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Chapter 9: Problem 6

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.

Short Answer

Expert verified
(a) The standard heat of the direct decomposition of methanol to form formaldehyde is \( \Delta H_{decomp}^\circ = 40.1 kJ/mol \). (b) The indirect method using Hess's law is safer and more manageable than conducting a direct experiment to measure the heat of methanol decomposition.

Step by step solution

01

Determine the Heat of Methanol Decomposition

The given reaction \[2 CH_{3}OH(l) + O_{2}(g) \rightarrow 2 HCHO(g) + 2 H_{2}O(l): \quad \Delta H_{r}^\circ = -326.2 kJ\]defines the production of formaldehyde and water from methanol and oxygen. Let's rearrange it to match the reaction asked in part (a):\[CH_{3}OH(l) \rightarrow HCHO(g) + H_{2}O(l): \quad \Delta H_{r}^\circ = -326.2 kJ / 2\]Subtract the combustion of hydrogen from the new equation:\[CH_{3}OH(l) \rightarrow HCHO(g) + H_{2}O(l) - [H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H_{2}O(l)]\]This simplifies to:\[CH_{3}OH(l) \rightarrow HCHO(g) + H_{2}(g)\]Using Hess's Law:\[\Delta H_{decomp}^\circ = \Delta H_{r}^\circ - \Delta H_{c}^\circ = -326.2 kJ / 2 - (-285.8 kJ/mol) = 40.1 kJ/mol\]
02

Discuss the Advantages of the Indirect Method

Conducting an actual lab experiment to measure the heat of methanol decomposition can be a challenging and dangerous task. It may not be feasible due to unpredictable conditions or hazards associated with decomposition reactions. By using Hess's law, we can indirectly determine energy changes using known heats of other chemical reactions under standard conditions. This avoids messing with difficult chemicals or reactions directly, making it safer and more manageable.

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Key Concepts

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

Standard Heat of Combustion
The standard heat of combustion, denoted by \( \Delta \hat{H}_{c}^\circ \), is a fundamental concept in thermochemistry. It refers to the heat energy released when one mole of a substance combusts completely with oxygen under standard conditions. Standard conditions generally mean at a pressure of 1 bar and a specific temperature, usually 25掳C.

To put it simply, it's like measuring how much energy you'd get if you set a mole of a substance on fire in a controlled setting. For example, the standard heat of combustion of hydrogen describes the energy released when hydrogen gas is combined with oxygen to produce liquid water, and it holds immense relevance when dealing with chemical reactions involving hydrocarbons.

Understanding this concept is crucial because it underpins the energy changes involved in chemical reactions and allows us to calculate unknown reaction enthalpies, as shown in Hess's Law calculations.
Methanol Decomposition
Methanol, a simple alcohol, can break down into formaldehyde and hydrogen gas, a reaction that can be studied through methanol decomposition. This process is particularly interesting because it has various applications in industrial chemistry. As such, getting an accurate measurement of the energy changes associated with methanol decomposition is vital not only for theoretical studies but also for practical implications in synthesis and energy production.

In educational settings, decomposing methanol provides a tangible example for students to grasp the intricacies involved in chemical process calculations. It's like taking apart a toy to see what's inside; by breaking down methanol, you learn about the bonds formed and broken in the reaction, and it's a perfect segue into the discussion of reaction energetics and applications of Hess's Law.
Thermochemical Calculations
Thermochemical calculations are the bread and butter of understanding the energy aspects of chemical reactions. Think of it as accounting, but instead of money, you're counting how much heat energy goes in and out of a chemical system. By foraying into this field, you delve into quantifying the heat absorbed or released during reactions. This is done by employing known values, such as the standard heats of combustion and formation.

To perform these calculations accurately, the law of conservation of energy is applied to the reaction. Since energy cannot be created or destroyed, the total energy of the system must remain constant. Thermochemical equations are balanced not only for mass in terms of atoms but also for energy. This dual balancing act provides precise insights into the energetic feasibility and the conditions necessary for a reaction to occur.
Chemical Reaction Energy Changes
Every chemical reaction involves a change in energy. This change can either be absorbed from the surroundings (endothermic), or released to the surroundings (exothermic). These energy changes are the 'give and take' of the chemical world. They're incredibly important because they determine whether a reaction will occur spontaneously and what energy might be harnessed for use in other applications.

For instance, the decomposition of methanol is a process that, while not energetically complex, highlights the importance of tracking these changes meticulously. In a classroom or an industrial setting, understanding how much energy a reaction requires or releases is paramount for safety, efficiency, and predictive purposes. This knowledge forms the basis of designing chemical processes, selecting materials, and in the case of explosive reactions, taking appropriate safety measures.

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Most popular questions from this chapter

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.

Liquid \(n\) -pentane at \(25^{\circ} \mathrm{C}\) is burned with \(30 \%\) excess oxygen (not air) fed at \(75^{\circ} \mathrm{C}\). The adiabatic flame temperature is \(T_{\mathrm{ad}}\left(^{\circ} \mathrm{C}\right)\) (a) Take as a basis of calculation \(1.00 \mathrm{mol} \mathrm{C}_{5} \mathrm{H}_{12}(1)\) burned and use an energy balance on the adiabatic reactor to derive an equation of the form \(f\left(T_{\mathrm{ad}}\right)=0,\) where \(f\left(T_{\mathrm{ad}}\right)\) is a fourth-order polynomial \(\left[f\left(T_{\mathrm{ad}}\right)=c_{0}+c_{1} T_{\mathrm{ad}}+c_{2} T_{\mathrm{ad}}^{2}+c_{3} T_{\mathrm{ad}}^{3}+c_{4} T_{\mathrm{ad} \mathrm{d}}^{4}\right]\). If your derivation is correct, the ratio \(c_{0} / c_{4}\) should equal \(-6.892 \times 10^{14} .\) Use a spreadsheet program to determine \(T_{\mathrm{ad}}\) (b) Repeat the calculation of Part (a) using successively the first two terms, the first three terms, and the first four terms of the fourth-order polynomial equation. If the solution of Part (a) is taken to be exact, what percentage errors are associated with the linear (two-term), quadratic (three-term), and cubic (four-term) approximations? (c) Why is the fourth-order solution at best an approximation and quite possibly a poor one? (Hint: Examine the conditions of applicability of the heat capacity formulas in Table B.2.)

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.

Synthetically produced ethanol is an important industrial commodity used for various purposes, including as a solvent (especially for substances intended for human contact or consumption); in coatings, inks, and personal-care products; for sterilization; and as a fuel. Industrial cthanol is a petrochemical synthesized by the hydrolysis of ethylene: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v})$$ Some of the product is converted to diethyl ether in the undesired side reaction $$2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\mathrm{v}) \rightleftharpoons\left(\mathrm{C}_{2} \mathrm{H}_{5}\right)_{2} \mathrm{O}(\mathrm{v})+\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) $$The combined feed to the reactor contains 53.7 mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 36.7 \% \mathrm{H}_{2} \mathrm{O}\) and the balance nitrogen, and enters the reactor at \(310^{\circ} \mathrm{C}\). The reactor operates isothermally at \(310^{\circ} \mathrm{C}\). An ethylene conversion of \(5 \%\) is achieved, and the yield of ethanol (moles cthanol produced/mole cthylene consumed) is 0.900 . Data for Diethyl Ether $$\begin{aligned}&\Delta \hat{H}_{f}^{\circ}=-271.2 \mathrm{kJ} / \mathrm{mol} \text { for the liquid }\\\ &\left.\Delta \hat{H}_{v}=26.05 \mathrm{kJ} / \mathrm{mol} \quad \text { (assume independent of } T\right)\end{aligned}$$ $$C_{p}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.08945+40.33 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)-2.244 \times 10^{-7} T^{2}$$ (a) Calculate the reactor heating or cooling requirement in \(\mathrm{kJ} / \mathrm{mol}\) feed. (b) Why would the reactor be designed to yield such a low conversion of ethylene? What processing step (or steps) would probably follow the reactor in a commercial implementation of this process?

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?
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