CN4246E: CHEMICAL AND

BIOCATALYSIS

Term Paper: Water-Gas Shift Reaction (Carboxyl Mechanism)

TEAM 1

1 Wai Ming Hui A0066050R 2 Chong Xue Li Cherie A0066081J

1 DERIVATION FOR WATER-GAS SHIFT REACTION CARBOXYL MECHANISM

The water-gas shift reaction (CO+H2O CO2 + H2) is a slightly exothermic equilibrium-

controlled reaction. The elementary steps for the carboxyl mechanism is proposed by

Mhadeshwar and Vlachos (2005). The original 46 reactions has been narrowed to these few

elementary steps through principal component analysis. Although there appears to be 18

elementary steps, reaction pairings between R1-R2, R7-R8, R13-R14, R19-R20, R21-R22, R25-R26, R29-

R30, R31-R32, R33-R34 actually produces 9 reversible elementary steps. The reduced elementary

steps are mentioned by the authors to be thermodynamically consistent by keeping the

equilibrium constant fixed with changing the pre-exponential factors.

Here steady-state approximation assumption is applicable for species coverage which

provides the complete steady state balance for species coverage.

= 21 22 + 7 8 25 + 26 + 31 32 + 33 34 = 0 (1)

= 7 8 + 25 26 + 29 30 = 0 (2)

2

= 7 + 8 + 13 14 33 + 34 = 0 (3)

= 19 20 + 25 26 + 29 30 33 + 34 = 0 (4)

2

= 21 22 25 + 26 + 31 32 = 0 (5)

= 29 + 30 31 + 32 + 33 34 = 0 (6)

Overall site coverage equation:

+ + 2 + + 2 + + = 1 (7)

To simplify the expressions above, CO* and H* are found to be the most abundant reactive

intermediate (MARI). Furthermore, reversibility of reaction pairs are analyzed which results in

simplified steady state balance for species coverage.

= 21 22 + 31 32 + 33 = 0 (8)

= 7 8 26 30 = 0 (9)

2

= 13 14 = 0 13 = 14 (10)

= 19 20 = 0 19 = 20 (11)

2

= 21 22 = 0 21 = 22 (12)

= 31 + 32 + 33 = 0 31 = 32 + 33 (13)

MARI assumption is applicable for and .

+ + = 1 (14)

The following site coverage terms can be obtained:

2 = (1314

) 2 = 132 (15)

= (1920

) = 19 (16)

2 = (2122

) 2 = 212 (17)

33 = 31 32

332 = 31 322

=332 + 322

31 (18)

Substitute (13) into (8) to obtain the following expression for .

21 22 + 233 = 0

2122 22

2 + 2332 = 0

2122 22

2 + 233191322 = 0

22 = 12

2 + 33191322

= 12 + 3319132

2

Since 33

1 0.03 as 33 is rate-determining step. can be further simplified.

= 12

2 = 12 (19)

Substitute the (15), (16) and (19) into (9) and obtain following expression for .

7 8 26 30 = 0

72 8 26 30 = 0

71322 812 2619 3019 = 0

71322 = (812 + (26+30)19)

=7132

812 + (26+30)19 (20)

Substitute (15), (17) and (19) into (18) and obtain following expression for .

= (3313219 + 3221212

31)

33

1 0.03 as 33 is rate-determining step to simplify the expression into:

= (3221212

31) =

2121231

(21)

Substitute (16) and (19) into simplified site coverage equation (14)

12 + 19 + = 1

=1

1 + 12 + 19 (22)

2 DERIVATION FOR FORWARD REACTION

The net rate of 2 is used to determine overall reaction rate. Through the stoichiometry of

the global reaction (CO+H2O CO2 + H2), the net rate for other species can be determined

in terms of net rate of 2. 33 is chosen as the rate-determining step for the forward

reaction.

2 = 1 2 = 33 = 332 = .

. = 33191322

. =3319132

(1 + 12 + 19)2 (23)

3 DERIVATION FOR REVERSE REACTION AND SIMPLIFIED NET RATE

EQUATION

34 is chosen as the rate-determining step for the reverse reaction since this reaction is not

found to be in equilibrium for the reverse reaction. The global water-gas shift reaction is

equilibrium-controlled which implies that the terms that were derived for the forward

reaction is equivalent to reverse reaction. Hence, the site coverage expressions for the

intermediates and adsorbed species (15), (16), (17), (19), (20) and (21) can be used.

1 2 = 34 = 34 = .

. = 34 = 3421213112

2

. =34212131

12

(1 + 12 + 19)2 (24)

The net rate equation for global water-gas shift reaction is shown below:

. = . .

. = 33191322 3421131

1222 (25)

. =3319132 3421131

122

(1 + 12 + 19)2 (26)

This form of equation (26) will be used for model fitting against Grabow (2009) experimental

data.

4 DERIVATION FOR FULL NET RATE EQUATION

When MARI is not assumed in the site coverage equation (7), the net rate equation (25) will

be very detailed since the behavior of all coverage species is captured in the site coverage

equation (7) as shown below:

+ + 2 + + 2 + + = 1

12 +7132

812 + (26+30)19+ 132 + 19 + 212 + 21231

112 + = 1

=1

1 + 12 +7132

812 + (26+30)19+ 132 + 19 + 212 + 21231

112

(27)

Substitute (27) into (25)

. =3319132 3421131

122

(1 + 12 +7132

812 + (26+30)19+ 132 + 19 + 212 + 21231

112)

2 (28)

5 MODEL FITTING USING MATLAB

A universal water gas shift reaction mechanism is still not well-understood and agreed upon.

But kinetic studies on platinum (Pt) is especially limited. Current research on water-gas shift

reaction uses a lot of first-principle analysis and transition state theory ([2], [4], [5] and [6]) to

elucidate the reaction mechanism. However, such analysis is computationally intensive.

Another method to analyze and elucidate reaction mechanism efficiently is to conduct model

fitting and discrimination against available experimental data to determine possible reaction

mechanisms. The simplified carboxyl rate equation (26) will be used in model fitting against

experimental data from Grabow (2008) [2].

. =3319132 3421131

122

(1 + 12 + 19)2 (26)

The experiment on water-gas shift reaction was done on Pt/Al2O3 catalyst by introducing

different components (CO, H2, H2O and CO2) at different temperature. The total pressure was

kept constant at 1 atm with inert He introduced as balance gas. The turnover frequency (TOF)

is expressed as moles of product species produced per moles of active catalytic sites per unit

time (min-1). The experimental data from [2] is selected and compiled in Appendix 8A.

For model fitting and analysis, nlinfit command is first used to determine the equilibrium

constants in (26) at 548K. However in order to determine if the results obtained from nlinfit is

statistically significant, the nlparci function can be used to determine the upper bound and

lower bound of a coefficient at a certain percentage interval. For this analysis, 90%

confidence interval is used.

For nlinfit command to work, initial estimates are required and such estimates are obtained

through trial and error method to obtain positive coefficient. Several attempts to make initial

estimates has to be used. This is because negative equilibrium constant or rate constant does

not have physical meaning. Hence, the initial estimates that gives positive coefficient are

given in Table 1. The results for the 7 coefficients are tabulated in Table 3a, 3b and 3c.

Table 2: Initial estimates for constants for nlinfit function in MATLAB

k33 K19 K13 k34 K21 K1 K31

Initial estimates for equilibrium constants

10 100 0.1 500 0.9 20 1

Table 3a: Results of non-linear model fitting at 90% confidence interval

k33 K19 K13

T (K) MSE L.L mean U.L L.L mean U.L L.L mean U.L

548 1.1315 1.1315 118.7447 118.7459 118.747 4.887 9.7301 14.5715 1.0744 1.1875

Table 3b: Results of non-linear model fitting at 90% confidence interval

k34 K21 K1

T (K) MSE L.L mean U.L L.L mean U.L L.L mean U.L

548 1.1315 59.691 59.7024 59.7138 -6.2041 0.1075 6.4191 1.2532 17.2362 33.2193

Table 3c: Results of non-linear model fitting at 90% confidence interval

K31

Temperature(K) MSE L.L mean U.L

548 1.1315 4.7189 4.8588 4.9986

6 DISCUSSION

A) Equilibrium constants and statistical significance

The rate constants and equilibrium obtained from non-linear fitting display positive values

However if statistical significance is to be properly accounted for, the model may not

describe the reaction mechanism accurately because K21 which is the equilibrium constant

for CO2 adsorption and desorption from active sites is -6.2041 at the lower limit and 6.4191

at the upper limit. However, more attempts on initial estimates need to be done to confirm

that K21 is truly statistically insignificant.

B) Uncertainty in determining rate-determining step (RDS)

One possible reason for the statistical insignificance of [26] is the uncertainty in predicting

the rate-determining step in the carboxyl mechanism. R7-R8, R25-R26, R29-R30 are also potential

RDS identified because these reactions are found to be far from equilibrium at various

temperature [1]. L.C Grabow et al [2] conducted Campbells rate control analysis and found

that water activation (R7-R8) is the next possible rate-determining step after (COOH*+*

CO2*+H*). Possible attempts to better elucidate the reaction mechanism could include

deriving the rate equation based on possible rate-determining steps (R7-R8, R25-R26 and R29-

R30) and conduct non-linear fitting to determining the most likely reaction mechanism.

7 CONCLUSION

The net rate equation for water gas shift reaction catalyzed on Pt/Al2O3 has been derived

based on CO* and H* as the most abundant reactive intermediate (MARI) and R33-R34 as the

rate-determining step. Non-linear model fitting nearly yielded positive values for the rate

constants and equilibrium constants in the model at 90% confidence interval. However, only

K21 is found to be statistically insignificant which affects the validity of the model. There is

also uncertainty in determining the rate-determining step as R7-R8, R25-R26 and R29-R30 are

also potential RDS [2]. Future work involves deriving rate equation based on possible rate-

determining steps and fitting against experimental data to determine the most likely reaction

mechanism.

8 REFERENCE

[1] A.B Mhadeshwar, D.G Vlachos. Is the water-gas shift reaction on Pt simple? Computer-

aided microkinetic model reduction, lumped rate expression, and rate-determining step.

Catalysis Today (2005), 105, 162-172.

[2] L.C Grabow, A.A Gokhale, S.T Evans, J.A Dumesic, M Mavrikakis. Mechanism of the Water

Gas Shift Reaction on Pt: First Principles, Experiments and Microkinetic Modeling. Journal of

Physical Chemistry C (2008), 112, 4608-4617.

[3] W.F Podolski, Y.G Kim. Modeling the Water-Gas Shift Reaction. Ind. Eng. Chem. Process

Des. Dev (1974), 13 (4), 415-421.

[4] A.A Gokhale, J.A Dumesic, M Mavirikakis. On the mechanism of low temperature water

gas shift reaction on copper. J. Am. Chem. Soc (2008), 130(4), 1402-1414.

[5] H.N Chiang, J.C Jiang. Density Functional Theory Study of Water-Gas-Shift Reaction on

3Cu/-Al2O3(0001) Surface. J. Phys. Chem. C(2013), 117 (23), 1204512053.

[6] A.B Vidal, P Liu. Density functional study of water-gas shift reaction on M3O3x/Cu(111).

Phys. Chem. Chem. Phys (2012),14, 16626-16632.

9 APPENDIX

A) Selected experimental kinetics data on Pt/Al2O3 catalyst taken from [2]

No of runs T (K) PCO(atm) PH2O(atm) PCO2(atm) PH2(atm) measured TOF(min^-1)

1 523 0.154 0.208 0 0 3.68

2 548 0.055 0.208 0 0 8.56

3 548 0.105 0.208 0 0 8.06

4 548 0.137 0.062 0 0 3.63

5 548 0.144 0.104 0 0 4.81

6 548 0.148 0.145 0 0 5.56

7 548 0.145 0.208 0 0 7.27

8 548 0.106 0.208 0.068 0 6.05

9 548 0.104 0.208 0.109 0 5.59

10 548 0.14 0.208 0.151 0 6.12

11 548 0.102 0.208 0.192 0 6.03

12 548 0.134 0.208 0 0.037 4.13

13 548 0.156 0.208 0 0.097 2.77

14 548 0.13 0.208 0 0.123 2.67

15 548 0.134 0.208 0.177 0.123 2.67

16 548 0.132 0.208 0 0.173 2.55

17 548 0.146 0.208 0 0.191 2.28

18 548 0.159 0.208 0 0.208 2.29

19 548 0.198 0.208 0 0 7.29

20 548 0.223 0.208 0 0 7.09

21 573 0.15 0.208 0 0 15.44

B) MATLAB Code for nlinfit and nlparci function

Function file

function yhat=wgs_carboxylmechanismvlachos(beta,x) yhat=(x(:,1).*x(:,2).*beta(1)*beta(2)*beta(3)-

x(:,3).*x(:,4).*beta(4)*beta(5)*beta(6)*(beta(7)^-

1))./(1+((x(:,4).*beta(6)).^0.5)+x(:,1).*beta(2)).^2;

Domain file % Mhadeshwar&Vlachos 2005 model is fitted with Grabow 2008 experimental % data.p=partial pressure of components (atm),v=measured TOF(min^-1) % x(:,1) is the partial pressures of CO,x(:,2) is the partial pressures of

H2O,x(:,3) is the partial pressures of CO2,x(:,4) is the partial pressures

of H2, % previous intial values are [1000 1 1 1500 1 1 2] and eventually [375.8356

9.7301 0.3752 105.4530 0.0703 17.2363 5.6143],[10 100 0.1 500 0.9 20 1]

.The latter one produces the best results thus far. p=[0.055 0.105 0.137 0.144 0.148 0.145 0.106 0.104 0.14 0.102 0.134 0.156

0.13 0.134 0.132 0.146 0.159 0.198 0.223;0.208 0.208 0.062 0.104 0.145

0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208 0.208

0.208 0.208;0 0 0 0 0 0 0.068 0.109 0.151 0.192 0 0 0 0.177 0 0 0 0 0;0 0 0

0 0 0 0 0 0 0 0.037 0.097 0.123 0.123 0.173 0.191 0.208 0 0]'; v=[8.56 8.06 3.63 4.81 5.56 7.27 6.05 5.59 6.12 6.03 4.13 2.77 2.67 2.67

2.55 2.28 2.29 7.29 7.09]'; [beta,r,J,sigma,mse]=nlinfit(p,v,@wgs_carboxylmechanismvlachos,[10 100 0.1

500 0.9 20 1]) ci=nlparci(beta,r,'covar',sigma,'alpha',0.1)