/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 25 The hydrogenation of ethylbenzen... [FREE SOLUTION] | 91Ó°ÊÓ

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The hydrogenation of ethylbenzene to ethylcyclohexane over a nickelmordenite catalyst is zero order in both reactants up to an ethylbenzene conversion of \(75 \%\) [Ind. Eng. Chem. Res., 28 ( 3 ), 260 ( 1989 )]. At 553 K. \(k=5.8\) mol ethylbenzene/(dm \(^{3}\) of catalyst \(\cdot \mathrm{h}\) ). When a \(100 \mathrm{ppm}\) thiophene concentration entered the system, the ethylbenzene conversion began to drop. $$\begin{array}{l|lllllll}\text {Time (h)} & 0 & 1 & 2 & 4 & 6 & 8 & 12 \\ \hline \text {Conversion} & 0.92 & 0.82 & 0.75 & 0.50 & 0.30 & 0.21 & 0.10\end{array}$$ The reaction was carried out at \(3 \mathrm{MPa}\) and a molar ratio of \(\mathrm{H}_{2} / \mathrm{ETB}=10\). Discuss the catalyst decay. Be quantitative where possible.

Short Answer

Expert verified
In conclusion, the nickelmordenite catalyst experiences decay in the hydrogenation of ethylbenzene to ethylcyclohexane when thiophene is present in the system. By analyzing the conversion rates at different time intervals, we found that the catalyst becomes less effective per hour, indicating the catalyst's susceptibility to thiophene poisoning. This emphasizes the importance of addressing catalyst poisoning during catalyst selection and reaction design in industrial processes.

Step by step solution

01

Understand the data given in the problem

The hydrogenation of ethylbenzene follows zero-order kinetics up to 75% conversion, with a rate constant k=5.8 mol/(dm³ of catalyst∙hour) at 553K. The reaction is carried out at 3 MPa with an H₂/ETB molar ratio of 10. The effect of thiophene is to decrease the ethylbenzene conversion over time. The given data table shows the conversion of ethylbenzene at different times.
02

Calculate initial rate of conversion

First, we find the initial rate of conversion r0: \(r_0 = k = 5.8 \, mol\, etylbenzene/(dm^3\, of\, catalyst \cdot hour)\) The initial rate depends only on the rate constant in zero-order kinetics.
03

Analyze conversion data with time

Now, we can list the amount of ethylbenzene converted per hour for each period, by calculating the rate of decrease in time intervals: 1h: (0.92 - 0.82)/1 = 0.10 mol/ hour 2h: (0.82 - 0.75)/2 = 0.035 mol/ hour 4h: (0.75 - 0.5)/4 = 0.0625 mol/ hour 6h: (0.5 - 0.30)/6 = 0.0333 mol/ hour 8h: (0.30 - 0.21)/8 = 0.01125 mol/ hour 12h: (0.21 - 0.10)/12 = 0.00917 mol/ hour These numbers indicate that the catalyst is becoming less effective per hour, causing a reduction in ethylbenzene conversion.
04

Calculate relative catalyst decay

Calculate relative catalyst decay as the ratio of the conversion rate at different time intervals to the initial rate. The relative catalyst decay for each interval is: 1h: 0.10/5.8 ≈ 0.0172 2h: 0.035/5.8 ≈ 0.0060 4h: 0.0625/5.8 ≈ 0.01078 6h: 0.0333/5.8 ≈ 0.0057 8h: 0.01125/5.8 ≈ 0.0019 12h: 0.00917/5.8 ≈ 0.0016 We can see from these relative catalyst decay numbers that the catalyst loses efficiency over time when thiophene is present in the system. This demonstrates the susceptibility of the nickelmordenite catalyst to thiophene poisoning, which results in a decrease in ethylbenzene conversion. In conclusion, we have analyzed the catalyst decay in the hydrogenation of ethylbenzene to ethylcyclohexane over a nickelmordenite catalyst. By calculating the conversion rates at different time intervals and comparing them to the initial one, we showed that thiophene adversely affects the catalyst, causing a decrease in ethylbenzene conversion. This analysis highlights the importance of considering catalyst poisoning when designing and choosing catalysts for industrial reactions.

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Key Concepts

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

Zero-Order Kinetics
In chemical kinetics, zero-order reactions are characterized by a constant rate that does not depend on the concentration of the reactants. This means the rate at which the product is formed is fixed, as long as the reactant is available. An example provided in the exercise is the hydrogenation of ethylbenzene, which follows zero-order kinetics up to a 75% conversion threshold. At this point, the rate of the reaction is given by the reaction rate constant, represented by the variable 'k'.

In the context of the hydrogenation process, the initial rate of reaction, denoted by \(r_0\), is equal to the rate constant \(k\) and is calculated to be \(5.8 \) mol etylbenzene per \(dm^3\) of catalyst per hour. To students, this would underscore the concept that as long as the reactant (ethylbenzene) is present in sufficient quantity, and the reaction still exhibits zero-order kinetics, the production of the product (ethylcyclohexane) will continue at a consistent rate, unaffected by the decrease in reactants.
Ethylbenzene Hydrogenation
The hydrogenation of ethylbenzene involves the addition of hydrogen to ethylbenzene to produce ethylcyclohexane, which is typically facilitated by a catalyst. In this exercise, the catalyst used is nickelmordenite. At a certain temperature of 553 K and a pressure of 3 MPa, with a molar ratio of hydrogen to ethylbenzene (Hâ‚‚/ETB) of 10, the reaction proceeds consistently until roughly 75% of the ethylbenzene is converted. Beyond this point, any changes in the rate or efficiency of the reaction could indicate factors such as catalyst decay or the influence of contaminants.

The presence of thiophene, a common sulfur-containing impurity, can significantly affect the reaction by acting as a poison to the catalyst. The decrease in ethylbenzene conversion over time as observed in the data suggests a reduced effectiveness of the catalyst, which is a scenario common in industrial chemical processes and emphasizes the importance of catalyst stability for consistent production rates.
Catalyst Poisoning
Catalyst poisoning refers to the decrease in the effectiveness of a catalyst in facilitating a chemical reaction. Poisoning typically occurs when a substance, which may be a contaminant, binds to the catalyst surface more strongly than the reactants, effectively blocking the active sites of the catalyst and preventing the reaction from proceeding at its optimal rate. In our exercise example, the introduction of 100 ppm of thiophene into the ethylbenzene hydrogenation system illustrates catalyst poisoning. Over time, as the thiophene enters the system and comes into contact with the nickelmordenite catalyst, the ethylbenzene conversion rates decline, as evidenced by the decreasing conversion rates at each time interval.

Quantitatively, the relative catalyst decay can be determined by comparing the conversion rates at subsequent intervals to the initial rate. This provides a clear indication of the catalyst's declining performance. Understanding catalyst poisoning is crucial in the field of chemical engineering, as identifying and mitigating the effects of poisons can significantly improve catalyst lifetime and reaction efficiency.

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Most popular questions from this chapter

Sketch qualitatively the reactant, product, and activity profiles as a function of length at various times for a packed-bed reactor for each of the following cases. In addition. sketch the effluent concentration of \(A\) as a function of time. The reaction is a simple isomerization: \(\longrightarrow B\) (a) Rate law: \(-r_{\mathrm{A}}^{\prime}=k a C_{\mathrm{A}}\) Decay law: \(r_{d}=k_{d} a C_{\mathrm{A}}\) Case I: \(k_{d} \ll k,\) Case II: \(k_{d}=k,\) Case III: \(k_{d} \geqslant k\) (b) \(-r_{\mathrm{A}}^{\prime}=k a C_{\mathrm{A}}\) and \(r_{d}=k_{d} a^{2}\) (c) \(-r_{\mathrm{A}}^{\prime}=k a C_{\mathrm{A}}\) and \(r_{d}=k_{d} a C_{\mathrm{B}}\) (d) Sketch similar profiles for the rate laws in parts (a) and (c) in a moving-bed reactor with the solids entering at the same end of the reactor as the reactant. (e) Repeat part (d) for the case where the solids and the reactant enter at opposite ends.

In 1981 the U.S. government put forth the following plan for automobile manufacturers to reduce emissions from automobiles over the next few years. All values are in grams per mile. An automobile emitting 3.74 lb of \(\mathrm{CO}\) and 0.37 lb of \(\mathrm{NO}\) on a journey of 1000 miles would meet the current government requirements. To remove oxides of nitrogen (assumed to be \(\mathrm{NO}\) ) from automobile exhaust, a scheme has been. proposed that uses unburned carbon monoxide (CO) in the exhaust to reduce the NO over a solid catalyst, according to the reaction. $$\mathrm{CO}+\mathrm{NO} \longrightarrow \text { Products }\left(\mathrm{N}_{2}, \mathrm{CO}_{2}\right)$$Experimental data for a particular solid catalyst indicate that the reaction rate can be well represented over a large range of temperatures by $$-r_{\mathrm{N}}^{\prime}=\frac{k P_{\mathrm{N}} P_{\mathrm{C}}}{\left(1+K_{1} P_{\mathrm{N}}+K_{2} P_{\mathrm{C}}\right)^{2}}$$ where \(\quad P_{\mathrm{N}}=\) gas-phase partial pressure of \(\mathrm{NO}\) \(P_{\mathrm{C}}=\) gas-phase partial pressure of \(\mathrm{CO}\) \(k, K_{1}, K_{2}=\) coefficients depending only on temperature (a) Based on your experience with other such systems, you are asked to propose an adsorption-surface reaction-desorption mechanism that will explain the experimentally observed kinetics. (b) A certain engineer thinks that it would be desirable to operate with a very large stoichiometric excess of CO to minimize catalytic reactor volume. Do you agree or disagree? Explain. (c) When this reaction is carried out over a supported Rh catalyst [J. Phys. Chem., 92,389 ( 1988 )], the reaction mechanism is believed to be $$\begin{array}{c}\mathrm{CO}+\mathrm{S} \rightleftarrows \mathrm{CO} \cdot \mathrm{S} \\ \mathrm{NO}+\mathrm{S} \rightleftarrows \mathrm{NO} \cdot \mathrm{S} \\ \mathrm{NO} \cdot \mathrm{S}+\mathrm{S} \longrightarrow \mathrm{N} \cdot \mathrm{S}+\mathrm{O} \cdot \mathrm{S} \\\\\mathrm{CO} \cdot \mathrm{S}+\mathrm{O} \cdot \mathrm{S} \longrightarrow \mathrm{CO}_{2}+2\mathrm{S} \\\\\mathrm{N} \cdot \mathrm{S}+\mathrm{N} \cdot \mathrm{S} \longrightarrow \mathrm{N}_{2}+2 \mathrm{S}\end{array}$$ When the ratio of \(P_{\mathrm{CO}} / P_{\mathrm{NO}}\) is small, the rate law that is consistent with the experimental data is $$-r_{\mathrm{co}}^{\prime}=\frac{k P_{\mathrm{co}}}{\left(1+K_{\mathrm{CO}} P_{\mathrm{Co}}\right)^{2}}$$ What are the conditions for which the rate law and mechanism are consistent?

Methyl ethyl ketone (MEK) is an important industrial solvent that can be produced from the dehydrogenation of butan- 2 -ol (Bu) over a zinc oxide catalyst [Ind. Eng. Chem. Res.. 27, 2050 (1988)]: $$\mathrm{Bu} \rightarrow \mathrm{MEK}+\mathrm{H}_{2}$$ The following data giving the reaction rate for MEK were obtained in a differential reactor at \(490^{\circ} \mathrm{C}\) $$\begin{array}{lllllll}\hline P_{\mathrm{Bu}}(\mathrm{atm}) & 2 & 0.1 & 0.5 & 1 & 2 & 1 \\ P_{\mathrm{MEK}}(\mathrm{atm}) & 5 & 0 & 2 & 1 & 0 & 0 \\ P_{\mathrm{H}_{2}}(\mathrm{atm}) & 0 & 0 & 1 & 1 & 0 & 10 \\ r_{\mathrm{MEK}}^{\prime}(\mathrm{mol} / \mathrm{h} \cdot \mathrm{g} \text { cat. }) & 0.044 & 0.040 & 0.069 & 0.060 & 0.043 & 0.059 \\\\\hline\end{array}$$ (a) Suggest a rate law consistent with the experimental data. (b) Suggest a reaction mechanism and rate-limiting step consistent with the rate law. (Hint: Some spccies might be weakly adsorbed.) (c) What do you believe to he the point of this problem? (d) Plot conversion (up to \(90^{\circ}\) is and reaction rate as a function of catalyst weight for an entering molar flow rate of pure butan-2-ol of \(10 \mathrm{mol} / \mathrm{min}\) and an entering pressure \(P_{0}=10\) atm. \(W_{\max }=23 \mathrm{kg}\) (e) Write a question that requires critical thinking and then explain why your question requires critical thinking. [Hint: See Preface Section B.2.] (f) Repeat part (d) accounting for pressure drop and \(\alpha=0.03 \mathrm{kg}^{-1} .\) Plot \(y\) and \(X\) as a function of catalyst weight down the reactor.

The elementary irreversible gas phase catalytic reaction $$A+B \stackrel{k}{\longrightarrow} C+D$$ is to be carried out in a moving-bed reactor at constant temperature. The reactor contains \(5 \mathrm{kg}\) of catalyst. The feed is stoichiometric in \(\mathrm{A}\) and \(\mathrm{B}\). The entering concentration of \(\mathrm{A}\) is \(0.2 \mathrm{mol} / \mathrm{dm}^{3}\). The catalyst decay law is zero order with \(k_{\mathrm{D}}=0.2 \mathrm{s}^{-1}\) and \(k=1.0 \mathrm{dm}^{6} /(\mathrm{mol} \cdot \mathrm{kg} \text { cat } \cdot \mathrm{s})\) and the volumetric flow rate is \(v_{0}=1 \mathrm{dm}^{3} / \mathrm{s}\) (a) What conversion will be achieved for a catalyst feed rate of \(0.5 \mathrm{kg} / \mathrm{s} ?\) (b) Sketch the catalyst activity as a function of catalyst weight (i.e., distance) down the reactor length for a catalyst feed rate of \(0.5 \mathrm{kg} / \mathrm{s}\) (c) What is the maximum conversion that could be achieved (i.e., at infinite catalyst loading rate)? (d) What catalyst loading rate is necessary to achieve \(40 \%\) conversion? (e) At what catalyst loading rate (kg/s) will the catalyst activity be exactly zero at the exit of the reactor? (f) What does an activity of zero mean? Can catalyst activity be less than zero? (g) How would your answers change if \(k=5\) mol/kg cat"s and the catalyst and reactant were fed at opposite ends? (h) Now consider the following economics: \(\therefore\) The product sells for \(\$ 160\) per gram mole. "The cost of operating the bed is \(\$ 10\) per kilogram of catalyst exiting the bed. What is the feed rate of solids ( \(\mathrm{kg} / \mathrm{min}\) ) that will give the maximum profit? (Ans.: \(U_{s}=4 \mathrm{kg} / \mathrm{min.}\) ) (Note: For the purpose of this calculation, ignore all other costs, such as the cost of the reactant, etc.) (i) Qualitatively how will your answer change if \(k_{r}=5 \mathrm{mol} / \mathrm{kg}\) cat \(\cdot \min\) and the reactant and catalyst are fed to opposite ends of the bed.

In the production of ammonia $$\mathrm{NO}+\frac{5}{2} \mathrm{H}_{2} \rightleftarrows \mathrm{H}_{2} \mathrm{O}+\mathrm{NH}_{3}$$ the following side reaction occurs: $$\mathrm{NO}+\mathrm{H}_{2} \rightleftarrows \mathrm{H}_{2} \mathrm{O}+\frac{1}{2} \mathrm{N}_{2}$$ Ayen and Peters [Ind. Eng. Chem. Process Des. Dev., 1.204(1962) ] studied catalytic reaction of nitric oxide with Girdler \(G-50\) catalyst in a differential reactor at atmospheric pressure. Table \(\mathrm{P} 10-16\) shows the reaction rate of the side reaction as a function of \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{NO}}\) at a temperature of \(375^{\circ} \mathrm{C}\) $$\begin{array}{lcc} & \text { TABLE PIO-16. } & \text { FoRMATION OF WATER } \\ \hline & & \text {Reaction Rate} \\ & & r_{\mathrm{H}_{2}} \times 10^{5}(\mathrm{g} \mathrm{mol} / \mathrm{min} \cdot \mathrm{g} \text { cat }) \\ P_{\mathrm{H}_{2}}(\mathrm{atm}) & P_{\mathrm{NO}}(\mathrm{atm}) & T=375^{\circ} \mathrm{C}, W=2.39 \mathrm{g} \\ \hline 0.00922 & 0.0500 & 1.60 \\\0.0136 & 0.0500 & 2.56 \\\0.0197 & 0.0500 & 3.27 \\\0.0280 & 0.0500 & 3.64 \\ 0.0291 & 0.0500 & 3.48 \\\0.0389 & 0.0500 & 4.46 \\\0.0485 & 0.0500 & 4.75 \\\0.0500 & 0.00918 & 1.47 \\\0.0500 & 0.0184 & 2.48 \\ 0.0500 & 0.0298 & 3.45 \\\0.0500 & 0.0378 & 4.06 \\\0.0500 & 0.0491 & 4.75 \\\\\hline\end{array}$$ The following rate laws for side reaction (2), based on various catalytic mechanisms, were suggested: $$\begin{array}{l}r_{H, 0}=\frac{k K_{\mathrm{N} 0} P_{\mathrm{NO}} P_{\mathrm{H}_{2}}}{1+K_{\mathrm{N} 0} P_{\mathrm{NO}}+K_{\mathrm{H}_{2}} P_{\mathrm{H}_{2}}} \\ r_{\mathrm{H}_{2} \mathrm{O}}=\frac{k K_{\mathrm{H}_{2}} K_{\mathrm{NO}} P_{\mathrm{NO}}}{1+K_{\mathrm{NO}} P_{\mathrm{NO}}+K_{\mathrm{H}_{2}} P_{\mathrm{H}_{2}}} \\ r_{\mathrm{H}_{2} \mathrm{O}}=\frac{k_{1} K_{\mathrm{H}_{2}} K_{\mathrm{NO}} P_{\mathrm{NO}} P_{\mathrm{H}_{2}}}{\left(1+K_{\mathrm{NO}} P_{\mathrm{KO}}+K_{\mathrm{H}_{2}} P_{\mathrm{H}_{2}}\right)^{2}} \end{array}$$ Find the parameter values of the different rate laws and determine which rate law best represents the experimental data

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