© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-1 The proton exchange membrane (PEM) fuel cell requires hydrogen as the fuel.
Unfortunately, hydrogen does not readily occur and it must therefore be generated from
another fuel. One way to do this is to reform a hydrocarbon fuel such as methane (CH4).
A preliminary step in the reformation process is to react methane with water in a catalytic
converter to produce hydrogen and carbon monoxide according to:
CH 4  H 2 O  3H 2  CO . Methane and water are fed to reactor in molar proportions of
1 mole of methane to 4 moles of water.
a.) Prepare a plot of the equilibrium hydrogen mole fraction versus temperature for
temperatures between 600 K and 1000 K at 1 atm
b.) How will the equilibrium mole fraction of hydrogen be affected if the pressure in the
converter is raised to 5 atm?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-11 Hydrogen cyanide gas can be formed by reacting acetylene and nitrogen gases in
stoichiometric proportions, according to C2 H 2  N 2  2HCN at 300°C. It has been
proposed that the equilibrium mole fraction of HCN could be increased by increasing the
pressure. To check this possibility, prepare a plot of the mole fraction of HCN versus
pressure for pressures between 1 and 200 atm. At the high pressures encountered, nonideal gas behavior is expected. Assume that the gases form an ideal solution. Critical
point property information for the gases is shown in Table 14.A.11.
Table 14.A-11: Critical properties for C2H2, N2, and HCN
Tcrit [K]
Pcrit [atm]
acentric
factor
C2H2
N2
HCN
308.3 226.2 456.8
60.6 33.5 53.2
0.184 0.040 0.399
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-12 The reaction forming hydrogen from methane and water is CH 4  H 2 O  3H 2  CO .
One more of methane and four moles of water are heated to 1000 K. Prepare a plot of the
pressure required to obtain 1.5 moles of hydrogen as a function of the temperature for
temperatures between 800 K and 1200 K, assuming ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-2 Nitrogen oxide (NO) is one of several pollutants that can be generated in an internal
combustion engine by the reaction between oxygen and nitrogen. Oxides of nitrogen are
precursors to the atmospheric smog that is common in large cities. The rate of reaction
between oxygen and nitrogen increases with increasing temperature.
At high
temperatures, and equilibrium amounts of NO may be generated. In the present case, a
mixture of octane (C8H18) and 20% excess air at 25°C, 1 atm is adiabatically compressed
with a compression ratio of 8. Combustion then initiates at constant volume and
proceeds to complete combustion in an adiabatic manner. It is necessary to estimate the
maximum mole fraction of NO that can occur in the combustion products. This result
can be obtained by answering the following questions.
a.) What is the temperature and pressure of the mixture of octane and air after the
adiabatic compression process has concluded and before combustion is initiated?
b.) What is the temperature and pressure of the combustion products in the cylinder after
combustion occurs? Assume that the combustion process is adiabatic and occurs at
constant volume.
c.) Assume that the reaction of oxygen and nitrogen proceeds to equilibrium while the
temperature and pressure remain constant at the values found in part b.) Also assume
that no other reactions occur. What will the equilibrium mole fraction of NO be
under these conditions? Assume ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-3 A mixture of methane and 350% stoichiometric pure oxygen at 25°C, 1 bar is ignited in a
constant volume, well-insulated container. The only significant decomposition is
assumed to be that of carbon dioxide reacting to produce carbon monoxide and oxygen.
Estimate the maximum temperature, pressure and composition, assuming no hydrogen or
decomposition products other than carbon monoxide are present in the reaction vessel.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-4 Methanol can be mixed with gasoline and used in internal combustion engines. The
oxygen provided in methanol can reduce the concentration of pollutants in the exhaust.
Methanol can be produced in many ways. One way is to react carbon monoxide with
hydrogen according to the following reaction.
CO  2H 2  CH 3OH
a.) Calculate and plot the equilibrium yield of methanol per mole of CO at 125°C as a
function of pressure for pressures between 1 and 10 bar. (Assume ideal gas
behavior.) assuming that CO and H2 are provided in stoichiometric proportions.
b.) It is possible to provide excess carbon monoxide or excess hydrogen rather than
stoichiometric amounts of the two gases. What ratio of CO to H2 would you
recommend if the concentration of methanol is to be maximized at 125°C and 5 bar?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-5 A gas mixture at 400°C, consisting of 7.8% SO2, 10.8% O2 with the remainder being N2,
is passed through a catalytic converter in which the reaction
1/ 2 O 2  SO 2  SO3
occurs adiabatically. The percentages apply on a volumetric basis. Prepare a plot of the
equilibrium temperature at the reactor outlet as a function of pressure for pressures
between 1 atm and 10 atm. Assume ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-6 Portable propane stoves are a concern because they can easily be dropped which could
cause them to malfunction resulting in carbon monoxide generation. Also, the stoves are
sometimes used in closed spaces, against manufacturer’s guidelines. Assume that the
products consist of CO2, CO, O2, N2 and H2O. Plot the mole fraction of CO versus %
theoretical air for values between 80% and 200% at temperatures of 1000 K, 1500 K and
2000 K. What conditions result in the largest mole fraction of carbon monoxide?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-7 One method of producing hydrogen gas is to react hydrogen sulfide (H2S) with water
vapor in proportions of 1 mole of H2S to 5 moles of water vapor. The mixture of H2S and
H2O is provided to the reaction at 1.5 atm and 110°C. The vapor phase reaction is
H 2S  2 H 2 O  3H 2  SO 2
Calculate and plot the required heat input per mole of H2 produced and the equilibrium
mole fraction of hydrogen from this reaction as a function of temperature for
temperatures between 1000 K and 1500 K.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-8 The dissociation of the hydrogen molecule (H2) into elemental hydrogen atoms is being
studied at high temperatures and 1 atm total pressure. Prepare a plot of the mole fraction
of elemental hydrogen as a function of temperature for temperatures between 3000 K and
4000 K by directly minimizing the Gibbs free energy.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.A-9 When ammonia dissociates into hydrogen and nitrogen according to
NH 3  1/ 2 N 2  3 / 2 H 2 , the moles of gas are increased. An engineer has proposed that
the increased moles would increase the pressure and thus the power output of a turbine.
As a preliminary evaluation of this concept, assume ammonia enters an isentropic turbine
at 300°C and 3.5 bar and is exhausted to 1 bar. Assume ideal gas behavior.
a.) Calculate the work per mole of ammonia, assuming dissociation does not occur.
b.) Calculate the work per mole of ammonia, assuming chemical equilibrium is
achieved. NH 3  1/ 2 N 2  3 / 2 H 2 . Compare the result with the value from part a.).
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
1  H 


n  T  P
where n is the total moles of the mixture and H is the enthalpy of the mixture. An
augmentation of the effected molar specific heat can result when a chemical reaction
occurs as a result of a temperature change. An example of this situation can occur in
mixtures of NO2 and N2O4, for which the reaction N 2 O 4  2 NO 2 achieves chemical
equilibrium rapidly at the temperatures considered in this problem. Calculate and plot the
effective molar specific heat capacity of an equilibrium mixture of NO2 and N2O4 as a
function of temperature for temperatures between 300 K and 400 K at 1 atm and at 5 atm.
Compare the effective specific with the “frozen specific heat capacity”, i.e., the specific
heat capacity of the mixture at the equilibrium composition, assuming no reaction occurs.
14.A-10 An effective molar specific heat capacity of a mixture can be defined as
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-1 Furnaces are designed so that the combustion of the fuel occurs with excess air.
However, an improperly sized fuel jet or an air restriction can result in insufficient air
supply. The major concern in this case is the formation of carbon monoxide gas, which is
deadly. In the present case, the fuel is methane. The combustion gas that exits the
furnace when 90% of theoretical air is provided is believed to be a mixture of CH4, CO2,
CO, N2, NO, H2O, H2 and O2.
a.) Prepare a plot of the mole fraction of CO versus temperature for temperatures between
1500 K and 2500 K at atmospheric pressure using the LaGrange method.
b.) What is the maximum temperature that the combustion products gas mixture can
reach without external heating?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-2 The combustion process that occurs in spark-ignition engines produces small amounts of
carbon monoxide (CO), nitrogen oxide (NO) and nitrogen dioxide (NO2). Although the
amounts of these gases that are produced are small, the large number of engines and the
subsequent reactions involving these gases that take place in the atmosphere causes these
gases to be a concern. Assume that octane (C8H18) and air are provided in stoichiometric
amounts at atmospheric pressure and 25°C to an engine and that the combustion process
occurs adiabatically. Estimate the molar amounts of CO, NO and NO2 that are produced
for each molar of octane combusted and the adiabatic combustion temperature.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-3 Internal combustion engines are responsible for the production of carbon monoxide and
oxides of nitrogen that are major contributors to atmospheric pollution. The rate at which
oxygen and nitrogen react to form NO increases with increasing temperature. At the high
temperatures achieved during the combustion process, the rate is sufficient for NO to
reach its equilibrium value. The combustion mixture is then exhausted to the
atmosphere, which freezes the reverse reaction so that the NO remains in the exhaust. In
a particular case, octane is combusted with 20% excess air resulting in a gas mixture
consisting of CO2, CO, N2, NO, H2O, and O2. Prepare a plot of the equilibrium mole
fractions of CO and NO as a function of maximum combustion temperature for
temperatures between 1500 K and 2000 K at 1 atm. Determine the equilibrium state by
directly minimizing the Gibbs free energy of the products.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-4 Higher compression ratios tend to increase internal combustion engine efficiency, but
they also result in higher rates of CO and NO production. Consider an eight cylinder
engine with each cylinder having a bore of 4.00 in and a stroke of 4.52 in operating at
3000 rpm (4-stroke cycle) combusting octane (C8H18) with stoichiometric air at 75°F, 1
atm. Assume the compression process occurs isentropically. The combustion products
are CO2, CO, N2, NO, H2O, and O2. Assume that the equilibrium amounts of CO and NO
are produced at the adiabatic combustion temperature and then “frozen” at these
compositions so that they appear in the exhaust gas. Prepare plots of adiabatic
combustion temperature and the rates of production of CO and NO as a function of
compression ratio, for compression ratios between 6 and 12. Comment on the trends that
you observe.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-5 You have been asked to investigate methods to improve the energy efficiency of the
ammonia synthesis process. Currently the process is operated at 300 atm and 425°C with
the nitrogen and hydrogen provided in stoichiometric proportions at 25°C, 300 atm. One
idea that you have is to provide excess nitrogen since nitrogen is inexpensive. Prepare
plots of the mole fraction of ammonia and the required heat input per mole of ammonia
produced as a function of the ratio of the actual nitrogen provided to the stoichiometric
amount. Note that, because of the high pressures, ideal gas law behavior is not valid.
Assume that the mixture obeys ideal solution theory.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-6 Hydrogen reforming is one of the main processes used for the industrial production of
hydrogen. It is based on the following reaction of methane with water vapor:
CH4 + H2 O  CO + 3H2
The reaction is endothermic and the equilibrium constant at low temperature results in a
very small yield of hydrogen. Thus, the reforming is performed at 1100°C. This
temperature remains constant during the reaction by combusting controlled amounts of
methane with oxygen which reacts according to:
2CH 4 + 3O2  2CO + 4H 2 O
A well-insulated reactor operating at steady conditions is fed with separate streams of 1
kmol/sec of methane, 1 kmol/sec of water vapor and oxygen at a rate which is to be
determined. All streams are preheated so that they enter the reactor at 1100°C and all
streams are at 1 atm pressure. The oxygen is completely consumed. Leaving the reactor
is a mixture of methane, water vapor, carbon monoxide, and hydrogen in chemical
equilibrium at 1100°C, 1 atm. Determine the required molar flow rate of oxygen and the
mole fraction of hydrogen in exit stream.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-7 The presence of even small amounts of the various oxides of nitrogen in combustion
products is an important factor from an air pollution perspective. Consider a mixture
consisting of the following basic products of combustion: 11% CO2, 12% H2O, 4% O2
and 73% N2 with the percentages on a volumetric basis. At the high temperatures and
pressure occurring within the cylinder of an engine both NO and NO2 may form; Carbon
monoxide will also likely be formed. Prepare plots showing the moles fractions of CO,
NO and NO2 as a function of pressure for pressures between 5 and 15 atm at 2000 K.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-8 Acetylene (C2H2) at 25°C, 1 atm is used a fuel for a cutting torch. The fuel is reacted
with air at 25°C, 1 atm resulting in products that include CO2, CO, H2O, H, and N2, all at
1 atm. Calculate the equilibrium temperature of the products as a function for %
theoretical air for values between 60% and 120%. At what theoretical % does the highest
temperature occur?
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-9 1.6 grams of methane (CH4) are placed into an evacuated 2 liter pressure cylinder at
25°C. The cylinder and its contents are then slowly heated to 1500°C. Methane is
expected to dissociate into elemental carbon and hydrogen gas during this heating process
according to: CH 4  C  2H 2 . Prepare plots of the expected pressure in the cylinder
and the methane mole fraction as a function of temperature for temperatures between
50°C and 1500°C. Assume ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-10 The vast coal deposits in the U.S. and elsewhere are a likely result of a chemical
equilibrium process in which small hydrocarbon molecules disassociated into carbon. A
simple model to study this process is provided by the chemical equilibrium of the ethane
formation reaction 2 C  3H 2  C2 H 6 . As a part of a study of this reaction, a 4 liter
volume is filled with pure ethane at 15 bar and 25°C. The ethane is then slowly heated to
1000°C.
a.) Determine the pressure and mole fraction of hydrogen assuming ideal gas behavior.
b.) Non-ideal gas behavior can be expected at the high pressures involved in this process.
Repeat the calculations requested in part a), but assume that the gases form an ideal
solution, but not necessarily an ideal gas mixture.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-11 Coal is increasingly less desirable as a fuel because it contains trace elements (e.g.,
mercury, sulfur) that form pollutant when combusted and because of the large amount of
CO2 that is produced per unit energy. A proposed alternative is react coal (assumed here
to be pure carbon) with steam at 825°C and a pressure that is to be determined. The
following reactions are believed to occur simultaneously.
C  H 2 O  CO  H 2
CO  H 2 O  CO 2  H 2
C  CO 2  2CO
Prepare plots of the hydrogen can CO mole fractions as a function of pressure for
pressures between 1 and 12 atm. Assume ideal gas behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-12 Methane needs to be steam-reformed to produce hydrogen for use in a fuel-cell system.
The desired reaction is: CH 4  2 H 2 O  CO 2  4 H 2 . However, other species may be
present at equilibrium. The equilibrium condition can be considered to be a mixture of
CO2, CO, H2, H2O, CH4 and solid carbon. Molecular oxygen has been shown to not be
one of the products. The presence of CO is a problem since CO is a poison to some types
of fuel cell systems.
a.) Calculate and plot the equilibrium mole fractions of hydrogen and carbon monoxide
for a stoichiometric mixture of methane and water at 1 atm as a function of
temperature for temperatures between 500 and 1000 K. Assume that solid carbon
does not form. Ideal gas behavior can be assumed.
b.) Repeat part b but in this case, allow for the possibility that solid carbon may be
present at equilibrium. Plot the moles of solid carbon per mole of methane that form.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-13 Acetylene (C2H2) at 25°C, 1 atm is used a fuel for a cutting torch. The fuel is reacted
with air at 25°C, 1 atm resulting in products that include CO2, CO, H2O, H, and N2, all at
1 atm. The proportions of the acetylene and air are controlled by adjustable valves. A
student has noticed that smoke appears if he adjusts the torch to run lean, i.e., with
insufficient air. He suspects that the smoke could be visible carbon particles that form
during the reaction. Is this possible? Assume that the products exit the torch at
equilibrium at 800 K. Calculate and plot the moles of solid carbon that form per mole of
acetylene for theoretical air percentages between 20% and 100%. Assume ideal gas
behavior.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-14 Calcium carbonate (CaCO3) will spontaneously dissociate into calcium oxide (CaO) and
carbon dioxide gas (CO2) when heated if the equilibrium pressure of CO2 is sufficiently
low. Calcium carbonate is placed in an evacuated container and its temperature is raised
from 25°C to 1000°C. Prepare a plot of the expected pressure as a function of
temperature. Note that property data for solid CaCO3 and CaO are provided in the NASA
external procedure. Instructions for using this procedure can be found in the Function
Information dialog (Options menu) with the External routines button selected.
© S.A. Klein and G.F. Nellis
Cambridge University Press, 2011
14.B-15 A constant volume bomb is charged with 62 g of pure ethane (C2H6) at 24°C, 5 bar. The
bomb and its contents are then heated to 500°C and allowed to come to equilibrium. The
equilibrium products are expected to be ethane, methane (CH4), ethylene (C2H4),
acetylene (C2H2), hydrogen (H2), and possibly solid carbon.
a) What is the pressure and the composition of the bomb contents at the 500°C
equilibrium state assuming that carbon does not form. Assume the gases form an
ideal gas mixture.
b) Repeat part a assuming carbon may be a product. Note that properties of solid carbon
are available from the Solid/Liquid property library in EES with the species name set
to ‘C(gr)’.