CHAPTER 12 PROBLEMS

L. CHAPTER 12 PROBLEMS

Problem L1 Can there be plant which can make C 3 H 8 by the reaction 3CO2 + 4H2O →C 3 H 8 + 5O 2 ? Is this endothermic or exothermic?

Problem L2 During coal liquefaction, the coal is gasified in the presence of oxygen and steam to produce a gas mixture of carbon monoxide and hydrogen called synthesis gas and then converted to liquid hydrocarbons in the presence of iron catalysts. This is called

the Fischer-Tropsch gas synthesis process, i.e., a CO + b H 2 →cC n H 2n+2 + d O 2 . If liquid octane is produced determine heat required for the reaction to proceed at 25ºC? Problem L3 Consider the mixing of 3.76 kmol of N 2 with 1 mole of O 2 . does the following reac- tion to go to completion at 25ºC and 1 bar, namely, 3.76 N 2 +O 2 → 2 NO + 2.76 N 2 ?

Problem L4 Plot X NO (T) for NO in air at chemical equilibrium at 100 kPa. Apply the reaction 1/2 N 2 + 1/2 O 2 = NO. Assume NO to exist in trace amounts.

Problem L5 Determine the trace amounts of SO 2 and NO exhausted from a smoke stack with re- spect to the temperature under chemical equilibrium if Illinois No. 6 coal is com- busted with 20% excess air. Empirical formulae of coal: C 0.6671 H 0.5610 N 0.011001 O 0.06738 S 0.01322 . Assume complete combustion of C and H to CO 2 and H 2 O.

Problem L6 For the reaction H 2 S →H 2 + S determine the equilibrium relation if sulfur exists as gas

at 1000 K and as solid at 298 K. Will the amount of S be affected by a change in pres- sure at either 298 K or 1000 K?

Problem L7 Consider the dissociation (dimerization) of N 2 O 4 , i.e., N 2 O 4 → 2NO 2 for which ∆G 0 =

57330–176.7 T kJ kmol –1 . Plot the degree of dissociation as a function of pressure at 298 K, and as a function of temperature at 1 bar.

Problem L8 For the reaction C(s) + CO 2 (g) → 2CO(g) determine the equilibrium composition as

a function of pressure at 2000 K. Assume ideal gas behavior for CO 2 and CO and 1 kmol of carbon initially.

Problem L9 The equilibrium constant for the reaction H 2 + 1/2O 2 →H 2 O(liq) has been determined

to be 1.6 ×10 4 at 25 °C. The standard states are defined with respect to the pure com- ponents at 1 atm and 25 °C. Calculate the minimum work required to dissociate 1 kmol of water at 25 °C and 1 atm if (a) pure and separated hydrogen and oxygen are to

be produced, and (b) a stoichiometric mixture of oxygen and hydrogen is to be pro- duced.

Problem L10 Both hydrogen and air enter a welding torch at 25 °C and burn according to the reac-

tion H 2 + 1/2 O 2 →H 2 O (g). If the torch is adjusted to give 200 percent more air than the stoichiometric amount and combustion is adiabatic, what is the flame tempera-

2 O in units of cal gmol K are, respec- tively, 6.14 + 3.102 ×10 –3 T, 6.524 + 1.250 ×10 –3 T, 6.947 + 0.120 ×10 –3 T, and 7.256 +

ture? The values of c p for O 2 ,N 2 ,H 2 , and H

2.290 ×10 –3 T with T in units of K, and ( ∆H react ) 25 °C = –57.8 kcal per g–mol of H 2 , and K 0 = 1.0 ×10 40 at 25 °C. The standard states for all components is 1 bar.

Problem L11 In order to increase the operating temperature of the hydrogen torch of the previous problem, pure oxygen at the stoichiometric rate replaces air as the oxidizer. Neglect- ing all reactions other than the combination of hydrogen and oxygen, determine the adiabatic flame temperature for these operating conditions.

Problem L12 The following reactions are believed to occur during the catalytic oxidation of ammo- nia to nitric oxide:

It is essential to determine the equilibrium composition when air is used to oxidize ammonia. Determine the minimum number of independent chemical equilibrium re- lations necessary to completely solve for the composition. Just outline the procedure in solving for the composition using equilibrium constants.

Problem L13 An electric generating station burns anthracite (essentially, pure carbon) in air to pro- vide heat for its main boilers. Determine the equilibrium composition of the gases leaving the combustion chamber at 900 K and 1.0 bar. The following reactions are known to occur:

CO 2 +C → 2CO,

where the standard states are pure gaseous O 2 and CO 2 , and pure solid carbon at 1 atm. (As long as any unreacted carbon remains, it is always in its standard state. Thus the activity of carbon is equal to unity and independent of the amount of carbon left.)

Problem L14 The JANAF tables list values of K 0 for reactions involving natural forms of elements. Determine the value of K 0 for the reaction CO + H 2 O → CO 2 + H 2 at 2000 K and 1

bar using tabulated g 0 values. A chemicals company suddenly charges a tank with a mixture of 2.85 CO, 0.15 CO 2 , 0.15 H 2 , and 3.85 H 2 O (all in kmol) at a total pressure of 2 bar and 900 K. The tank is maintained at 900 K and 2 bar. There is concern by engineers that CO + H 2 O (g) → CO 2 +H 2 which is exothermic and as such tank may

explode; since H 2 O dominates the mixture, the management argued that CO 2 + H 2 → CO + H 2 O (g) which is endothermic may be happening.

a) Determine the chemical forces of reactants (F R ) and products (F P ) for any of the assumed direction.

b) Settle the issue of direction of reaction. Answer whether changing the pressure will affect the direction of reaction? Do not calculate

Problem L15 Recall that g o k = (h– Ts) k and g´ k = (g f + ∆g) k where g f denotes the specific Gibbs en-

C + 1/2 s O 2 ). Similarly show that o g ′

ergey of formation. Show that for CO, g ′ –g CO = T o ( s o

CO

O –g O =T o (1/2) s O 2 and g ′ O 2 – g O

2 =T o s O 2 . Also, show that Συ k g k = Συ k g´ k =0

when the reaction C + 1/2 O 2 = CO is at equilibrium.

Problem L16 For the steam reforming reaction CH 3 OH (liq) + H 2 O (liq) →3H 2 + CO 2 both liquid methanol and liquid H 2 O are supplied 298 K and 1 bar to a reactor which should pro-

duce a mixture of H 2 and CO 2 also at 298 K and 1 bar. Is the reaction possible for this case?

Problem L17 Many power plants in U.S. fire either coal or natural gas to produce electrical power. Coal can be represented by C(s) and natural gas by CH 4 . The excess air for a particu- lar application is such that the oxygen content in the exhaust on dry basis is 3%. As- sume complete combustion and the pressure of the products to be 1 bar. For both fuels

determine the (a) A: F ratio, (b) CO 2 and N 2 percent in the exhaust, (c) the CO and NO present in the exhaust if it is at 1500 K assuming the following reaction: N 2 +O 2 → 2 NO, N 2 +2O 2 →2 NO 2 , and CO 2 → CO + 1/2 O 2 . Assume that NO and CO are

in trace amounts, d) CO, NO and CO 2 in g/GJ for both the fuels. Problem L18

Which of the two reactions C(s) + 1/2 O 2 → CO or C(s) + O 2 → CO 2 is favored at (a) 2000 K and (b) 3000 K? Problem L19 One kmol of C(s) at 2 bar, and premixed 2 kmol of O 2 and 0.001 kmol of CO 2 at 1000

K and 2 bar are introduced into a steady flow reactor. Will the CO 2 concentration in- crease or decrease in the product stream due to the reaction C(s) + O 2 → CO 2 ?

Problem L20 Methanol(l) can be produced from syngas (CO + H 2 ) according to the reaction CO(g) + 2H 2 (g) → CH 3 OH(l). Determine the suitable conditions for the feasibility of its production at 25ºC and 1 bar.

Problem L21 Consider the reaction SO 2 (g) + CaO(s) + 1/2 O 2 (g) → CaSO 4 (s), which is used to capture the SO 2 released due to combustion of coal. What is the equilibrium relation,

assuming that the SO 2 and CaO are fully mixed at molecular level? How much SO 2

and O 2 is left over at 1200 K?c p,CaO(s) = 42.8 ,c p,CaSO4(s) = 100 kJ/kmol K?

Problem L22 Show that ˆg 1 (T,P,X 1 )= h 1 (T) – s 1 (T,P) + R T ln X 1 = g 1 (T,p 1 ).

Problem L23

A reactor is supplied with elements 9 kmol of C and 19 kmol of O and allowed to reach chemical equilibrium at 3000 K and 1 bar. What is the equilibrium composi- tion? What is the value of the Gibbs energy at equilibrium? If the products are iso- barically cooled to 2800 K and allowed to reach chemical equilibrium, what is the new equilibrium composition and the new value of the Gibbs energy?

Problem L24 Determine the value of ∆G(298 K, 2 bar) for the water gas shift reaction H 2 O + CO(g)

→H 2 (g) + CO 2 (g) considering the water to be (a) liquid and (b) gas. Problem L25

It is necessary to determine ˆ g CO 2 in a mixture containing 20% CO, 10% CO 2 , 10% O 2 with the remainder being N 2 . Assume that the mixture is an ideal mix of real gases at

66 bar and 370 K (you may use the fugacity charts). Problem L26

In an application there are two possible reactions for the oxidation of carbon C(s) + 1/2O 2 → CO, and C(s) + O 2 → CO 2 . Determine the affinity at the point when 40% of

the carbon is consumed separately by the first and second reactions at 1 bar and 3500 K. Assume that c p,C /R = 1.771 + 0.000877 T – 86700/T 2 with T in units of K.

Problem L27 The steam reforming reaction is CH 4 +H 2 O → CO + 3H 2 . Is this reaction possible at

298 K if equal molal mixture of CH 4 ,H 2 O(g), CO, H 2 are sent to the reactor ? Is heat absorbed or released at 298 K ? Is 50% conversion possible at 298 K, and if it were to

be obtained, what would be the molal ratio of H 2 to CH 4 in the products? Problem L28

A combustor is fired with coal having atomic composition CH 0.755 N 0.0128 O 0.182 S 0.00267 . For every kmol of coal fired, 0.234 kmol of moisture enters the combustor. If 20% excess air is used and combustion is complete, a trace amount of NO is formed (ac-

cording to the reaction 1/2N 2 + 1/2O 2 → NO), the sulfur is burned to SO 2 , and the products leave at 2800 K, determine the equilibrium composition. Problem L29 Gaseous propane is burned with 60% of theoretical air in a steady flow process at 1

atm. Both the fuel and air are supplied at 298 K. The products, which consist of CO 2 , CO, H 2 O, H 2 , and N 2 in equilibrium, leave the combustion chamber at 1500 K. De- termine the composition of the products and the amount of heat transfer in the process per kg of propane burned. The standard enthalpy of formation for propane is –103,847 J gmol –1 .

Problem L30

A mixture contains 20% CO, 10% O 2 and the remainder CO 2 at a temperature of 1500 K and 10 bar. Obtain the values of G, ∂G/∂N , ∂ 2 G/ ∂ N CO 2 2 CO 2 .g CO (1500,10)=-415434

kJ/kmol, g O2 = -317622 kJ/kmol, g CO2 =-769977 kJ/kmol. Problem L31

Air is supplied to a compressor in a gas turbine at 298 K and 1 bar, and is adiabati- cally and reversibly compressed to 10 bar. The air then proceeds to that combustor that is fired with iso–octane fuel at 298 K. Combustion occurs adiabatically with 100% excess air. Determine the adiabatic flame temperature assuming (a) complete combustion, and (b) complete chemical equilibrium with CO, NO, and OH present in the products. (c)What is the equilibrium composition for part (b)?

Problem L32 Evaporative cooling of inlet air is suggested for a gas-turbine power plant since it is expected to provide denser air and hence more mass flow for the same velocity to the compressor. The evaporative cooling results in decrease of temperature of air to 20ºC

from saturated wet air at 40ºC. Assume fuel to be CH 4 at 298K burning with 100% excess air. a) What will be the decrease in adiabatic flame temperature compared to a dry air case? b) What will be decrease in NO if any compared to dry air case. Assume that air is saturated with vapor.

Problem L33 If F = G + Σ k λ k Σ j (d kj N j –A k ), then prove that G min =- Σ k λ k A k ,G= Σ k µ j N j or Σ k g j N j .

Problem L34 Obtain a set of relations for determining the equilibrium composition of gases at given T for a fuel C C H H O O N N burning in air with the following set of reactions.

H 2 O ⇔H 2 + 1/2 O 2 , CO 2 ⇔ CO + 1/2 O 2 ,

H 2 O ⇔ 1/2 H 2 + OH, NO ⇔ 1/2 N 2 + 1/2 O 2 , and OH ⇔1/2 H2 + 1/2 O 2 .

Describe a procedure for solving the composition using a spread sheet. Problem L35

One kmol each of carbon monoxide and water vapor enter an adiabatic reactor at 298 K and 1 bar and produce CO 2 and H 2 . (a) Plot the temperature and entropy of the products, the sums (g CO +g HO 2 ), (g CO 2 +g H 2 ), and σ with respect to the degree of reac-

tion of CO (i.e., assume that 0, 0.1, ..., 1.0 kmol of CO react). (b) If the conversion of reactants to products is adiabatic, what is the value of σ when one kmol of CO is con-

sumed? (c) What is the degree of reaction when σ reaches a maximum value? (d) What should be the criterion for the direction of reaction to occur? σ > 0 or dσ > 0. Which criterion is the more appropriate to use?