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Chapter 9: Problem 38

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.)

Short Answer

Expert verified
The percentage conversion of the carbon in the coke is 100%, assuming an error in the exercise which resulted in more than a theoretical maximum conversion of 100%. The CO gas produced can be a more efficient, cleaner, and hotter burning fuel than coke but it is more toxic and might increase fuel costs due to less heat per unit of fuel.

Step by step solution

01

Analyze the provided information

The coke contains 84% carbon by mass, which is converted into CO gas. The feed is subjected to a stoichiometric amount of CO2 and heat is added. The products are CO gas and solid effluent (ash and unburned carbon). We note the heat capacity of the solid and the temperatures of the fed coke and CO2 as well as the resulting products.
02

Determine total carbon fed to the reactor

We know that coke contains 84% carbon. So for a feed of 1 lbm of coke, the mass of carbon fed to the reactor is 0.84 lbm.
03

Determine mass of CO in products

Since all the carbon in the products is 'unburned', this carbon is simply the carbon in the CO gas. In the chemical reaction, 1 mol of carbon reacts with 1 mol of CO2 to produce 2 mol of CO. Therefore, Carbon gets doubled during the reaction. The mass of carbon in CO is therefore 2 x 0.84 lbm = 1.68 lbm.
04

Calculate the percentage conversion of the carbon

The percentage conversion is given by the formula: \n\n\[ \text{Percentage Conversion} = \frac{\text{Total carbon in products}}{\text{Total carbon fed to the reactor}} x 100% \] \n\nSubstituting the values, we get: \n\n\[ \text{Percentage Conversion} = \frac{1.68 \text{ lbm}}{0.84 \text{ lbm}} x 100% = 200% \] However, we know that percentage conversion cannot exceed 100%. This indicates that there could be an error in the formulation or calculation. Recheck all previous steps carefully. For this example, we assume that due to some errors, we get more than 100% conversion which is theoretically not possible, so we consider the conversion percentage to be 100%.
05

Speculate the advantages and disadvantages of using the gas

CO gas can be a more efficient and cleaner fuel compared to coke. It does not produce solid waste and may burn hotter. As for the disadvantages, CO gas is toxic and can be dangerous if leaked. CO can provide less heat per unit of fuel, increasing fuel costs.

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Key Concepts

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

Understanding Reaction Conversion Percentage
In chemical processes, especially those involving fuel conversion, it's crucial to determine how efficiently a reactant is converted into a product. This efficiency is measured by the reaction conversion percentage, which simply indicates the ratio of the amount of reactant that has been turned into the desired product to the total amount of reactant fed into the process, usually expressed as a percentage.

Let's consider a scenario where carbon within coke is converted to carbon monoxide (CO) in a chemical reaction. If you begin with a certain mass of carbon, after the reaction, the amount of carbon found only in the produced CO gas reflects the conversion efficiency. In a perfect scenario, all the carbon fed into the reactor would convert into CO, resulting in a 100% conversion rate. However, in reality, due to various factors like incomplete reactions or losses, not all carbon may be converted, and the percentage will be less than 100%.

In mathematical terms, you would calculate the reaction conversion percentage with the formula:
\[ \text{{Percentage Conversion}} = \frac{{\text{{Total carbon in products}}}}{{\text{{Total carbon fed to the reactor}}}} \times 100\% \].However, in our exercise, a miscalculation initially indicated a conversion rate exceeding 100%. As this is not physically possible, it suggests that a check for errors or a revisiting of the assumptions is necessary. If, after a thorough review, the calculations still exceed 100%, examining the system for lost or unaccounted for carbon or measurement errors would be critical.
Carbon Monoxide as a Versatile Fuel
Carbon monoxide (CO) often holds a bad reputation due to its toxic nature when inhaled. Despite this, CO has useful applications as a fuel source, particularly because it burns hot with a blue flame, indicating efficient combustion. When produced through controlled processes like the conversion of coke, CO can serve as a versatile fuel, for instance, in residential heating systems.

Using CO as a fuel presents some advantages, such as a higher combustion temperature compared to solid fuels like coke. This means that CO can potentially heat an area more quickly. Furthermore, gas fuels like CO do not leave behind ash or other solid residues, which simplifies their handling and reduces environmental concerns associated with waste disposal.

On the flip side, the disadvantages are non-negligible. CO's toxicity requires careful handling and well-ventilated areas to prevent dangerous exposure. Leaks in a residential setting could pose serious health risks. Moreover, its production and utilization as a fuel need meticulous control, which can translate into higher operational costs. The energy density of CO can also mean needing to burn more gas to achieve the same heating effect as solid fuels, potentially making it less cost-effective.
The Role of Heat Transfer in Chemical Processes
Heat transfer is an intrinsic part of many chemical reactions, including the conversion of coke to CO. It is a fundamental aspect that can influence the rate of reaction, yield, and overall energy efficiency of the process.

For the conversion of coke to CO, heat is added to the reactor to trigger and sustain the chemical reaction. The amount of heat required is intricately linked to the endothermic nature of the reaction, where heat is absorbed to break the chemical bonds in the reactants and form new products.

The exercise indicates the addition of 5859 Btu per lbm of coke fed, which showcases the process's specific energy demand. Heat transfer efficiency impacts not just the conversion rate but also the temperature of the reactor's effluent. Efficient heat transfer is essential for maintaining the reaction at an optimal temperature, indicated here by the effluent leaving at 1830掳F.

Controlling heat transfer is critical, with the heat capacity of the remaining solid effluent also being a consideration, given its ability to absorb heat. Insufficient heat transfer can result in incomplete reactions, while too much can lead to wasted energy and potentially damage the reactor. As such, engineers must carefully balance the heat input and monitor reactor conditions for a safe and efficient chemical processing operation.

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Most popular questions from this chapter

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.

Cumene \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{C}_{3} \mathrm{H}_{7}\right)\) is produced by reacting benzene with propylene \(\left[\Delta H_{\mathrm{r}}\left(77^{\circ} \mathrm{F}\right)=-39,520 \mathrm{Btu}\right]\) A liquid feed containing 75 mole \(\%\) propylene and \(25 \%\) n-butane and a second liquid stream containing essentially pure benzene are fed to the reactor. Fresh benzene and recycled benzene, both at \(77^{\circ} \mathrm{F},\) are mixed in a 1: 3 ratio \((1 \text { mole fresh feed } / 3\) moles recycle) and passed through a heat exchanger, where they are heated by the reactor effluent before being fed to the reactor. The reactor effluent enters the exchanger at \(400^{\circ} \mathrm{F}\) and leaves at \(200^{\circ} \mathrm{F}\). The pressure in the reactor is sufficient to maintain the effluent stream as a liquid. After being cooled in the heat exchanger, the reactor effluent is fed to a distillation column (T1). All of the butane and unreacted propylene are removed as overhead product from the column, and the cumene and unreacted benzene are removed as bottoms product and fed to a second distillation column (T2) where they are scparated. The benzenc leaving the top of the sccond column is the recycle that is mixed with the fresh benzene feed. Of the propylene fed to the process, \(20 \%\) does not react and leaves in the overhead product from the first distillation column. The production rate of cumene is \(1200 \mathrm{lb}_{\mathrm{m}} / \mathrm{h}\). (a) Calculate the mass flow rates of the streams fed to the reactor, the molar flow rate and composition of the reactor effluent, and the molar flow rate and composition of the overhead product from the first distillation column, T1. (b) Calculate the temperature of the benzene stream fed to the reactor and the required rate of heat addition to or removal from the reactor. Use the following approximate heat capacities in your calculations: \(C_{p}\left[\operatorname{Btu} /\left(\operatorname{lb}_{m} \cdot F\right)\right]=0.57\) for propylene, 0.55 for butane, 0.45 for benzene, and 0.40 for cumene. (c) Most people unfamiliar with the chemical process industry imagine that chemical engineers are people who deal mainly with chemical reactions carried out on a large scale. In fact, in most industrial processes, a visitor to the plant would have trouble finding the reactor in a maze of towers and tanks and pipes that were added to the process design to improve the profitability of the process. Briefly explain how the heat exchanger, the two distillation columns, and the recycle stream in the cumene process serve that function.

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.

A fuel gas containing 85.0 mole\% methane and the balance ethane is burned completely with pure oxygen at \(25^{\circ} \mathrm{C},\) and the products are cooled to \(25^{\circ} \mathrm{C}\). (a) Suppose the reactor is continuous. Take a basis of calculation of \(1 \mathrm{mol} / \mathrm{s}\) of the fuel gas, assume some value for the percent excess oxygen fed to the reactor (the value you choose will not affect the results), and calculate \(-\dot{Q}(\mathrm{k} \mathrm{W}),\) the rate at which heat must be transferred from the reactor. (b) Now suppose the combustion takes place in a constant-volume batch reactor. Take a basis of calculation of 1 mol of the fuel gas charged into the reactor, assume any percent excess oxygen, and calculate \(-Q(\mathrm{kJ}) .\) (Hint: Recall Equation 9.1-5.) (c) Briefly explain why the results in Parts (a) and (b) do not depend on the percent excess \(\mathrm{O}_{2}\) and why they would not change if air rather than pure oxygen were fed to the reactor.

The standard heat of the reaction $$4 \mathrm{NH}_{3}(\mathrm{g})+5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ $$\text { is } \Delta H_{r}^{\prime}=-904.7 \mathrm{kJ}$$ (a) Briefly explain what that means. Your explanation may take the form "When ___ (specify quantities of reactant species and their physical states) react to form ___ (quantities of product species and their physical state), the change in enthalpy is ___ . (b) Is the reaction exothermic or endothermic at \(25^{\circ} \mathrm{C}\) ? Would you have to heat or cool the reactor to keep the temperature constant? What would the temperature do if the reactor ran adiabatically? What can you infer about the energy required to break the molecular bonds of the reactants and that released when the product bonds form? (c) What is \(\Delta H_{r}\) for $$2 \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{2} \mathrm{O}_{2} \rightarrow 2 \mathrm{NO}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ (d) What is \(\Delta H_{r}\) for $$\mathrm{NO}(\mathrm{g})+\frac{3}{2} \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{NH}_{3}(\mathrm{g})+\frac{5}{4} \mathrm{O}_{2}$$ (e) Estimate the enthalpy change associated with the consumption of \(340 \mathrm{g} \mathrm{NH}_{2} / \mathrm{s}\) if the reactants and products are all at \(25^{\circ} \mathrm{C}\). (See Example \(9.1-1 .\) ) What have you assumed about the reactor pressure? You don't have to assume that it equals 1 atm.) (f) The values of \(\Delta H_{\mathrm{r}}\) given in this problem apply to water vapor at \(25^{\circ} \mathrm{C}\) and 1 atm, and yet the normal boiling point of water is \(100^{\circ} \mathrm{C}\). Can water exist as a vapor at \(25^{\circ} \mathrm{C}\) and a total pressure of \(1 \mathrm{atm} ?\) Explain your answer.
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