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Chapter 9: Problem 11

A culture of the fungus aspergillus niger is used industrially in the manufacture of citric acid and other organic species. Cells of the fungus have an ultimate analysis of \(\mathrm{CH}_{1,79} \mathrm{N}_{0.2} \mathrm{O}_{0.5}\), and the heat of formation of this species is necessary to approximate the heat duty for the bioreactor in which citric acid is to be produced. You collect a dried sample of the fungus and determine its heat of combustion to be \(-550 \mathrm{kJ} / \mathrm{mol} .\) Estimate the heat of formation \((\mathrm{kJ} / \mathrm{mol})\) of the dried fungus cells.

Short Answer

Expert verified
The heat of formation of the dried fungus cells is estimated to be -541.55 kJ/mol.

Step by step solution

01

Given Values

Identify the given values. The ultimate analysis of the fungus gives us its composition: \(CH_{1.79}N_{0.2}O_{0.5}\). We know the heat of combustion to be -550 kJ/mol.
02

Writing the Combustion Reaction

Write the combustion reaction for the fungus. A combustion reaction involves reacting the substance with oxygen (O2) to produce carbon dioxide (CO2), water (H2O), and for substances containing nitrogen - nitrogen dioxide (NO2). Thus, the combustion reaction for the fungus can be written as: \(CH_{1.79}N_{0.2}O_{0.5} + xO2 \rightarrow yCO2 + zH2O + wNO2\)
03

Balancing the Combustion Reaction

To balance the combustion reaction, balance the atoms one by one. Balancing the carbon, hydrogen, and nitrogen atoms yields:\(CH_{1.79}N_{0.2}O_{0.5} + 1.395O2 \rightarrow 1.79CO2 + 0.895H2O + 0.1NO2\)
04

Estimating the Heat Formation

Use the heat of combustion and the heats of formation of the elements in the product side to estimate the heat of formation of the fungus. The heats of formation (\( \Delta H_f^o\)) of CO2, H2O, and NO2 are -393.5 kJ/mol, -241.8 kJ/mol, and 33.18 kJ/mol respectively. The heat of formation of the oxygen is 0 because it comes from the element itself. The heat of combustion (\( \Delta H_C\)) is the difference between the heat of formation of the products and the heat of formation of the reactant (the fungus). Thus, we get:\(\Delta H_C = \sum \Delta H_f^o(products) - \Delta H_f^o(reactants)\)\(\Delta H_f^o(reactants) = \sum \Delta H_f^o(products) - \Delta H_C\)Substituting the values:\(\Delta H_f^o(fungus) = [1.79*(-393.5) + 0.895*(-241.8) + 0.1*33.18] - (-550)\)
05

Calculation

The final step is to plug in the numbers. Calculate the right side of the equation to obtain the heat of formation of the fungus. Let's calculate this.\(\Delta H_f^o(fungus) = -878.265 - 216.61 +3.32 + 550 = -541.55 kJ/mol\)

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Key Concepts

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

Combustion Reaction
Understanding combustion reactions is crucial when dealing with energy changes in chemical reactions. A combustion reaction typically occurs when a substance, often a hydrocarbon, reacts with oxygen to produce heat and light. In its general form, the reaction results in the production of carbon dioxide (CO2) and water (H2O). For organic compounds containing nitrogen, such as the fungus aspergillus niger in the exercise, nitrogen oxides (NOx) may also be produced.

In the context of the exercise, the combustion reaction is used to determine the heat released when a molecule of the fungus is burnt in the presence of oxygen. The heat of combustion is a measurable quantity and is crucial for estimating the heat of formation, which is the energy change when one mole of a compound is formed from its elements in their standard states.

When solving problems involving combustion reactions, it is essential to first write down a balanced chemical equation. To balance the equation, one must ensure that the number of atoms of each element is the same on both sides of the equation. If the equation is balanced, it can accurately represent the conservation of mass in the reaction.
Chemical Thermodynamics
At the heart of chemical thermodynamics is the study of energy transformations during chemical reactions. The heat of formation and the heat of combustion are two fundamental concepts under this domain. The heat of formation, \( \Delta H_f^o \), is defined as the energy change when one mole of a compound is formed from its elements under standard conditions (typically 25掳C and 1 atmosphere pressure).

On the other hand, the heat of combustion, \( \Delta H_C \), represents the energy released when one mole of a substance burns completely in oxygen. According to the first law of thermodynamics, energy cannot be created or destroyed, only transformed. Therefore, in the exercise, the heat of combustion is related to the heats of formation of the products and the reactant, providing a pathway to estimate the heat of formation of the dried fungus cells.

These concepts enable us to understand the energy flow in a bioreactor and optimize processes such as the production of citric acid referenced in the exercise. Calculating the heat of formation gives insight into the overall energy requirements for maintaining the bioreactor conditions necessary for production.
Stoichiometry
Stoichiometry is the quantitative relationship between the amounts of substances involved in a chemical reaction. It plays a vital role in understanding the proportions of reactants and products. In a well-balanced chemical reaction, the stoichiometry allows us to use the coefficients in the reaction to relate the moles of each substance consumed or produced.

Importance of Balancing Equations

For the equation in the exercise, balancing is performed for the fungus combustion: for every mole of CH1.79N0.2O0.5, we react it with oxygen to produce corresponding amounts of CO2, H2O, and NO2. Using stoichiometry ensures that the law of conservation of mass is obeyed and that the materials balance can be calculated.

Using Stoichiometry for Heat Calculations

After balancing the combustion equation of the fungus, stoichiometry tells us the ratio of the fungus to the formed compounds. We use this information along with the known heats of formation to calculate the heat of formation of the reactant (fungus) from the heat of combustion. This process is a practical application of stoichiometry where quantitative chemical information influences thermodynamic estimations in a real-world scenario like the citric acid production in the given exercise.

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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.

You are checking the performance of a reactor in which acetylene is produced from methane in the reaction $$2 \mathrm{CH}_{4}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g})$$ An undesired side reaction is the decomposition of acetylene: $$\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{C}(\mathrm{s})+\mathrm{H}_{2}(\mathrm{g})$$ Methane is fed to the reactor at \(1500^{\circ} \mathrm{C}\) at a rate of \(10.0 \mathrm{mol} \mathrm{CH}_{4} / \mathrm{s}\). Heat is transferred to the reactor at a rate of \(975 \mathrm{kW}\). The product temperature is \(1500^{\circ} \mathrm{C}\) and the fractional conversion of methane is 0.600 . A flowchart of the process and an enthalpy table are shown below. (a) Using the heat capacitics given below for enthalpy calculations, write and solve material balances and an energy balance to determine the product component flow rates and the yield of acctylene (mol \(\mathbf{C}_{2} \mathbf{H}_{2}\) produced/mol \(\mathbf{C H}_{4}\) consumed). $$\begin{aligned}\mathrm{CH}_{4}(\mathrm{g}): & C_{p} \approx 0.079 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{g}): & C_{p} \approx 0.052 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{H}_{2}(\mathrm{g}): & C_{p} \approx 0.031 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right) \\ \mathrm{C}(\mathrm{s}): & C_{p} \approx 0.022 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\end{aligned}$$ For example, the specific enthalpy of methane at \(1500^{\circ} \mathrm{C}\) relative to methane at \(25^{\circ} \mathrm{C}\) is \(\left[0.079 \mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]\left(1500^{\circ} \mathrm{C}-25^{\circ} \mathrm{C}\right)=116.5 \mathrm{kJ} / \mathrm{mol}\) (b) The reactor efficiency may be defined as the ratio (actual acetylene yield/acetylene yield with no side reaction). What is the reactor efficiency for this process? (c) The mean residence time in the reactor \([\tau(\mathrm{s})]\) is the average time gas molecules spend in the reactor in going from inlet to outlet. The more \(\tau\) increases, the greater the extent of reaction for every reaction occurring in the process. For a given feed rate, \(\tau\) is proportional to the reactor volume and inversely proportional to the feed stream flow rate. (i) If the mean residence time increases to infinity, what would you expect to find in the product stream? Explain. (ii) Someone proposes running the process with a much greater feed rate than the one used in Part (a), separating the products from the unconsumed reactants, and recycling the reactants. Why would you expect that process design to increase the reactor efficiency? What else would you need to know to determine whether the new design would be cost-effective?

The heating value of a fuel oil is to be measured in a constant-volume bomb calorimeter. The bomb is charged with oxygen and \(0.00215 \mathrm{lb}_{\mathrm{m}}\) of the fuel and is then sealed and immersed in an insulated container of water. The initial temperature of the system is \(77.00^{\circ} \mathrm{F}\). The fuel-oxygen mixture is ignited, and the fuel is completely consumed. The combustion products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{v}) .\) The final calorimeter temperature is \(89.06^{\circ} \mathrm{F}\). The mass of the calorimeter, including the bomb and its contents, is 4.62 \(\mathrm{Ib}_{\mathrm{m}},\) and the average heat capacity of the system \(\left(C_{v}\right)\) is \(0.900 \mathrm{Btu} /\left(\mathrm{b}_{\mathrm{m}} \cdot^{\circ} \mathrm{F}\right)\). (a) Calculate \(\Delta \hat{U}_{\mathrm{S}}^{\circ}\) \(\left(\mathrm{B} \mathrm{tu} / \mathrm{lb}_{\mathrm{m}} \text { oil }\right)\) for the combustion of the fuel oil at \(77^{\circ} \mathrm{F}\). Briefly explain your calculation. (b) What more would you need to know to determine the higher heating value of the oil?

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 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.
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