Thermo II Lacture 31-33
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Transcript of Thermo II Lacture 31-33
CH321 Thermodynamics & Phase Equilibria
GIK Institute of Engineering Sciences and TechnologyFaculty of Chemical Engineering
Fall Semester 2014
Dr Khurram Imran Khan
Lecture # 31-33
Multireaction: Alternate Criterion of Equilibrium for Computer Program
• The criterion is based on that at equilibrium the total Gibbs energy of the system has its minimum value.
• The total Gibbs energy of a single phase system:
• We will find the set of {ni} which minimizes Gt for specified T and P, subject to constraints of material balance.
• The standard solution of this method is based on the Method of Lagrange’s undetermined multipliers
• On next slides the method is described for Gas-Phase Reactions.
1 2 3,, , ,....,t
NT PG g n n n n
1, 2,....,i ik ki
n a A k w
0 1, 2,....,i ik ki
n a A k w Total number of
elements comprising the system
Total Number of atomic masses of the kth elementNumber of atoms of the kth element present in each molecule
1
2
0 1, 2,....,k i ik ki
n a A k w
0k i ik kk i
n a A
Summed over k
Constraining Equations
Lagrange Multiplier
3
tk i ik k
k i
F G n a A
4
, , , ,
0 1, 2,....,j j
t
k ikki iT P n T P n
F Ga i N
n n
0 1, 2,....,i k ikk
a i N
New function formed, identical to Gt and incorporates the constraints of material balance.
Criterion of the equilibrium
ˆln /i i i iG RT f f
ˆln /i i i iG RT f P
ii fG G ˆ ˆi i if y P
ˆln /i i i i iG RT y P P
ˆln / 0 1, 2,...,i i i i k ikk
G RT y P P a i N
1, 2,....,i ik ki
n a A k w N-Equilibrium equations
w- material balance equations
Example 13.14Calculate the equilibrium composition at 1000 K and 1 bar of a gas phase system containing the species CH4, H2O, CO, CO2 and H2. In the initial unreacted state there are present 2 mole of CH4 and 3 mole of H2O.
4 2
2
-1 -1
-1 -1
19 720 J mol , 192 420 J mol
200 240 J mol , 395 790 J mol
CH H O
CO CO
f f
f f
G G
G G
ˆln / 0 1, 2,...,i i i i k ikk
G RT y P P a i N
1, 2,....,i ik ki
n a A k w
Element k
Carbon Oxygen Hydrogen
Ak = no. of atomic masses of k in the system
AC = 2 AO = 3 AH = 14
Species i aik = no. of atoms of k per molecule of i
CH4
H2O
CO
CO2
H2
aCH4,C = 1
aH2O,C
aCO,C
aCO2,C
aH2,C
aCH4,O = 0
aH2O,O
aCO,O
aCO2,O
aH2,O
aCH4,H = 4
aH2O,H
aCO,H
aCO2,H
aH2,H
Fuel CellsAcid electrolyte
2H 2H 2e
12 22 O 2 2H H O ge
12 2 22H O H O g
Reaction at Anode
Reaction at Cathode
Overall Reaction
Alkaline electrolyte
2 2H 2OH 2H O g 2e
122 O 2 H2O g 2OHe
12 2 22H O H O g Reaction at Anode
Reaction at Cathode
Overall Reaction
Taken from: http://energydesignresources.com/resources/e-news/e-news-90-fuel-cells.aspx
Proton-Exchange Membrane
Taken from: http://www.rsc.org/Publishing/ChemTech/Volume/2008/06/spray_electrodes.asp
(PANI-F)Polyaniline Fiberswith Pt nanoparticles
NafionSulfonated TetrafluoroethyleneIonomer
Fuel Cell OperationelectH Q W
Q T S electH T S W
electW H T S G
Q H G 2 coulombAq N e
AeNF
12 , Faraday's constant 96 485 coulomb molq F F
For steady-state flow process, the energy balance
Electrical Work of a reversible Cell
For each molecule of hydrogen consumed, 2 electrons pass to the external circuit
(Faraday’s constant)
elect 2 jouleW E F elect
2 2
W GE
F F
Calculations example of above formula’s of Hydrogen/Oxygen fuel cell at 25oC and 1 bar with assumption of Ideal gas (Pure H2, O2 as gases and H2O vapour.
Calculations example of above formula’s of Hydrogen/Air fuel cell at 25oC and 1 bar with assumption of Ideal gas (Pure H2, air as gases and H2O vapour.
(volt)
lnig igi i iG G RT y Hint