(a)
Interpretation:
The equilibrium mole fraction of methanol at
Concept introduction:
Mole fraction formethanol synthesis reaction is calculated with the help of the extent of reaction which is defined as a measure of the extent to which the reaction proceeds.
Where,
The overall stoichiometric coefficient for this reaction is,
The individual stoichiometric coefficients for all the components in this reaction is:
Equilibrium constant of this reaction from equation 14.28 can be written as:
Where,
Gibbs free energy in terms of equilibrium constant is written as:
Also, Gibbs free energy is calculated using heat of reaction from the equation given as
Here,
Where,
(a)
Answer to Problem 14.21P
The equilibrium mole fraction of methanol at
Explanation of Solution
From Table C.4 the standard heat of reaction and Gibbs free energy for methanol formation is:
From Table C.1 the coefficients for the heat capacity of the component gases are given as:
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Now, use equations set (6) to evaluate the values of
Now, use equation (5) to calculate the value of
The equilibrium constant for the methanol synthesis reaction at 300 K can be calculated as given below:
The initial and final pressure of the system is kept at
The mole fraction of all the species in terms of extent of reaction are:
Now, use equation (3) for the equilibrium constant of this reaction to calculate the extent of reaction as:
Use this extent of reaction to calculate the mole fraction of methanol as:
Therefore, the equilibrium mole fraction of methanol at
(b)
Interpretation:
The temperature for the given equilibrium mole fraction of methanol at
Concept introduction:
Mole fraction for methanol synthesis reaction is calculated with the help of the extent of reaction which is defined as a measure of the extent to which the reaction proceeds.
Where,
The overall stoichiometric coefficient for this reaction is,
The individual stoichiometric coefficients for all the components in this reaction is:
Equilibrium constant of this reaction from equation 14.28 can be written as:
Where,
Gibbs free energy in terms of equilibrium constant is written as:
Also, Gibbs free energy is calculated using heat of reaction from the equation given as
Here,
Where,
(b)
Answer to Problem 14.21P
The equilibrium mole fraction of methanol at
Explanation of Solution
The initial and final pressure of the system is kept at
The mole fraction of all the species in terms of extent of reaction
Now, use equation (3) to calculate the equilibrium constant of this reaction as:
Use this equilibrium constant to calculate
From Table C.4 the standard heat of reaction and Gibbs free energy for methanol formation is:
From part (a), the calculated values of
Now, use equations set (6) in equation (5) along with the value of
Now, by trying different values of
Thus, the temperature at which the equilibrium mole fraction of methanol is
(c)
Interpretation:
The temperature for the given equilibrium mole fraction of methanol at
Concept introduction:
Mole fraction for methanol synthesis reaction is calculated with the help of the extent of reaction which is defined as a measure of the extent to which the reaction proceeds.
Where,
The overall stoichiometric coefficient for this reaction is,
The individual stoichiometric coefficients for all the components in this reaction is:
Equilibrium constant of this reaction from equation 14.28 can be written as:
Where,
Gibbs free energy in terms of equilibrium constant is written as:
Also, Gibbs free energy is calculated using heat of reaction from the equation given as
Here,
Where,
(c)
Answer to Problem 14.21P
The equilibrium mole fraction of methanol at
Explanation of Solution
The initial and final pressure of the system are taken as:
The mole fraction of all the species in terms of extent of reaction
Now, use equation (3) to calculate the equilibrium constant of this reaction as:
Use this equilibrium constant to calculate
From Table C.4 the standard heat of reaction and Gibbs free energy for methanol formation is:
From part (a), the calculated values of
Now, use equations set (6) in equation (5) along with the value of
Now, by trying different values of
Thus, the temperature at which the equilibrium mole fraction of methanol is
(d)
Interpretation:
The temperature for the given equilibrium mole fraction of methanol at
Concept introduction:
Mole fraction for methanol synthesis reaction is calculated with the help of the extent of reaction which is defined as a measure of the extent to which the reaction proceeds.
Where,
The overall stoichiometric coefficient for this reaction is,
The individual stoichiometric coefficients for all the components in this reaction is:
Gibbs free energy in terms of equilibrium constant is written as:
Also, Gibbs free energy is calculated using heat of reaction from the equation given as
Here,
Where,
Equilibrium constant of this reaction for an ideal solution of gases from equation 14.28 can be written as:
Where,
The formula to calculate
Here,
(d)
Answer to Problem 14.21P
The equilibrium mole fraction of methanol at
Explanation of Solution
The initial and final pressure of the system are taken as:
The mole fraction of all the species in terms of extent of reaction
From Table-B.1 of appendix B, the critical properties and acentric factor of methanol is:
Component | Pc (bar) | Tc (K) | |
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Let the guessed value of the temperature be
Use equations set (9) to calculate the values of
Use equation (8) to calculate the value of
Now, use equation (7) to calculate the equilibrium constant of this reaction as:
Use this equilibrium constant to calculate
From Table C.4 the standard heat of reaction and Gibbs free energy for methanol formation is:
From part (a), the calculated values of
Now, use equations set (6) in equation (5) and calculate the value of
Since, the calculated value of
Thus, the temperature at which the equilibrium mole fraction of methanol is
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Chapter 14 Solutions
GEN, ORG & BIOL CHEM: CUSTOM SSC
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