference are given in the question itself.
02

Calculate the change in Enthalpy for Products

Again, by using the formula, \(\Delta H = \sum C_{p}*\Delta T\), we can calculate the change in enthalpy for the products of the reaction. Again these values are derived from the data provided in the question.
03

Calculate the Overall Enthalpy Change

The total change in enthalpy for the reaction is then calculated by summing up the enthalpy change of the reactants and products.
04

Calculate the Fractional Conversion

Using the total enthalpy change, the amount of heat transferred from the reactor (\(41 kJ/mol\) given), and the total balance of the process, we can estimate the fractional conversion achieved in the reactor, which would give us the efficiency of the process. This fundamental principle of stoichiometry would be used to calculate the percentage conversion of reactants to products.
05

Discuss the Part B & C scenarios

Without the enthalpy of reaction given, you would have to estimate this value based on the heat capacity and temperature changes, and calculate the enthalpy of formation with given standard heat of formation. Also, several suggestions to improve the energy economy of the process could be provided, such as improving catalyst performance or optimizing operating temperatures.

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Key Concepts

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

Enthalpy Change Calculation
Understanding enthalpy change is crucial for chemical engineers as it provides insights into the heat exchange within chemical reactions. Enthalpy, symbolized as \( H \), is a concept from thermodynamics that represents the total heat content of a system. An enthalpy change, \( \Delta H \), occurs when a reaction absorbs or releases heat under constant pressure.

To calculate enthalpy change, use the formula \( \Delta H = \sum C_p \times \Delta T \), where \( C_p \) is the heat capacity at constant pressure, and \( \Delta T \) is the change in temperature. Heat capacity is the amount of heat required to raise the temperature of a substance by one degree Celsius and depends on the substance's properties and phase (solid, liquid, gas).

In the given exercise, the enthalpy change calculation required determining the heat content change for both reactants and products from a specified reference temperature. The exercise solution mentions applying the formula to calculate the changes separately and then summing the results to get the overall enthalpy change of the chemical process. Understanding this concept allows chemical engineers to design thermally efficient processes and evaluate reaction feasibility.
Chemical Process Efficiency
Efficiency in chemical processes is quantified by how well resources such as energy and raw materials are converted into desired products. This efficiency is often represented as a fraction or percentage indicating the completeness of the desired reaction, or the fractional conversion. This conversion is crucial for determining process yields and optimizing economic returns.

To calculate the fractional conversion in the given exercise, engineers must consider the total enthalpy change and the heat transferred from the reactor, which is provided at \( 41.0 \mathrm{kJ/mol} \). By establishing the relationship between the heat transfer and the theoretical enthalpy change of the process, one can estimate the proportion of reactants converted to products. Improving process efficiency can involve enhancing energy recovery, increasing catalyst activity, or optimizing reaction conditions 鈥� all of which contribute to a more sustainable and cost-effective operation.
Stoichiometry in Chemical Reactions
Stoichiometry is the study of the quantitative relationships, or ratios, between reactants and products in chemical reactions. It is a fundamental concept in chemistry that ensures the conservation of mass and helps in predicting the amounts of substances required and produced in a given reaction.

In the context of the textbook exercise, stoichiometry involves using the balanced chemical equation to assess the quantities of methane and sulfur vapor reacting to produce carbon disulfide and hydrogen sulfide. Importantly, the exercise emphasizes the stoichiometric proportion in which methane and molten sulfur are fed to the heat exchanger, meaning they are in the exact ratio needed to react completely without excess. By meticulously applying stoichiometric principles, chemical engineers can optimize the design of reactors and the overall efficiency of industrial processes, thereby reducing waste and improving yield.

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Most popular questions from this chapter

Formaldehyde may be produced in the reaction between methanol and oxygen: $$2 \mathrm{CH}_{3} \mathrm{OH}(\mathrm{l})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{HCHO}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta H_{\mathrm{r}}^{\circ}=-326.2 \mathrm{kJ}$$ The standard heat of combustion of hydrogen is $$\mathrm{H}_{2}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(\mathrm{l}): \quad \Delta \hat{H}_{\mathrm{c}}^{\circ}=-285.8 \mathrm{kJ} / \mathrm{mol}$$ (a) Use these heats of reaction and Hess's law to determine the standard heat of the direct decomposition of mcthanol to form formaldchyde: $$\mathrm{CH}_{3} \mathrm{OH}(\mathrm{l}) \rightarrow \mathrm{HCHO}(\mathrm{g})+\mathrm{H}_{2}(\mathrm{g})$$ (b) Explain why you would probably use the method of Part (a) to determine the heat of the methanol decomposition reaction experimentally rather than carrying out the decomposition reaction and measuring \(\Delta H_{f}^{\circ}\) directly.

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?

A 12.0-molar solution of sodium hydroxide ( \(\mathrm{SG}=1.37\) ) is neutralized with \(75.0 \mathrm{mL}\) of a \(4.0 \mathrm{molar}\) solution of sulfuric acid ( \(\mathrm{SG}=1.23\) ) in a well-insulated container. (a) Estimate the volume of the sodium hydroxide solution and the final solution temperature if both feed solutions are at \(25^{\circ} \mathrm{C}\). The heat capacity of the product solution may be taken to be that of pure liquid water, the standard heat of solution of sodium sulfate is \(-1.17 \mathrm{kJ} / \mathrm{mol},\) and the energy balance reduces to \(Q=\Delta H\) for this constant-pressure batch process. (b) List several additional assumptions you made to arrive at your estimated volume and temperature.

The wastewater treatment plant at the Ossabaw Paper Company paper mill generates about 24 tonnes of sludge per day. The consistency of the sludge is \(35 \%,\) meaning that the sludge contains 35 wt\% solids and the balance liquids. The mill currently spends \(\$ 40\) /tonne to dispose of the sludge in a landfill. The plant environmental cngincer has determined that if the sludge consistency could be increased to \(75 \%\) the sludge could be incinerated (burned) to generate useful energy and to eliminate the environmental problems associated with landfill disposal. A flowchart for a preliminary design of the proposed sludge-treatment process follows. For simplicity, we will assume that the liquid in the sludge is just water. Process description: The sludge from the wastewater treatment plant (Stream ? passes through a dryer where a portion of the water in the sludge is vaporized. The heat required for the vaporization comes from condensing saturated steam at 4.00 bar (Stream ?. The steam fed to the dryer is produced in the plant's oil-fired boiler from feedwater at \(20^{\circ} \mathrm{C}\) (Stream ? The heat required to produce the steam is transferred from the boiler furnace, where fuel oil (Stream ? from the boiler furnace, where fuel oil (Stream ? .The concentrated sludge coming from the dryer (Stream ? which has a consistency of \(75 \%,\) is fed to an incinerator. The heating value of the sludge is insufficient to keep the incinerator temperature high enough for complete combustion, so natural gas (Stream ? is used as a supplementary fuel. A stream of outside air at \(25^{\circ} \mathrm{C}\) (Stream ? Is heated to \(110^{\circ} \mathrm{C}\) and fed to the incinerator along with the concentrated sludge and natural gas. The waste gas from the incinerator is discharged to the atmosphere. Fuel oil: The oil is a low-sulfur No. 6 fuel oil. Its ultimate (elemental) analysis on a weight basis is \(87 \% \mathrm{C}, 10 \% \mathrm{H}, 0.84 \% \mathrm{S},\) and the balance oxygen, nitrogen, and nonvolatile ash. The higher heating value of the oil is \(3.75 \times 10^{4} \mathrm{kJ} / \mathrm{kg}\) and the heat capacity is \(C_{p}=1.8 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\) Boiler: The boiler has an efficiency of \(62 \%,\) meaning that \(62 \%\) of the heating value of the fuel oil burned is used to produce saturated steam at 4.00 bar from boiler feedwater at 20^{\circ } \mathrm { C } \text { . Fuel oil at } 6 5 ^ { \circ } \mathrm { C } and dry air at \(125^{\circ} \mathrm{C}\) are fed to the boiler furnace. The air feed rate is \(25 \%\) in excess of the amount theoretically required for complete consumption of the fuel. Sludge: The sludge from the wastewater treatment plant contains \(35 \%\) w/w solids (S) and the balance liquids (which for the purposes of this problem may be treated as only water) and enters the dryer at \(22^{\circ} \mathrm{C} .\) The sludge includes a number of volatile organic species, some of which may be toxic, and has a terrible odor. The heat capacity of the solids is approximately constant at \(2.5 \mathrm{kJ} /\left(\mathrm{kg} \cdot^{\circ} \mathrm{C}\right)\). Dryer: The dryer has an efficiency of \(55 \%,\) meaning that the heat transferred to the sludge, \(Q_{2},\) is \(55 \%\) of the total heat lost by the condensing steam, and the remainder, \(Q_{3}\), is lost to the surroundings. The dryer operates at 1 atm, and the water vapor and concentrated sludge emerge at the corresponding saturation temperature. The steam condensate leaves the dryer as a liquid saturated at 4.00 bar. Incinerator: The concentrated sludge has a heating value of \(19,000 \mathrm{kJ} / \mathrm{kg}\) dry solids. For a feed sludge of \(75 \%\) consistency, the incinerator requires 195 SCM natural gas/tonne wet sludge \(\left[1 \mathrm{SCM}=1 \mathrm{m}^{3}(\mathrm{STP})\right]\) The theoretical air requirement for the sludge is 2.5 SCM air/ 10,000 kJ of heating value. Air is fed in \(100 \%\) excess of the amount theoretically required to burn the sludge and the natural gas. (a) Use material and energy balances to calculate the mass flow rates (tonnes/day) of Streams ? ? ? ? ? ? and ? and heat flows \(\dot{Q}_{0}, \dot{Q}_{1}, \ldots, \dot{Q}_{4}(\mathrm{kJ} / \text { day }) .\) Take the molecular weight of air to be \(29.0 .\) (Caution: Before you start doing lengthy and unnecessary energy balance calculations on the boiler furnace, remember the given furnace efficiency.) Exploratory Exercises - Research and Discover (b) The money saved by implementing this process will be the current cost of disposing of the wastewater plant sludge in a landfill. Two major costs of implementing the process are the installed costs of the new dryer and incinerator. What other costs must be taken into account when determining the economic feasibility of the process? Why might management decide to go ahead with the project even if it proves to be unprofitable? (c) What opportunities exist for improving the energy economy of the process? (Hint: Think about the need to preheat the fuel oil and the boiler and incinerator air streams and consider heat exchange possibilities.) (d) The driving force for the introduction of this process is to eliminate the environmental cost of sludge disposal. What is that cost- -that is, what environmental penalties and risks are associated with using landfills for hazardous waste disposal? What environmental problems might incineration introduce?

Biodiesel fuel - a sustainable alternative to petroleum diesel as a transportation fuel- -is produced via the transesterification of triglyceride molecules derived from vegetable oils or animal fats. For every \(9 \mathrm{kg}\) of biodiesel produced in this process, \(1 \mathrm{kg}\) of glycerol, \(\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3},\) is produced as a byproduct. Finding a market for the glycerol is important for biodiesel manufacturing to be economically viable. A process for converting glycerol to the industrially important specialty chemical intermediates acrolein, \(C_{3} \mathrm{H}_{4} \mathrm{O},\) and hydroxyacetone (acetol), \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2},\) has been proposed. $$\begin{array}{l}\mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{4} \mathrm{O}+2 \mathrm{H}_{2} \mathrm{O} \\ \mathrm{C}_{3} \mathrm{H}_{8} \mathrm{O}_{3} \rightarrow \mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}_{2}+\mathrm{H}_{2} \mathrm{O} \end{array}$$ The reactions take place in the vapor phase at \(325^{\circ} \mathrm{C}\) in a fixed bed reactor over an acid catalyst. The feed to the reactor is a vapor stream at \(325^{\circ} \mathrm{C}\) containing 25 mol\% glycerol, \(25 \%\) water, and the balance nitrogen. All of the glycerol is consumed in the reactor, and the product stream contains acrolein and hydroxyacctone in a 9: 1 mole ratio. Data for the process species are shown below. $$\begin{array}{|l|c|c|}\hline \text { Species } & \Delta \hat{H}_{\mathrm{f}}(\mathrm{kJ} / \mathrm{mol}) & C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right] \\ \hline \text { glycerol(v) } & -620 & 0.1745 \\ \hline \text { acrolein(v) } & -65 & 0.0762 \\\\\hline \text { hydroxyacetone(v) } & -372 & 0.1096 \\ \hline \text { water(v) } & -242 & 0.0340 \\\\\hline \text { nitrogen(g) } & 0 & 0.0291 \\ \hline\end{array}$$ (a) Assume a basis of 100 mol fed to the reactor, and draw and completely label a flowchart. Carry out a degree-of-freedom analysis assuming that you will use extents of reaction for the material balances. Then calculate the molar amounts of all product species. (b) Calculate the total heat added or removed from the reactor (state which it is), using the constant heat capacities given in the above table. (c) Assuming this process is implemented along with biodiesel production, how would you determine whether the biodiesel is an cconomically viable alternative to petroleum diesel? (d) If you do a degree-of-freedom analysis based on atomic species balances, you are likely to count one more equation than you have unknowns, and yet you know the system has zero degrees of freedom. Guess what the problem is, and then prove it.
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