Chapter 13: Energy Balances-Thermochemistry (Solution)
Problem 13.1: Using Hess’s law evaluate the heat of formation of solid CaCO3. The following data are available:
Ca(s)+\frac12O_2(g)\rightarrow CaO(s);\;\triangle H_{298}^0=-635.77kJ C(s)+O_2(g)\rightarrow CO_2(s);\;\triangle H_{298}^0=-393.51kJ CaO(s)+CO_2(g)\rightarrow CaCO_3(s);\;\triangle H_{298}^0=-178.15kJProblem 13.2: The heats of combustion of gaseous benzene, gaseous cyclohexane (C6H12), and hydrogen are respectively -3287.4, -3949.2 and -285.58 kJ. Calculate the heat of reaction for the hydrogenation of benzene to cyclohexane.
Problem 13.3: The standard heats of combustion of gaseous ethane and acetaldehyde are 1559.9 kJ/ kmol and – 1192.36 kJ/kmol respectively. The heat of vaporization of water at 298 K is 44.014 kJ/mol. Calculate the heat of oxidation of gaseous ethane to acetaldehyde.
Problem 13.4: Find the standard heat of the formation of methyl chloride from the following data:
CO_2(g)+H_2O(l)+HCl(aq)\rightarrow CH_3Cl(g)+\frac32O_2+aq;\;\triangle H^0=765.4kJ C(s)+O_2(g)\rightarrow CO_2(g);\;\triangle H^0=-393.51kJ H_2(g)+\frac12O_2(g)\rightarrow H_2O(l);\;\triangle H^0=-285.84kJ \frac12H_2(g)+\frac12Cl_2(g)\rightarrow HCl(g);\;\triangle H^0=-92.31kJ HCl(g)+aq\rightarrow HCl(aq);\;\triangle H^0=-75.2kJProblem 13.5: Using Hess’s law, calculate the heat of formation of chloroform (CHCl3) with the help of the following data:
CHCl_3(g)+\frac12O_2(g)+H_2O(l)\rightarrow CO_2(g)+3HCl(g);\;\triangle H_{298}^0=-281.67kJ H_2(g)+\frac12O_2(g)\rightarrow H_2O(l);\;\triangle H_{298}^0=-285.84kJ C(s)+O_2(g)\rightarrow CO_2(g);\;\triangle H_{298}^0=-393.51kJ \frac12H_2(g)+\frac12Cl_2(g)\rightarrow HCl(g);\;\triangle H_{298}^0=-92.31kJProblem 13.6: Heats of reactions were measured experimentally for the following reactions as given below:
C(s)+O_2(g)\rightarrow CO_2(g);\;\triangle H_r=-393.51kJ CO(g)+\frac12O_2(g)\rightarrow CO_2(g);\;\triangle H_r=-282.99kJUse the above data to calculate the heat of formation of CO, which is difficult to measure experimentally.
Problem 13.7: Calculate the heat of formation of methane gas from the following heat of combustion data:
CH_4(g)+2O_2(g)\rightarrow CO_2(g)+2H_2O(l);\;\triangle H_{298}^0=-890.4kJ C(s)+O_2(g)\rightarrow CO_2(g);\;\triangle H_{298}^0=-393.51kJ H_2(g)+\frac12O_2(g)\rightarrow H_2O(l);\;\triangle H_{298}^0=-285.84kJProblem 13.8: The heats of combustion of solid carbon and gaseous CO are respectively -393.51 kJ/mol and 282.99 kJ/mol. Determine the heat of formation of CO.
Problem 13.9: Bituminous coal with a calorific value of 20000 kJ/kg is used for generating steam in a boiler. The efficiency of combustion is 75 %. Assume that coal contains 67 % carbon and 33 % ash. (a) How much coal has to be burned to generate 1 MW of energy? (b) How much air is needed if 50 % excess air is to be used?
Problem 13.10: Calculate the gross and net heating value (kJ/m3 at STP) of a fuel gas analysing 80 % methane, 10 % ethane, 6 % propane and 4 % butane. The standard heats of combustion are -890.4, -1559.9, -2220, -2878.52 kJ/mol, respectively, for methane, ethane, propane, and butane, and the latent heat of vaporization of water at 298 k is 44.014 kJ/mol.
Problem 13.11: Hydrocarbon fuels can be produced from methanol by reactions such as the following:
6CH_3OH(g)\rightarrow C_6H_{12}(g)+6H_2O;\;\triangle H_{298}^0=-142.216kJCompare the standard heat of combustion at 298 K of CH3OH (g) with the standard heat of combustion at 298 K of C6H12 (g), reaction products in both cases being CO2(g) and H2O (g).
Problem 13.12: Calculate the standard heat of reaction at 298 K for the following reaction:
4HCl(g)+O_2(g)\rightarrow2H_2O(g)+2Cl_2(g)The standard heats of formation are -92.311 kJ/mol for HCl (g) and −241.826 kJ/mol for H2O (g).
Problem 13.13: Calculate the heat of reaction for the following reaction:
4NH_3(g)+5O_2(g)\rightarrow4NO(g)+6H_2O(g)The heat of formation data are as follows: NH3 = 46.191 kJ/mol; NO = 90.374 kJ/mol; H2O (g) = −241.826 kJ/mol
Problem 13.14: Calculate the standard heat of reaction for the following:
2FeS_2(s)+11/2O_2(g)\rightarrow Fe_2O_3(s)+4SO_2(g)The standard heats of formation at 298 K are -178.02 kJ/mol for FeS2(s), -822.71 kJ/mol for Fe2O3 (s) and −296.9 kJ/mol for SO2 (g).
Problem 13.15: If the standard heat of formation of H2O (1) is -285.84 kJ/mol and the heat of vaporization of water is 44.01 kJ/mol, what is the standard heat of formation of H2O (g)?
Problem 13.16: The heat of formation in kJ/mol of C3H8(g), CO2(g) and H2O(g) are, respectively, -103.85, -393.51 and -241.826. Estimate the heat of reaction in the standard state for the following:
C_3H_8(l)+5O_2(g)\rightarrow3CO_2(g)+4H_2O(l)The heats of vaporization at 298 K in kJ/mol are 16.00 and 44.04, respectively, for C3H8 and H2O.
Problem 13.17: The standard heat of combustion of benzene at 298 K is – 3267.6 kJ/mol when burned completely to CO2 and liquid water. The standard heat of combustion of hydrogen to liquid water is – 285.84 kJ/mol and that of carbon to carbon dioxide is -393.51 kJ/mol. Calculate the standard heat of formation of liquid benzene.
Problem 13.18: Calculate the standard heat of formation of 1-butene if the standard heat of combustion is 2720.4 kJ/mol and the heats of formation of gaseous CO2 and liquid water are -393.51 kJ/mol and 286.03 kJ/mol respectively.
Problem 13.19: In the production of ethylene from ethane and propane, the following yields were found:
| Reaction | Percent of reactant proceeding by the reaction |
| C_2H_6\rightarrow C_2H_4+H_2 | 100 |
| C_3H_8\rightarrow C_2H_4+CH_4 | 60 |
| C_3H_8\rightarrow C_3H_6+H_2 | 40 |
Calculate the standard heat of reaction for a mixture consisting of equimolar amounts of ethane and propane, given the following heat of formation in kJ/mol:
C2H6(g): -84.667, C3H8: -103.85, C2H4: 52.283, CH4: -74.84, C3H6(g): 20.41.
Problem 13.20: An iron pyrite ore containing 85.0 % FeS2 and 15.0 % gangue is roasted with 200 % excess air according to the reaction
4FeS_2+11O_2\rightarrow2Fe_2O_3+8SO_2in order to produce SO2. The cinder analyzed 5.0 % FeS2. Determine the standard heat of reaction per kilogram of ore. The standard heat of formation data (kJ/mol) are as follows: FeS2(s) = −177.9, Fe2O3 (s) = −822.156, SO2 (g) = 296.90.
Problem 13.21: Calculate the standard heat of reaction for the following:
NH_3+HCl(g)\rightarrow NH_4Cl(s)The standard heats of formation of ammonia, hydrogen chloride and ammonium chloride are -46.2 KJ, -92.4 kJ and -315.6 kJ respectively.
Problem 13.22: Calculate the standard heat of the following reaction:
2FeO(s)+\frac122O_2\rightarrow Fe_2O_3(s)The standard heat of formation of FeO(s) and Fe2O3(s) are -268.1 kJ and –822.7 kJ, respectively.
Problem 13.23: What would be the heat of reaction at constant pressure for the following reaction if the heat evolved under constant volume conditions is 111.760 kJ/mol at 298 K.
C+\frac12O_2\rightarrow CO(g)Problem 13.24: Calculate the heat of reaction at constant volume at 298 K for the following gas phase reaction:
C_2H_4(g)+2H_2(g)\rightarrow2CH_4(g)The standard heat of formation at 298 K is 52.283 kJ/mol for gaseous ethylene and -74.84 kJ/mol for gaseous methane.
Problem 13.25: The standard heat of combustion of liquid benzene at 298 K is -3269.8 kJ/mol. 2.5 g of liquid benzene is placed in a bomb calorimeter at 298 K. The water equivalent of the bomb and surrounding water is 18.4 kJ/K. Determine the rise in temperature of water assuming all water formed on the combustion of benzene is condensed.
Problem 13.26: Calculate the heat of combustion of methane at 800 K given that the heat of combustion at 298 K is -890.4 kJ/mol and the mean heat capacity in the temperature range of 298 to 800 K are 41.868 J/mol K, 30.563 J/mol K, 41.449 J/mol K and 34.332 J/mol K for methane, oxygen, CO2 and water vapour respectively.
Problem 13.27: Calculate the constant pressure and constant volume heat requirements of a catalytic reactor oxidizing methanol to formaldehyde at 775 K using air according to the following reaction:
CH_3OH(g)+\frac12O_2(g)\rightarrow HCHO(g)+H_2O(g);\;\triangle H_{298}^0=-156.67\frac{kJ}{mol}The reactants are admitted in stoichiometric proportions, and methanol is completely converted to formaldehyde. The enthalpies of methanol and formaldehyde vapours at 775 K relative to 298 K are 29.84 kJ/mol and 21.44 kJ/mol, respectively. The mean heat capacities of air, nitrogen and water vapour are, respectively, 30.3 kJ/kmol, 30.0 kJ/kmol and 35.76 kJ/kmol.
Problem 13.28: CO at 1000 K is burned with 90 percent excess air at 800 K. The products of combustion leave the reaction chamber at 1250 K. Calculate the heat evolved in the reaction chamber per kmol of CO burned. The standard heat of reaction at 298 K is 282.99 kJ/mol CO. The mean specific heat applicable in the temperature range of this problem are 29.38, 49.91, 33.13 and 31.43 J/mol K for CO, CO2, O2 and N2 respectively.
Problem 13.29: Carbon monoxide at 473 K is burned at a rate of 1 kmol/h in a furnace using 100% excess air at 373 K. The combustion is complete and the gases leave at 1273 K. Calculate the heat removed in the furnace. The mean heat capacity values in kJ/kmol K in the temperature range of 298 to 1273 K are 49.91, 33.25, 31.43, 29.29, and 29.38 for CO2, O2, N2, air and CO, respectively. The standard heat of combustion of CO at 298 K is -282.99 kJ/mol.
Problem 13.30: Hydrochloric acid is produced from chlorine according to the following reaction:
Cl_2+H_2O\rightarrow2HCl+\frac12O_2The standard heats of formation at 298 K are -241.826, -92.311 kJ/mol for water vapour and hydrochloric acid respectively. Determine the amount of heat to be added or to be removed per kmol of acid obtained if the reactants enter at 500 K with a ratio of 3 mol steam per mol chlorine, reaction goes to completion, and the products leave at 500 K. The mean specific heats of chlorine gas, oxygen and HCl may be taken as 35.0, 33.0, 40.0 J/mol K respectively, and enthalpies of saturated water vapour at 298 K and 500 K are 2547 kJ/kg and 2801 kJ/kg respectively.
Problem 13.31: Ammonia oxidation occurs as per the reaction
4NH_3(g)+5O_2(g)\rightarrow4NO(g)+6H_2O(g);\;\triangle H_R^0=-226\frac{kJ}{mol\;NO}The reactor is fed at a rate of 100 mol/h ammonia and 200 mol/h oxygen, both at 298 K. The product leaves the reactor at 575 K. Given the following heat capacity data at 575 K, calculate the heat transferred from the reactor: O2 = 30.8 kJ/kmol K, NO = 30.74 kJ/kmol K and H2O = 34.8 kJ/kmol K.
Problem 13.32: The standard heat of reaction at 298 K for the following reaction is -42.433 kJ.
C_2H_2(g)+H_2O(g)\rightarrow C_2H_5OH(g)Calculate the heat of reaction at 400 K given that the constants in the heat capacity equation C_p=\alpha+\beta T+\gamma T^2 are as given below: (Cp is in J/mol K and T in K).
| α | β | γ | |
| C2H4 | 11.85 | 119.75×10-3 | -36.53×10-6 |
| H2O | 30.38 | 9.62×10-3 | +1.19×10-6 |
| C2H5OH | 29.27 | 166.39×10-3 | -49.93×10-6 |
Problem 13.33: For the following reaction the standard heat of reaction at 298 K is 164.987 kJ.
CO_2(g)+4H_2(g)\rightarrow2H_2O(g)+CH_4(g)The constants in the heat capacity (J/mol K) equation are given below:
| α | β | γ | |
| CO2 | 26.75 | 42.26×10-3 | -14.25×10-6 |
| H2 | 26.88 | 4.35×10-3 | -0.33×10-6 |
| H2O | 29.16 | 14.49×10-3 | -2.02×10-6 |
| CH4 | 13.41 | 77.03×10-3 | -18.74×10-6 |
Calculate the standard heat of reaction at 773 K.
Problem 13.34: For the following gas-phase reaction, determine the heat of reaction if the reactants enter and products leave at 800 K.
CO_2+4H_2\rightarrow2H_2O+CH_4The standard heats of formation are -393.51 kJ/mol for CO2, -241.826 kJ/mol for H2O(g) and -74.84 kJ/mol for CH4. The constants in the heat capacity equation Cp = a + bT + cT2 are given below where Cp is in kJ/kmol K and T in K.
| a | b×103 | c×106 | |
| Carbon dioxide | 26.540 | 42.454 | -14.2979 |
| Hydrogen | 29.082 | -0.821 | 1.9917 |
| Methane | 13.415 | 77.079 | -18.7569 |
| Water vapor | 30.38 | 9.62 | -1.19 |
Problem 13.35: Methane is burned in a furnace with 100 % excess air to generate steam in a boiler. Methane and dry air enter the combustion chamber at 500 K and the product leaves the furnace at 1200 K. If the effluent gases contain only CO2, O2, H2O and N2, how much heat is absorbed by water per kg of methane burned? The standard heat of combustion of methane at 298 K is -890.4 kJ/mol. The latent heat of vaporization of water at 298 K is 44.014 kJ/mol. The constants in the heat capacity equation Cp = a + bT + cT2 where Cp is in kJ/kmol and T in K are as follows:
| a | b×103 | c×106 | |
| Water | 30.38 | 9.62 | 1.19 |
| Carbon dioxide | 26.540 | 42.454 | -14.2979 |
| Methane | 13.415 | 77.079 | -18.7569 |
| Nitrogen | 27.034 | 5.815 | -0.2889 |
| Oxygen | 25.611 | 13.260 | -4.2077 |
Problem 13.36: The standard heat of combustion of graphite at 298 K is -393.51 kJ/mol. Determine the heat of combustion at 800 K. The heat capacities in J/mol K are given as follows:
Carbon:11.19+1.096\times10^{-2}T-\frac{4.894\times10^5}{T^2} Oxygen:34.62+1.08\times10^{-3}T-\frac{7.859\times10^5}{T^2} CO_2:43.29+1.147\times10^{-2}T-\frac{8.185\times10^5}{T^2}Problem 13.37: Calculate the heat of the following gas-phase reaction
H_2+\frac12O_2\rightarrow H_2O;\;\triangle H_{298}^0=-241.826kJif the reactants are at 473 K and the product is at 993 K. The specific heats (J/mol K) may be evaluated using the data given below: Cp = α + βT + γT2
| α | β | γ | |
| H2 | 29.09 | -8.374×10-4 | 2.0139×10-6 |
| O2 | 25.74 | 12.987×10-3 | -3.864×10-6 |
| H2O | 30.38 | 9.621×10-3 | -1.185×10-6 |
Problem 13.38: A gaseous mixture at 600 K and 1 bar consisting of methane and steam in the ratio 1:2 by mole is sent to a catalytic reformer where the following reaction occurs.
CH_4(g)+H_2O(g)\rightarrow CO(g)+3H_2(g);\;\triangle H_{298}^0=206.284kJThe following side reaction may also occur:
CO(g)+H_2O(g)\rightarrow CO_2(g)+H_2(g);\;\triangle H_{298}^0=-41.20kJMethane is completely converted during the reaction and the product stream contains 17.4 % (mol) CO. Heat is supplied in the reactor so that the products reach a temperature of 1300 K. The mean heat capacities in the temperature range of 298-600 K are 43.8 kJ/kmol K for methane and 34.8 kJ/kmol K for steam, and the mean heat capacities in the temperature range of 298-1300 K are 31.8 kJ/kmol K for CO, 29.8 kJ/kmol K for hydrogen, 50.1 kJ/kmol K for CO2 and 38.9 kJ/kmol K for steam, respectively. Calculate the heat requirement for the reactor per kmol methane.
Problem 13.39: 0.5 mol hydrogen at 300 K, a mixture of 1.5 mol nitrogen and 0.5 mol oxygen at 400 K, and 0.3 mol CO at 500 K are mixed. 50 percent of CO present reacts. If the final temperature of the system raises to 882 K under adiabatic conditions, calculate the standard heat of formation of CO2, if it is four times the standard heat of formation of CO. The mean heat capacities in J/mol K are 32.5 for O2, 31.1 for N2, 29.0 for H2, 31.0 for CO, and 49.0 for CO2.
Problem 13.40: A gas with the analysis 8.5 % SO2, 2.0 % SO3, 9.5 % O2 and 80 % N2 is admitted to a catalytic converter where SO2 gets converted to SO3. The outlet gases contain 82.47 % N2. The reaction occurs at 700 K. Determine the heat evolved per 100 mol gas entering the converter. The data given are: heat of formation of SO3 at 298 K = −395.72 kJ/mol, heat of formation of SO2 at 298 K = 296.9 kJ/mol, mean heat capacity of SO3 = 51.6 J/mol K, mean heat capacity of SO2 = 45.7 J/mol K, mean heat capacity of O2 32.5 J/mol K.
Problem 13.41: Calculate the standard heat of reaction at 800 K for the combustion of pentane gas given that the mean heat capacities in J/mol K are 247 for C5H12, 33.62 for O2, 52.32 for CO2, and 38.49 for H2O. The standard heat of combustion at 298 K is – 3271.67 kJ/mol.
Problem 13.42: Sulphur dioxide gas is oxidized in 100 % excess air with 80 % conversion to sulphur trioxide. The gases enter the converter at 673 K and leave at 723 K. The mean heat capacities are 45, 51, 32 and 31 J/mol K for SO2, SO3, O2, and N2 respectively, and the standard heat of reaction is 98.8 kJ/mol. How much heat is absorbed in the heat exchanger of the converter per kilomole of SO2 introduced?
Problem 13.43: In a fermentation process, sucrose (C12H22O11) is used as a nutrient and is oxidized to CO2 gas and H2O liquid. Calculate the heat of oxidation at 318 K in this fermentation. The standard heat of combustion of sucrose at 298 K = 5648.8 kJ/mol. Mean heat capacities are 1.25 kJ/kg K for sucrose (s), 4.20 kJ/kg K for H2O (1), 29.38 J/mol K for O2 and 37.55 J/mol K for CO2.
Problem 13.44: Pure CO is mixed with 100 % excess air and burned. Only 80 % of CO burns. The reactants are at 373 K and the products at 573 K. Calculate the amount of heat to be added or removed per kmol of CO fed to the reactor. Standard heats of formation in kJ/mol at 298 K are 110.6 for CO and -393.51 for CO2. The mean molal heat capacity between 298 K and T K in kJ/kmol K are
| Gas | T = 373 K | T = 573 K |
| CO | 29.22 | 30.61 |
| CO2 | 43.77 | |
| O2 | 29.84 | 30.99 |
| N2 | 29.17 | 29.66 |
Problem 13.45: An internal combustion engine uses octane as fuel. The air and fuel vapour mixture enter the engine at 298 K. 20 percent excess air is supplied. 75 percent of the carbon present in the fuel is converted to CO2 and the rest to CO, and the combustion products leave the engine at 800 K. Calculate the energy transferred as heat to the engine per kg of fuel burned. The mean heat capacities in J/mol K are 32.5 for O2, 31.1 for N2, 31.0 for CO, 50.0 for H2O and 49.0 for CO2. The heat of formation of n-octane, CO2, CO and H2O vapour at 298 K are -208.75 kJ/mol, – 393.51 kJ/mol, – 110.6 kJ/mol and 241.826 kJ/mol respectively.
Problem 13.46: A mixture of methane and steam at 600 K in the ratio 1:2 is sent to the reactor where the following reaction occurs:
CH_4(g)+H_2O(g)\rightarrow CO(g)+3H_2(g);\;\triangle H_{298}^0=205.813kJThe following undesired side reaction also occurs:
CO(g)+H_2O(g)\rightarrow CO_2(g)+H_2(g);\triangle H_{298}^0=-41.198kJMethane is completely converted and the products contain 15.0 % (mole) CO. If the products get heated to 1300 K, determine the quantity of heat supplied per mole of methane. The following mean heat capacity values (J/mol K) are applicable-methane: 43.79, steam: 34.83, CO: 31.82, H2: 29.81 and CO2: 50.12.
Problem 13.47: One hundred kilograms per hour of dry pyrites at 298 K containing 85 % FeS2 and the rest inert gangue is burned with dry air in a plant for the manufacture of sulphuric acid.
4FeS_2+11O_2\rightarrow2Fe_2O_3+8SO_2 4FeS_2+15O_2\rightarrow2Fe_2O_3+8SO_3The cinder is at 800 K and contains 5 % sulphur as FeS2. Burner gas at 800 K contains 10 % SO2, 7.0 % O2 and 83 % N2 on SO3-free basis. Standard heats of reaction are -827.1 kJ for the first reaction and 1023.7 kJ for the second reaction. The heat capacity of the cinder is 0.75 kJ/kg K. The mean heat capacities in kJ/kmol K are 50.2 for SO3, 46.9 for SO2, 31.4 for O2 and 29.9 for N2. The pressure is 101.3 kPa. Calculate the following: (a) The amount of FeS2 lost in the cinder, kg/h (b) The amount of burner gas, m3/h (c) The amount of heat dissipated in the burner, kJ/h
Problem 13.48: Vinyl chloride is manufactured by the pyrolysis of 1,2,dichloroethane at 773 K.
C_2H_4Cl_2(g)\rightarrow C_2H_3Cl(g)+HCl(g);\;\triangle H_r^0=70.224kJThe conversion is estimated to be 55 %. How much heat is to be supplied to produce 500 kg/h of vinyl chloride from a feed of pure liquid dichloroethane at 290 K? The specific heat in kJ/kmol K is represented by the equation Cp = a + bT + cT2 + dT3 with the following values for the constants:
| Component | a | b×102 | c×105 | d×109 |
| Vinyl chloride | 5.94 | 20.16 | -15.34 | 47.65 |
| HCl | 30.28 | -0.761 | 1.325 | -4.305 |
| Dichloroethane | 20.45 | 23.07 | -14.36 | 33.83 |
Take the specific heat of liquid dichloroethane to be 116 kJ/kmol K, which is constant and the latent heat of vaporization at 298 K is 34300 kJ/kmol.
Problem 13.49: Calculate the maximum flame temperature attained when methane is burned with theoretical air when both fuel and air are at 298 K initially. The mean heat capacities in J/mol K are 62.75 for CO2, 52.96 for H2O, 38.67 for O2 and 37.13 for N2. The standard heat of combustion of methane at 298 K is – 890.4 kJ/mol.
Problem 13.50: A gas mixture consisting of 20 % ethane and 80 % oxygen at 298 K is burned completely after diluting it with double the volume of CO2, also at 298 K. The mean heat capacities in J/mol K are 54.56 for CO2, 43.02 for water vapour and 35.52 for oxygen. The standard heat of reaction is 1428 kJ/mol of ethane at 298 K. Determine the theoretical flame temperature.
Problem 13.51: Calculate the theoretical flame temperature for a gas containing 25 % CO and 75 % N2 when burned with 100 % excess air when both the reactants are at 298 K. The standard heat of formation are -393. 51 kJ/mol for CO2 and -110.6 kJ/mol for CO. The mean molar specific heats in J/mol K are
| T (K) | CO2 | O2 | N2 |
| 800 | 45.43 | 31.59 | 30.31 |
| 1000 | 47.56 | 32.37 | 30.64 |
| 1200 | 49.35 | 33.02 | 31.22 |
| 1400 | 50.82 | 33.60 | 31.77 |
| 1600 | 51.99 | 34.05 | 32.25 |
| 1800 | 53.18 | 34.40 | 32.65 |
Problem 13.52: Dry methane is burned with dry air. Both are at 298 K initially. The flame temperature is 1573 K. If complete combustion is assumed, how much excess air is used?
CH_4+2O_2\rightarrow CO_2+2H_2OStandard heat of reaction is -8.028×105 J/mole of methane reacted. Mean molal heat capacities of gases between 298 K and 1573 K in J/mol K are: 51.88 for CO2, 34.01 for O2, 40.45 for H2O, and 32.21 for N2.
Problem 13.53: The dehydrogenation of butene is an endothermic reaction:
C_4H_8(g)\rightarrow C_4H_6(g)+H_2(g)This reaction is to be carried out adiabatically and at atmospheric pressure, and in order to minimize the temperature drop, the reactor feed will consist of 10 moles of steam per mole of butene. The steam is unreactive. 20 % of butene is converted. The feed mixture enters the reactor at 900 K. Calculate the temperature of the products if mean molar heat capacity in kJ/kmol K for the temperature range of 298 to 900 K are 148.7, 131.2, 36.6, and 29.4 for butene, butadiene, steam and hydrogen respectively. The standard heats of formation are -0.54 kJ/mol for butene and 109.24 kJ/mol for butadiene.
Problem 13.54: Calculate the theoretical flame temperature of a gas mixture consisting of 20 % CO and 80 % N2 when burned with 100 % excess air, both air and gas initially being at 298 K. The standard heat of reaction at 298 K is -282.99 kJ/mol CO. The heat capacities in J/mol K are given by Cp = α + βT+ γT2 where the values of the constants are given as follows:
| α | β | γ | |
| CO2 | 26.54 | 42.45×10-3 | -14.298×10-6 |
| O2 | 25.61 | 13.26×10-3 | -4.208×10-6 |
| N2 | 27.03 | 5.815×10-3 | -0.289×10-6 |
Problem 13.55: Calculate the adiabatic reaction temperature for complete combustion of ethyl alcohol with 25 % excess air. The alcohol and air are supplied at 298 K, and the water formed is in the vapour state. The standard heat of combustion of alcohol is 1366.91 kJ/mol, the latent heat of vaporization of water is 44 kJ/mol, and heat capacities in kJ/kmol K where T is in K are:
CO_2:\;24.55+0.0423T H_2O:\;31.57+0.0069T O_2:\;25.90+0.0116T N_2:\;28.40+0.0022TProblem 13.56: Aluminium metal powder is investigated as a fuel source for jet engines. Calculate the theoretical flame temperature when aluminium metal is burned with 100 % excess air. Assume that the air and metal powder enter at 25 °C and that combustion is complete. Heat capacities in kJ/kg are 140.26 for Al2O3(s) and 142.35 for Al2O3(l). The heat of fusion of Al2O3 is 108.857 kJ/mol. The standard heat of formation of Al2O3(s) is – 1670.91 kJ/mol. The heat capacities of gases in J/mol K are as follows:
C_p(O_2)=30.255+4.207\times10^{-3}T-1.8873\times10^5T C_p(N_2)=27.270+4.930\times10^{-3}T-3.3256\times10^4T^2Problem 13.57: The catalytic converter in a sulphuric acid plant is supplied with a gas mixture analysing 7.8 % SO2, 11.0 % O2 and 81.2 % N2, which enters the converter at a temperature of 675 K where 80 % of SO2 is oxidized to SO3 by combination with the oxygen present in the gases. Assume that there is no heat losses from the reactor. Calculate the temperature of the gas leaving the converter.
Standard heats of formation at 298 K in kJ/mol are: SO2 = -296.9 and SO3 = -395.72. The heat capacities in kJ/kmol K and T in K are as follows:
| Gas | a | b×103 | c×106 |
| Nitrogen | 27.034 | 5.815 | -0.2889 |
| Oxygen | 25.611 | 13.260 | -4.2077 |
| Sulphur dioxide | 29.077 | 41.910 | -15.8847 |
| Sulphur trioxide | 31.208 | 80.093 | -27.7501 |
Problem 13.58: Methane is burned with 20 percent excess air, both methane and air being at 298 K. The standard heat of combustion of methane at 298 K is – 890.4 kJ. The heat capacities in J/mol K are as follows:
C_p(CH_4)=14.150+75.499\times10^{-3}T-17.9915\times10^{-6}T^2 C_p(O_2)=30.255+4.207\times10^{-3}T-1.8873\times10^5T^{-2} C_p(N_2)=27.270+4.930\times10^{-3}T-3.3256\times10^4T^{-2} C_p(CO_2)=45.369+8.688\times10^{-3}T-9.6193\times10^5T^{-2} C_p(H_2O)=28.850+12.055\times10^{-3}T-1.006\times10^5T^{-2}Calculate the adiabatic flame temperature attained.