﻿ Problems and Solutions Chapter 2

# ## Problems and SolutionsChapter 12 Enthalpy of Reaction and Chemical Equilibria

### Textbook Examples:

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12.01           Enthalpy of Reaction of the Ammonia Synthesis in the Ideal Gas State (p. 510)

12.02           Enthalpy of Reaction of the Ammonia Synthesis at Higher Pressure Using VTPR (p. 511)

Mathcad Solution see 12.01

12.03           Equilibrium Constant and Equilibrium Conversion of the Ammonia Synthesis Assuming Ideal Gas Behavior (p. 517)

Mathcad Solution see 12.01

12.04           Equilibrium Conversion of the Ammonia Synthesis Assuming Real Gas Behavior Using SRK, PSRK and VTPR (p. 522)

Mathcad Solution see 12.01

12.05           MTBE-synthesis - Chemical Equilibrium in a Real Liquid Mixture (p. 526)

12.06           Simultaneous Chemical Reaction Equilibria Via Relaxation - Steam-Reforming (p. 535)

12.07           Molar Gibbs Energy as Function of Composition and Equilibrium Con­centration for then n-Butane – i-Butane Isomerization Reaction (p. 538)

12.08           Simultaneous Chemical Reaction Equilibria Via Gibbs Energy Minimization - Steam-Reforming (p. 541)

### Additional Problems:

P12.01         Influence of n-Pentane on the Equilibrium Composition (TAME Synthesis)

Calculate the equilibrium composition of the TAME (tert. amylmethylether) synthesis in the liquid phase using equimolar amounts of methanol (MeOH) and 2-methyl-2-butene (2M2B) at 25 and 80 °C
MeOH + 2M2B TAME
with the help of the standard thermodynamic properties for the ideal gas state given below
a) without a solvent
b) in the presence of  n-pentane with
nMeOH/npentane = 1:1 and nMeOH/npentane = 1:4

Calculations should be performed
1) assuming ideal behavior; i.e.
gi =1.
2) taking into account the real behavior
and
a)  using the Wilson equation
b)  modified UNIFAC

Standard thermodynamic properties in the ideal gas state and Antoine constants (log Pis (mm Hg) = A – B/(
J (°C) +C)) Parameters for the description of the molar heat capacities cP for the ideal gas as a function of temperature (cP = a + bT + cT2 +dT3) Molar volumes and Wilson parameters for the compounds considered P12.02         Influence of Different Solvents on the Equilibrium Composition (TAME Synthesis)

For the TAME synthesis the influence of the equilibrium conversion in the presence of the solvents benzene, THF and acetone in the liquid phase should be calculated with the help of the modified UNIFAC model at 80°C. The initial mixture should consist of equimolar amounts of methanol (MeOH), 2-methyl-2-butene (2M2B), and solvent. All required properties and parameters can be found in Example P12.01 and in the Appendix.

P12.03        Equilibrium Conversion For Ethanol Synthesis From Ethylene and Water

Ethanol can be produced from a feed of about 60 vol% ethylene and 40 vol% water. The mixture is reacted over a phosphoric acid catalyst at 300°C and 60 bar. Calculate the equilibrium constant at 25°C and 300°C for this reaction. Calculate the effect of the real vapor phase behavior on the equilibrium constant KP and equilibrium composition at 300°C as function of pressure up to a pressure of 100 bar using VTPR.The standard thermodynamic data of formation and ideal gas heat capacity correlations can be found in Appendix A.

P12.04        Equilibrium Constant of Ethane Dehydrogenation

At high temperatures, ethane dissociates via the reaction (ethane cracker)
C2H6 C2H4 + H2

Calculate the equilibrium concentrations at T = 800 K and P = 2 bar. All required data can be found in Appendix A.

P12.05       Optimal Feed Ratio (N2 to H2) in Ammonia Synthesis Using Ideal Behavior and VTPR

Calculate the optimal feed ratio of nitrogen and hydrogen for the ammonia synthesis at 450°C and a pressure of 600 atm using the parameters given in examples 12.1 to 12.4 using
-
ideal gas behavior
- taking into account the real behavior using the VTPR group contribution
equation of state

P12.06       Residual Part of the Heat Capacity of a Dissociative Gas

The dissociative gas and important rocket propellant dinitrogen tetroxide is in rapid equilibrium with nitrogen dioxide following the reaction:

N2O4 2 NO2
At a total pressure of 1 bar, the equilibrium concentration of N2O4 in the gas phase was reported to be 0.6349 (30°C), 0.4088 (50°C), 0.2113 (70°C), and 0.09321 (90°C). Calculate the residual part of the heat capacity of the reactive mixture between 20°C and 100°C.

P12.07       Equilibrium Constant of the Oxyhydrogen Reaction

Calculate the equilibrium of water formation from the elements in their most stable state for a stoichiometric feed of oxygen and hydrogen at P = 0.01 Pa and T = 2000 K using the data from Appendix A and assuming ideal gas phase behavior:

H2 + 0.5 O2 H2O

P12.08        Equilibrium Conversion of the Steam Reforming Process

In Example 12.6 the equilibrium conversion for the steam reforming process was calculated for a water/methane ratio of 2.7 and a pressure of 1 atm as a function of temperature. Please check how the equilibrium conversion is changed, if the:
a)  water/methane ratio is changed to 2
b)   the reaction is performed at 5 atm