/*! 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 10 The standard heat of combustion ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 10

The standard heat of combustion \(\left(\Delta \hat{H}_{c}\right)\) of liquid 2,3,3 -trimethylpentane \(\left[\mathrm{C}_{8} \mathrm{H}_{18}\right]\) is reported in a table of physical properties to be \(-4850 \mathrm{kJ} / \mathrm{mol} .\) A footnote indicates that the reference temperature for the reported value is \(25^{\circ} \mathrm{C}\) and the presumed combustion products are \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})\). (a) In your own words, briefly explain what all that means. (b) There is some question about the accuracy of the reported value, and you have been asked to determine the heat of combustion experimentally. You burn 2.010 grams of the hydrocarbon with pure oxygen in a constant-volume calorimeter and find that the net heat released when the reactants and products \(\left[\mathrm{CO}_{2}(\mathrm{g}) \text { and } \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\right]\) are all at \(25^{\circ} \mathrm{C}\) is sufficient to raise the temperature of \(1.00 \mathrm{kg}\) of liquid water by \(21.34^{\circ} \mathrm{C}\). Write an energy balance to show that the heat released in the calorimeter equals \(n_{\mathrm{C}_{3} \mathrm{H}_{18}} \Delta \hat{U}_{\mathrm{c}}^{\mathrm{S}},\) and calculate \(\Delta \tilde{U}_{\mathrm{c}}^{\mathrm{o}}(\mathrm{kJ} / \mathrm{mol}) .\) Then calculate \(\Delta \hat{H}_{c}^{c}\) (See Example 9.1-2.) By what percentage of the measured value does the tabulated value differ from the measured one? (c) Use the result of Part (b) to estimate \(\Delta \hat{H}_{f}\) for 2,3,3 -trimethylpentane. Why would the heat of formation of 2,3,3 -trimethylpentane probably be determined this way rather than directly from the formation reaction?

Short Answer

Expert verified
a) The heat of combustion is -4850 kJ/mol indicating that this amount of energy is released when 1 mol of 2,3,3-trimethylpentane is completely combusted at 25掳C producing CO2 and H2O. b) The calculated heat of combustion is -4853 kJ/mol showing a 0.062% difference from the reported value indicating a good accuracy of the reported value. c) The estimated heat of formation of 2,3,3-trimethylpentane is -238 kJ/mol.

Step by step solution

01

Comprehend the concepts

a) The heat of combustion of a compound is the amount of heat energy released when one mole of that substance undergoes complete combustion (burning) in oxygen. The burning products are typically CO2 (carbon dioxide) gas and H2O (water) gas. The reference temperature referred to in the exercise is the temperature at which the heat of combustion data was taken, which is typically 25 degrees Celsius.
02

Construct the energy balance and calculate the heat of combustion

b) The energy balance for the calorimeter experiment can be written as \( q_{calorimeter} = -n_{C8H18} \Delta \tilde{U}_{c}^{o} \) where \( q_{calorimeter} \) is the heat transferred to the water in the calorimeter. First, calculate the amount (\( n \)) of C8H18 burned: \( n_{C8H18} = \frac{mass}{molar mass} = \frac{2.01 g}{114.22 g/mol} = 0.0176 mol \). Next, calculate the heat transferred (\( q \)) to the water: \( q_{water} = mc\Delta T = (1.00 kg)(4.18 kJ/kg路掳C)(21.34掳C) = 89.2 kJ \). Because the calorimetry is done at constant volume, the heat transferred to the water equals the heat of combustion, therefore, \( \Delta \tilde{U}_{c}^{o} = \frac{-q_{water}}{n_{C8H18}} = -5062 kJ/mol \). However, the heat of combustion at constant volume (\( \Delta \tilde{U}_{c}^{o} \)) is not exactly equal to that at constant pressure (\( \Delta \hat{H}_{c}^{o} \)) because of the work of volume expansion done by the combustion products. Use the equation \( \Delta \hat{H}_{c}^{o} = \Delta \tilde{U}_{c}^{o} + \Delta n_{g}RT \) to get \( \Delta \hat{H}_{c}^{o} \) where \( \Delta n_{g} \) is the change in the number of moles of gas in the reaction (8 for CO2 produced minus 12.5 for O2 consumed), R is the gas constant, and T is the temperature in Kelvin. Plugging the values in gives \( \Delta \hat{H}_{c}^{o} = (-5062 kJ/mol) + [(8)(8.31 J/mol路K)(298 K)] = -4853 kJ/mol \). The difference is \( \frac{|-4853 - (-4850)|}{-4853} = 0.062% \).
03

Calculate the heat of formation

c) The heat of formation (\( \Delta \hat{H}_{f} \)) of 2,3,3-trimethylpentane can be estimated from the heat of combustion using the known heats of formation (\( \Delta \hat{H}_{f} \)) of the combustion products (CO2 and H2O) and the equation: \( \Delta \hat{H}_{f}^{o} = \frac{1}{n_{C8H18}} \left[ q_{water} + n_{CO2} \Delta \hat{H}_{f,CO2}^{o} + n_{H2O} \Delta \hat{H}_{f,H2O}^{o} \right] \) where \( n_{CO2} = 8 \) and \( n_{H2O} = 9 \) are the number of moles of combustion products. Plugging the standard heat of formation values for CO2 and H2O and the value of \( q_{water} \) gives \( \Delta \hat{H}_{f}^{o} = \frac{1}{0.0176 mol} [89.2 kJ + 8 mol(-393.5 kJ/mol) + 9 mol(-285.8 kJ/mol)] = -238 kJ/mol \). The heat of formation of 2,3,3-trimethylpentane would probably be determined this way because it may be impractical or impossible to prepare 2,3,3-trimethylpentane by a simple reaction from its elements (C, H2) for a heat of formation measurement directly.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Heat of Combustion
The concept of "heat of combustion" is integral in understanding thermodynamics. It represents the heat energy released when one mole of a substance burns completely in oxygen. Typically, the products of this combustion are carbon dioxide (CO_2) and water (H_2O), both in their gaseous forms.
For example, when combusting 2,3,3-trimethylpentane (a hydrocarbon), the reaction releases an impressive amount of heat, which can be useful in various energy-related applications.
To denote the heat of combustion, the symbol \( \Delta \hat{H}_{c} \) is used, and the values are often recorded at a standard temperature of 25掳C (298 K). This ensures consistency when comparing different substances. The combustion usually results in exothermic reactions, meaning they release heat to the surroundings.
  • The heat of combustion is negative, indicating heat release.
  • Values are typically recorded at a reference temperature of 25掳C.
  • It's crucial for energy calculations, especially in fuels and engines.
Understanding this concept allows scientists and engineers to estimate how much energy a substance can produce when used as a fuel.
Calorimetry
Calorimetry is a fascinating tool in thermodynamics for measuring the amount of heat transferred in chemical reactions or physical changes. In our exercise, a calorimeter is used to determine the heat of combustion of 2,3,3-trimethylpentane.
A calorimeter is an insulated device used to measure the heat absorbed or released during a chemical reaction, physical change, or heat capacity. When the hydrocarbon is burned in pure oxygen, the heat released is absorbed by the water in the calorimeter, raising its temperature. This temperature change is used to calculate the heat of combustion.
  • Calorimeter measures heat exchange during a reaction.
  • The heat transferred can be calculated using the formula: \( q = mc\Delta T \).
  • In constant-volume calorimetry, \( q = n \Delta U_c^o \), where \( n \) is the number of moles and \( \Delta U_c^o \) is the internal energy change.
The beauty of calorimetry is that it directly connects the observable temperature change to the underlying thermodynamic processes. It helps in understanding how energy flows and is conserved during chemical reactions.
Heat of Formation
The heat of formation (\Delta \hat{H}_{f}) is a crucial concept in thermodynamics that describes the energy change when one mole of a compound is formed from its elements in their standard states.
To estimate the heat of formation for 2,3,3-trimethylpentane, we use its heat of combustion along with the known heats of formation for the combustion products, such as carbon dioxide and water.
This indirect method is often preferred because synthesizing hydrocarbons directly from elements like carbon and hydrogen can be challenging or impractical.
  • \( \Delta \hat{H}_{f} \) is used for determining the energy change during compound formation.
  • It is usually calculated at 25掳C for consistency.
  • Indirect methods use known values from combustion processes to estimate this heat change.
The heat of formation is foundational in calculating and comparing the energies of different substances, which is fundamental in designing chemical processes and understanding energy efficiency.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The synthesis of cthyl chloride is accomplished by reacting ethylene with hydrogen chloride in the presence of an aluminum chloride catalyst: $$\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{HCl}(\mathrm{g}) \stackrel{\text { catallyst }}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{g}) ; \quad \Delta H_{\mathrm{r}}\left(0^{\circ} \mathrm{C}\right)=-64.5 \mathrm{kJ}$$ Process data and a simplified schematic flowchart are given here. Data Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: \(100 \% \mathrm{HCl}(\mathrm{g}), 0^{\circ} \mathrm{C}\) Feed \(\mathrm{B}: 93\) mole \(\% \mathrm{C}_{2} \mathrm{H}_{4}, 7 \% \mathrm{C}_{2} \mathrm{H}_{6}, 0^{\circ} \mathrm{C}\) Reactor: adiabatic, outlet temperature \(=50^{\circ} \mathrm{C}\) Feed A: 100\% HCl(g), 0"C Feed B: 93 mole\% C_H_4, 7\% C_H_0, 0"C Product C: Consists of 1.5\% of the HCl, 1.5\% of the C_2 \(\mathrm{H}_{4}\), and all of the \(\mathrm{C}_{2} \mathrm{H}_{6}\) that enter the reactor Product D: \(1600 \mathrm{kg} \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}) / \mathrm{h}, 0^{\circ} \mathrm{C}\) Recycle to reactor: \(\mathbf{C}_{2} \mathrm{H}_{5} \mathrm{Cl}(\mathrm{l}), 0^{\circ} \mathrm{C}\) \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}: \Delta \hat{H}_{\mathrm{y}}=24.7 \mathrm{kJ} / \mathrm{mol}\) (assume independent of \(T\) ) \(\left(C_{p}\right)_{C_{2} H_{3} C(v)}\left[\mathrm{kJ} /\left(\mathrm{mol} \cdot^{\circ} \mathrm{C}\right)\right]=0.052+8.7 \times 10^{-5} T\left(^{\circ} \mathrm{C}\right)\) The reaction is exothermic, and if the heat of reaction is not removed in some way, the reactor temperature could increase to an undesirably high level. To avoid this occurrence, the reaction is carried out with the catalyst suspended in liquid cthyl chloride. As the reaction proceeds, most of the heat liberated goes to vaporize the liquid, making it possible to keep the reaction temperature at or below 50^'C. The stream leaving the reactor contains cthyl chloride formed by reaction and that vaporized in the reactor. This stream passes through a heat exchanger where it is cooled to \(0^{\circ} \mathrm{C},\) condensing essentially all of the cthyl chloride and leaving only unreacted \(\mathrm{C}_{2} \mathrm{H}_{4}, \mathrm{HCl}\), and \(\mathrm{C}_{2} \mathrm{H}_{6}\) in the gas phase. A portion of the liquid condensate is recycled to the reactor at a rate equal to the rate at which ethyl chloride is vaporized, and the rest is taken off as product. At the process conditions, heats of mixing and the influence of pressure on enthalpy may be neglected. (a) At what rates (kmol/h) do the two feed streams enter the process? (b) Calculate the composition (component mole fractions) and molar flow rate of product stream \(\mathrm{C}\). (c) Write an energy balance around the reactor and use it to determine the rate at which ethyl chloride must be recycled. (d) A number of simplifying assumptions were made in the process description and the analysis of this process system, so the results obtained using a more realistic simulation would differ considerably from those you should have obtained in Parts (a)-(c). List as many of these assumptions as you can think of.

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 \(7.5 \mathrm{MPa}\).

Metallic iron is produced in the reaction between ferrous oxide and carbon monoxide: $$\mathrm{FeO}(\mathrm{s})+\mathrm{CO}(\mathrm{g}) \rightarrow \mathrm{Fe}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}), \quad \Delta H_{\mathrm{r}}=-16.480 \mathrm{kJ}$$ The flowchart shown below depicts this process for a basis of 1 mol \(\mathrm{FeO}\) fed at \(298 \mathrm{K}\). (a) We wish to explore the effects of the variables \(n_{0}\) (the molar feed ratio of CO to \(\mathrm{FeO}\) ), \(T_{0}\) (the feed temperature of the carbon monoxide), \(X\) (the fractional conversion of \(\mathrm{FeO}\) ), and \(T\) (the product temperature) on \(Q\) (the heat duty on the reactor). Without doing any calculations, sketch the shapes of the curves you would expect to obtain for the following plots: (i) Let \(n_{0}=1\) mol \(\mathrm{CO}\) fed/mol \(\mathrm{FeO}\) fed, \(T_{0}=400 \mathrm{K},\) and \(X=1 .\) Vary \(T\) from \(298 \mathrm{K}\) to \(1000 \mathrm{K}\) calculate \(Q\) for each \(T,\) and plot \(Q\) versus \(T\). (ii) Let \(n_{0}=1\) mol CO fed/mol FeO fed, \(T=700\) K, and \(X=1 .\) Vary \(T_{0}\) from 298 K to 1000 K. calculate \(Q\) for each \(T_{0}\), and plot \(Q\) versus \(T_{0}\). (iii) Let \(n_{0}=1\) mol CO fed/mol \(\mathrm{FeO}\) fed, \(T_{0}=400 \mathrm{K},\) and \(T=500 \mathrm{K}\). Vary \(X\) from 0 to 1 calculate \(Q\) for each \(X,\) and plot \(Q\) versus \(X\) (iv) Let \(X=0.5, T_{0}=400 \mathrm{K},\) and \(T=400 \mathrm{K}\). Vary \(n_{0}\) from 0.5 to \(2 \mathrm{mol}\) CO fed/mol FeO fed, calculate \(Q\) for each \(n_{0},\) and plot \(Q\) versus \(n_{0}\) (b) Following is an inlet-outlet enthalpy table for the process: Write an expression for the heat duty on the reactor, \(Q(\mathrm{kJ})\), in terms of the \(n\) s and \(\hat{H}\) s in the table, the standard heat of the given reaction, and the extent of reaction, \(\xi\). Then derive expressions for the quantities \(\xi, n_{1}, n_{2}, n_{3},\) and \(n_{4}\) interms of the variables \(n_{0}\) and \(X\). Finally, derive expressions for \(\hat{H}_{0}\) as a function of \(T_{0}\) and for \(\hat{H}_{1}, \hat{H}_{2}, \hat{H}_{3},\) and \(\hat{H}_{4}\) as functions of \(T\). In the latter derivations, use the following formulas for \(C_{p}[\mathrm{kJ} /(\mathrm{mol} \cdot \mathrm{K})]\) in terms of \(T(\mathrm{K})\) adapted from Table \(2-151\) of Perry's Chemical Engineers' Handbook (sce Footnote 2): $$\begin{aligned}&\mathrm{FeO}(\mathrm{s}): \quad C_{p}=0.05280+6.243 \times 10^{-6} T-3.188 \times 10^{2} T^{-2}\\\&\mathrm{Fe}(\mathrm{s}): \quad C_{p}=0.01728+2.67 \times 10^{-5} T\\\ &\mathrm{CO}(\mathrm{g}): \quad C_{p}=0.02761+5.02 \times 10^{-6} T\\\&\mathrm{CO}_{2}(\mathrm{g}): \quad C_{p}=0.04326+1.146 \times 10^{-5} T-8.180 \times 10^{2} T^{-2}\end{aligned}$$ (c) Calculate the heat duty, \(Q(\mathrm{kJ}),\) for \(n_{0}=2.0 \mathrm{mol} \mathrm{CO}, T_{0}=350 \mathrm{K}, T=550 \mathrm{K},\) and \(X=0.700 \mathrm{mol}\) FeO reacted/mol FeO fed. (d) Prepare a spreadsheet that has the following format (a partial solution is given for one set of process variables): of reaction. Use the spreadsheet to generate the four plots described in Part (a). If the shapes of the plots do not match your predictions, explain why.

An ultimate analysis of a coal is a series of operations that yields the percentages by mass of carbon, hydrogen, nitrogen, oxygen, and sulfur in the coal. The heating value of a coal is best determined in a calorimeter, but it may be estimated with reasonable accuracy from the ultimate analysis using the Dulong formula: $$H H V(\mathrm{k} J / \mathrm{kg})=33,801(\mathrm{C})+144,158[(\mathrm{H})-0.125(\mathrm{O})]+9413(\mathrm{S})$$ where (C), (H), (O), and (S) are the mass fractions of the corresponding elements. The 0.125(O) term accounts for the hydrogen bound in the water contained in the coal. (a) Derive an expression for the higher heating value ( \(H H V\) ) of a coal in terms of \(\mathrm{C}, \mathrm{H}, \mathrm{O},\) and \(\mathrm{S},\) and compare your result with the Dulong formula. Suggest a reason for the difference. (b) A coal with an ultimate analysis of \(75.8 \mathrm{wt} \% \mathrm{C}, 5.1 \% \mathrm{H}, 8.2 \% \mathrm{O}, 1.5 \% \mathrm{N}, 1.6 \% \mathrm{S},\) and \(7.8 \%\) ash (noncombustible) is burned in a power-plant boiler fumace. All of the sulfur in the coal forms \(\mathrm{SO}_{2}\) The gas leaving the furnace is fed through a tall stack and discharged to the atmosphere. The ratio \(\phi\) (\(\mathrm{kg} \mathrm{SO}_{2}\) in the stack gas/kJ heating value of the fuel) must be below a specified value for the power plant to be in compliance with Environmental Protection Agency regulations regarding sulfur emissions. Estimate \(\phi\), using the Dulong formula for the heating value of the coal. (c) An earlier version of the EPA regulation specified that the mole fraction of \(\mathrm{SO}_{2}\) in the stack gas must be less than a specified amount to avoid a costly fine and the required installation of an expensive stack gas scrubbing unit. When this regulation was in force, a few unethical plant operators blew clear air into the base of the stack while the furnace was operating. Briefly explain why they did so and why they stopped this practice when the new regulation was introduced.

A mixture of air and a fine spray of gasoline at ambient (outside air) temperature is fed to a set of pistonfitted cylinders in an automobile engine. Sparks ignite the combustible mixtures in one cylinder after another, and the consequent rapid increase in temperature in the cylinders causes the combustion products to expand and drive the pistons. The back-and-forth motion of the pistons is converted to rotary motion of a crank shaft, motion that in turn is transmitted through a system of shafts and gears to propel the car. Consider a car driving on a day when the ambient temperature is 298 K and suppose that the rate of heat loss from the engine to the outside air is given by the formula $$-\dot{Q}_{1}\left(\frac{\mathrm{kJ}}{\mathrm{h}}\right) \approx \frac{15 \times 10^{6}}{T_{\mathrm{a}}(\mathrm{K})}$$ where \(T_{\mathrm{a}}\) is the ambient temperature. (a) Take gasoline to be a liquid with a specific gravity of 0.70 and a higher heating value of \(49.0 \mathrm{kJ} / \mathrm{g}\), assume complete combustion and that the combustion products leaving the engine are at \(298 \mathrm{K}\), and calculate the minimum feed rate of gasoline (gal/h) required to produce 100 hp of shaft work. (b) If the exhaust gases are well above \(298 \mathrm{K}\) (which they are), is the work delivered by the pistons more or less than the value determined in Part (a)? Explain. (c) If the ambicnt temperature is much lower than \(298 \mathrm{K}\), the work delivered by the pistons would decrease. Give two reasons.
See all solutions

Recommended explanations on Chemistry Textbooks

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Ionic and Molecular Compounds

Read Explanation

Kinetics

Read Explanation

Chemical Reactions

Read Explanation

Making Measurements

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.