Methane can be produced from CO and H2.The process might be done in two steps, as shown below, with each step carried out in a separate reaction vessel within the production plant.
Reaction 1
Reaction 2
NOTE: You should be able to work this problem without using any additional tabulated data.
(a) Calculate
(b) Calculate
(c) Calculate S° for O2(g).
(d) At what temperatures is reaction 1 spontaneous?
(e) Suggest a reason why these two steps would need to be carried out separately.
Substance |
|
|
|
CO(s) | -110.5 | 197.674 | |
CH3OH( ) |
-238.7 | -166.4 | 126.8 |
CH4(g) | -74.8 | 186.2 |
Interpretation:
Thermodynamic entropy, enthalpy and Gibb’s free energy as asked must be calculated for the reactions given.
Concept Introduction:
Enthalpy change for a process is determined as:
where v is for stoichiometric coefficients
Similarly entropy change for a process is determined as:
where v is for stoichiometric coefficients and
Gibb’s free energy is a state function which predicts whether a process is spontaneous or not at conditions of constant pressure and temperature. Gibb’s free energy change for a process at constant temperature is defined as:
where
Similar to enthalpy and entropy, standard Gibb’s free energy change can be calculated as:
Also
Answer to Problem 10.84PAE
Solution:
a)
b)
c)
d) Hence reaction 1 is spontaneous at lower temperatures.
e) Since reaction 1 is spontaneous at lower temperatures and reaction 2 is spontaneous at higher temperatures, they must be carried out separately.
a)
Explanation of Solution
Given reaction 1 is:
Calculate enthalpy change the above reaction that is
b)
Using the value of enthalpy change of reaction 1 calculated in part a) and the given entropy change calculate the Gibb’s free energy change for reaction 1. Since we are using standard values the temperature will be 298 K.
Now use the formula described above in the concept introduction to calculate
c)
Given reaction 2 is:
The entropy change for the above reaction is
d)
Gibb’s free energy is a state function which predicts whether a process is spontaneous or not at conditions of constant pressure and temperature. Gibb’s free energy change for a process at constant temperature is defined as:
Where
Given reaction 1 is:
The entropy change for the above reaction is
Hence reaction 1 is spontaneous at lower temperatures.
e)
As explained above in part c) reaction 1 is spontaneous at lower temperatures. Similarly given reaction 2 is:
The entropy change for the above reaction is
. Calculate enthalpy change for this reaction:
Gibb’s free energy is a state function which predicts whether a process is spontaneous or not at conditions of constant pressure and temperature. Gibb’s free energy change for a process at constant temperature is defined as:
Where
Now since both
Since reaction 1 is spontaneous at lower temperatures and reaction 2 is spontaneous at higher temperatures, they must be carried out separately.
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