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

Thank

you!