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Chapter 9: Problem 2

The standard heat of combustion of liquid \(n\) -octane to form \(\mathrm{CO}_{2}\) and liquid water at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm}\) is \(\Delta \hat{H}_{\mathrm{c}}=-5471 \mathrm{kJ} / \mathrm{mol}\) (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 states), 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) If \(25.0 \mathrm{mol} / \mathrm{s}\) of liquid octane is consumed and the reactants and products are all at \(25^{\circ} \mathrm{C}\), estimate the required rate of heat input or output (state which) in kilowatts, assuming that \(Q=\Delta H\) for the process. What have you also assumed about the reactor pressure in your calculation? (You don't have to assume that it equals 1 atm.) (d) The standard heat of combustion of \(n\) -octane vapor is \(\Delta \hat{H}_{\mathrm{c}}=-5528 \mathrm{kJ} / \mathrm{mol}\). What is the physical significance of the \(57 \mathrm{kJ} / \mathrm{mol}\) difference between this heat of combustion and the one given previously? (e) The value of \(\Delta \hat{H}_{c}\) given in Part (d) applies to \(n\) -octane vapor at \(25^{\circ} \mathrm{C}\) and 1 atm, and yet the normal boiling point of \(n\) -octane is \(125.5^{\circ} \mathrm{C}\). Can \(n\) -octane exist as a vapor at \(25^{\circ} \mathrm{C}\) and a total pressure of 1 atm? Explain your answer.

Short Answer

Expert verified
a) 1 mole of octane reacts with oxygen to form CO2 and water, the enthalpy change is -5471 kJ/mol. b) The reaction is exothermic and cooling is needed to maintain a constant temperature. c) The rate of heat output is 136.775 kW. d) The difference of 57 kJ/mol can be attributed to the enthalpy of vaporization. e) At 25 掳C and 1 atm, octane can exist as a vapor through evaporation.

Step by step solution

01

Understand Heat of Combustion

The heat of combustion implies that when one mole of octane reacts completely with oxygen to form carbon dioxide and water, the change in enthalpy is -5471 kJ/mol. This is an enthalpy change at constant pressure and temperature (25 掳C and 1 atm).
02

Determine the Nature of the Reaction

As the change in enthalpy is negative, the reaction is exothermic, i.e., it releases heat. To keep the temperature constant at 25 掳C, the system would have to be cooled, as the reaction itself generates heat. If the reactor ran adiabatically (without exchange of heat with the surroundings), the temperature would increase. The negative enthalpy change also means that less energy is required to break the molecular bonds of the reactants compared to the energy that is released when the product bonds form.
03

Estimate the Required Rate of Heat Input or Output

First, calculate the total heat of combustion using the formula Q = 螖Hc * n, where n = 25 mol/s and 螖Hc = -5471 kJ/mol. Then, convert this value from kJ/s to kW (1 kJ/s = 1 kW). Note that in this calculation, it's assumed that the reactor pressure is 1 atm.
04

Understand the Physical Significance of the Difference between Heats of Combustion

The difference of 57 kJ/mol between the heat of combustion of liquid octane and octane vapor can be explained by the enthalpy of vaporization. This extra energy is required to transform the liquid octane into vapor. In the case of the vapor, the combustion process happens already above the boiling point of the substance, hence already incorporating the energy required for the phase transition.
05

Determine the Physical State of Octane at Given Conditions

Under normal atmospheric conditions, octane exists as a liquid. However, at 25 掳C and 1 atm, it can exist as a vapor through the process of evaporation, though not all of it would be evaporated. It doesn't have to be at its boiling point to exist as a vapor.

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Key Concepts

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

Enthalpy Change
Enthalpy change represents the heat absorbed or released during a chemical reaction under constant pressure. It's a vital component in understanding how reactions progress and the energy involved. In the context of combustion, when 1 mole of liquid octane combusts completely with oxygen to form carbon dioxide and water, the enthalpy change is \(-5471\) kJ/mol. The negative sign indicates that the reaction releases energy, as the system loses heat to the surroundings.
  • Energy is measured in terms of heat absorbed/released.
  • Negative enthalpy implies exothermic reactions.
  • Calculations often assume ideal conditions of pressure and temperature.
In real-life applications, understanding the enthalpy change helps in designing systems that manage heat effectively, ensuring reactions proceed safely and efficiently without undesired effects or heat build-up.
Exothermic Reactions
Exothermic reactions are characterized by the release of heat. This is an essential concept in understanding energy changes during chemical processes. In the combustion of octane, the \(-5471\) kJ/mol enthalpy change confirms that the reaction is exothermic.
Key characteristics of exothermic reactions include:
  • Release of heat to the surroundings, making them feel warm.
  • Negative enthalpy change values, indicating energy release.
  • Common in oxidations, combustion, and respiratory processes.
When these reactions occur, they may require cooling to maintain a constant temperature, as the natural tendency is for the system's temperature to increase. In controlled environments, understanding exothermic properties is crucial for preventing overheating and ensuring system stability.
Phase Transitions
Phase transitions involve changes between different states of matter, typically solids, liquids, and gases. During combustion, the phase transition of octane from a liquid to vapor requires energy, known as the enthalpy of vaporization.
The heat of combustion of octane vapor \(-5528\) kJ/mol is different from that of liquid octane, indicating that \(57\) kJ/mol is used for phase transition.
  • Energy is absorbed or released during phase transitions.
  • Liquid to vapor transition involves additional energy expenditure.
  • Combustion above boiling points incorporates this energy naturally.
Understanding phase transitions helps in designing processes that take these energy changes into account, ensuring efficient material and energy use in chemical processes.
Adiabatic Processes
Adiabatic processes are those that occur without the transfer of heat or mass between a system and its environment. When a reaction, like the combustion of octane, happens adiabatically, the system's temperature increases because the released energy isn't lost to the surroundings.
Considerations in adiabatic processes include:
  • No heat exchange with the environment, leading to temperature rise.
  • Ideal for insulated systems, minimizing external influences.
  • Essential in thermodynamic calculations and predictions.
In practical settings, understanding adiabatic processes helps in the effective design of reactors and thermal management systems, ensuring reactions are efficient without unintended energy loss or gain from the surroundings.

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Most popular questions from this chapter

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?

The standard heat of the reaction $$\mathrm{CaC}_{2}(\mathrm{s})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{l}) \rightarrow \mathrm{CaO}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g})+5 \mathrm{H}_{2}(\mathrm{g})$$ is \(\Delta H_{\mathrm{t}}^{\circ}=+69.36 \mathrm{kJ}\). (a) Is the reaction exothermic or endothermic at \(25^{\circ} \mathrm{C}\) ? Would you have to heat or cool the reactor to kecp 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? (b) Calculate \(\Delta U_{\mathrm{r}}^{\circ}\) for this reaction. (See Example \(9.1-2 .\) ) Briefly explain the physical significance of your calculated value. (c) Suppose you charge \(150.0 \mathrm{g}\) of \(\mathrm{CaC}_{2}\) and liquid water into a rigid container at \(25^{\circ} \mathrm{C}\), heat the container until the calcium carbide reacts completely, and cool the products back down to \(25^{\circ} \mathrm{C}\). condensing essentially all the unconsumed water. Write and simplify the energy balance equation for this closed constant-volume system and use it to determine the net amount of heat (kJ) that must be transferred to or from the reactor (state which). (d) If in Part (c) the term "rigid container" were replaced with "container at a constant pressure of 1 atm," the calculated value of \(Q\) would be slightly in error. Explain why. (e) If you placed 1 mol of solid calcium carbide and 5 mol of liquid water in a container at \(25^{\circ} \mathrm{C}\) and left them there for several days, upon returning you would not find 1 mol of solid calcium oxide, 2 mol of carbon dioxide, and 5 mol of hydrogen gas. Explain why not.

A methanol-synthesis reactor is fed with a gas stream at \(220^{\circ} \mathrm{C}\) consisting of 5.0 mole\% methane, \(25.0 \%\) CO, \(5.0 \% \mathrm{CO}_{2},\) and the remainder hydrogen. The reactor and feed stream are at \(7.5 \mathrm{MPa}\). The primary reaction occurring in the reactor and its associated equilibrium constant are $$\begin{array}{l}\mathrm{CO}+2 \mathrm{H}_{2} \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH} \\\K=\frac{y_{\mathrm{CH}, \mathrm{OH}} y_{\mathrm{H}_{2}}}{y_{\mathrm{CO}} y_{H_{2}}^{2} P^{2}}=\exp \left(\begin{array}{c}21.225+\frac{9143.6}{T}-7.492 \ln T \\ +4.076 \times 10^{-3} T-7.161 \times 10^{-8} T^{2}\end{array}\right)\end{array}$$ where \(T\) is in kelvins. The product stream may be assumed to reach equilibrium at \(250^{\circ} \mathrm{C}\). (a) Determine the composition (mole fractions) of the product stream and the percentage conversions of CO and \(\mathrm{H}_{2}\). (b) Neglecting the effect of pressure on enthalpies, estimate the amount of heat (kJ/mol feed gas) that must be added to or removed from (state which) the reactor. (c) Calculate the extent of reaction and heat removal rate (kJ/mol feed) for reactor temperatures between \(200^{\circ} \mathrm{C}\) and \(400^{\circ} \mathrm{C}\) in \(50^{\circ} \mathrm{C}\) increments. Use these results to obtain an estimate of the adiabatic reaction temperature. (d) Determine the effect of pressure on the reaction by evaluating extent of conversion and rate of heat transfer at \(1 \mathrm{MPa}\) and \(15 \mathrm{MPa}\). (e) Considering the results of your calculations in Parts (c) and (d), propose an explanation for selection of the initial reaction conditions of \(250^{\circ} \mathrm{C}\) and \(7.5 \mathrm{MPa}\).

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.
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