CP303 – Set #10 (January-May 2012)
Catalysis and Catalytic Reactors
A catalyst is a substance that increases a reaction rate without itself being consumed in the reaction. In principle, all of a catalyst can be recovered unchanged at the end of a reaction. The energy released or absorbed by a chemical reaction is exactly the same whether a catalyst is present or not.  A catalyst only affects the reaction rate.
Catalysis is the occurrence, study, and use of catalysts and catalytic processes. Three main types of catalysis are Homogeneous Catalysis, Heterogeneous Catalysis and Enzyme Catalysis (which will be learned in CP504).
Homogeneous Catalysis: Homogeneous implies that the reaction takes place in solution (a homogeneous system), with the soluble catalyst also in solution. The classic example is the catalysis of ester hydrolysis by hydrogen ion.
CH3COC2H5 + H2O → CH3COOH + C2H5OH
Without H+ the process is very slow and the rate depends only on ester concentration.
Rate = k [CH3COC2H5]
With H+, it is much more rapid and the catalyzed reaction is second order, that is, first order with respect to both ester and hydrogen ion concentration.
Rate = kc [CH3COC2H5] [H+]
By the definition of catalysis, kc > k
Heterogeneous Catalysis: Heterogeneous catalysis is widely used in industrial manufacture of chemicals. The catalyst is usually in the solid phase and the reactants are either gaseous or liquid. The gas or liquid molecules bond temporarily to the atoms at the surface of the catalyst, which allows their internal bonds to break more rapidly or at a lower temperature.
Catalytic Converter: In the automobile catalytic converter (a Cu or Cr oxide surface) catalyzes the rapid decomposition of toxic and smog-producing nitrogen oxides in the exhaust to harmless nitrogen and oxygen gas.
NOx(g) ® N2(g) + O2(g)
A precious metal catalyst, platinum (Pt), palladium (Pd) or rhodium (Rh), converts CO and O2 in the exhaust stream to CO2. 
The Haber Synthesis of Ammonia: Probably the most important industrial process converts nitrogen gas and hydrogen to ammonia for use in fertilizer. The reaction is exothermic (energetically favorable) but it is very slow.
H2 (g) + N2(g) ® NH3(g)
H2 molecules adhere readily to the surface of an iron metal catalyst and dissociate readily into H atoms which allows them to react rapidly with nitrogen gas. The reaction proceeds much faster at 500 ºC than it would without the catalyst and makes the reaction an economically favourable process.
Sulfuric Acid Production: Platinum (Pt) or vanadium (V) oxide catalyze the production of SO3 from SO2, a key step in the manufacture of sulfuric acid. Sulfuric acid is required for so many applications that annual production of the acid was used as an index of industrial productivity. 
         V2O5
SO2(g) + ½ O2(g)   ®     SO3(g) 
Catalytic packed bed reactor

Steps in a heterogeneous catalytic reaction

Step 1 – Mass transfer (diffusion) of the reactants from the bulk fluid to the external surface of the catalyst pellet
Step 2 – Diffusion of the reactant from the pore mouth through the catalyst pores to the intermediate vicinity of the internal catalytic surface
Step 3 – Adsorption of reactant (e.g., A) onto the catalyst surface
Step 4 – Reaction on the surface of the catalyst (e.g., A → B)
Step 5 – Desorption of the products (e.g., B) from the surface
Step 6 – Diffusion of the products from the interior of the pellet to the pore mouth at the external surface
Step 7 – Mass transfer of the products from the external pellet surface to the bulk fluid
Important Note: Reactions are not catalyzed over the entire surface but only at certain active sites or centers that result from unsaturated atoms in the surface. An active site is a point on the surface that can form strong chemical bonds with an adsorbed atom or molecule.

The adsorption step: In this step, reactant (A) combines with the active site (denoted by the letter S) and forms the complex A.S as follows: 
									(10.1)
In obtaining the rate law for the rate of adsorption, reaction in (10.1) can be treated as elementary reactions. 
Rate of attachment of the molecules of A to the surface 
Number of collisions that the molecules of A make with the surface 
(Partial pressure of A) x (Concentration of vacant site)  
(PA) x (CV)    
where PA is the partial pressure of A in the gas phase, and CV is the molar concentration of vacant sites per unit mass of catalyst (in mol/g cat), which is defined as the number of vacant sites per unit mass of catalyst divided by Avogadro’s number.
Rate of attachment = kAPACV							(10.2)
where kA is the constant of proportionality for the attachment process.
Rate of detachment of the molecules of A from the surface (assuming as a first-order process)
 Concentration of sites occupied by the molecules A.S (i.e., CA.S)    
Rate of detachment = k –ACA.S						(10.3)
where k –A is the constant of proportionality for the detachment process.
Combining (10.2) and (10.3), the net rate of adsorption (rAD) can be written as follows: 
rAD = kAPACV –  k –ACA.S 							(10.4)
Introducing the adsorption equilibrium constant KA (= kA /k–A) in (10.4), we get the following: 
							(10.5)
If A is the only material adsorbed on the catalyst, the active site balance gives the following:  
								(10.6)
where Ct is the total molar concentration of active sites per unit mass of catalyst (in mol/g cat) defined as the number of active sites per unit mass of catalyst divided by Avogadro’s number.
At equilibrium, the net rate of adsorption equals zero. That is, rAD = 0.  Therefore (10.5) gives the following: 
							(10.7)
Combining (10.6) and (10.7) and eliminating CV, we get
							(10.8)
Equation (10.8) is an adsorption isotherm, known as Langmuir Isotherm. Rearranging (10.8), we can get the following linearized equation:
						(10.9)

Let us now consider the dissociative adsorption reaction in which the molecule A2 dissociates upon adsorption onto active sites as shown below: 
								(10.10)
The net rate of adsorption (rAD) for this case would be 
 
At equilibrium, 
							(10.11)
Combining (10.6) and (10.11) and eliminating CV, we get
							(10.12)
Equation (10.12) is the Langmuir Isotherm for dissociative adsorption. Rearranging (10.12), we can get the following linearized equation:
						(10.13)

Exercise 10.1: Tabulated data were gathered during adsorption of hydrogen on powdered copper at 25oC. Determine if the data fit the Langmuir isotherm given by (10.8) or (10.12).
Increasing pressure, PH2 (torr)	CH2.S x 102 
(g mol/ g Cu)	Decreasing pressure, PH2 (torr)	CH2.S x 102 
(g mol/ g Cu)	
3.25	0.559	45.1	1.160	
8.90	0.761	21.5	0.995	
17.65	0.941	10.65	0.800	
36.2	1.212	5.40	0.659	
74.5	1.281	2.95	0.564	
204.8	1.471	1.70	0.464	
1 torr = 1 mm Hg = 0.133 Pa = 0.00132 atm	

Exercise 10.2: Show that the adsorption isotherm of A in the presence of adsorbent B is given by 
  
when the adsorption of both A and B and desorptions are first-order processes, and both A and B are adsorbed as molecules.  

The surface reaction step: Once a reactant had been adsorbed onto the surface, it is capable of reacting in a number of ways to form the reaction product, which are the single-site mechanism, dual-site mechanism, and the reaction between adsorbed molecule and a molecule in the gas-phase. 

1. 	Single site. In single-site mechanism, only the site on which the reactant is adsorbed is involved in the reaction. For example, an adsorbed molecule of A may isomerizes (or perhaps decompose) directly on the site to which it is attached. 
								(10.14)
An example is the n-pentene yielding i-pentene on Al2O3 surface. Assuming elementary reaction mechanism, the surface reaction rate can be given by 
							(10.15)
where KS is the surface reaction equilibrium constant given by KS (= kS /k –S).

2.	Dual site. The surface reaction may be a dual-site mechanism in which the adsorbed reactant interacts with another site (either unoccupied or occupied) to form the product. For example, adsorbed A may react with an adjacent vacant site to yield a vacant site and a site on which the product is adsorbed. 
							(10.16)
The corresponding surface reaction rate can be given by
						(10.17)
The single-site or dual-site mechanisams described above are referred to as Langmuir-Hinshelwood kinetics.

3.	Eley-Rideal mechanism is the reaction between an adsorbed molecule and a molecule in the gas-phase. 
							(10.18)
The corresponding surface reaction rate can be given by
						(10.19)

The desorption step: In each of the cases discussed above, the products of the surface reaction adsorbed on the surface are subsequently desorbed into the gas phase. 
									(10.20)
Rate of detachment = k –BCB.S
Rate of attachment = k BPBCV
The net rate of desorption (rD) can therefore be written as follows: 
				(10.21)
where the desorption equilibrium constant KB (= kB /k–B). 
 
The Rate Limiting Step: Which Step Has the Largest Resistance?

Hydrodemethylation of toluene:
Step 1: Adsorption of toluene (T) on an active site (S) of the catalyst surface

							(10.22)
Step 2: Toluene adsorbed on the active site reacts with hydrogen in the gas-phase to produce benzene (B) adsorbed on the surface and methane (M) in the gas-phase. 

						(10.23)
Step 3: Benzene is then desorbed from the surface.

							(10.24)
If the reaction is surface-reaction limiting then (-rS) < rAD and (-rS) < rD. 
Therefore, kS << kT and kS << kB.
Thus, we can set rAD / kT ≈ 0 and rD / kB ≈ 0. 
The net rate of reaction is indeed given by (10.23). 
We need to determine CT.S. and CB.S of (10.23), for which we will use rAD / kT ≈ 0 and rD / kB ≈ 0. 
rAD / kT ≈ 0 gives 						(10.25)
rD / kB ≈ 0 gives 						(10.26)
Site balance gives 					(10.27)
Combining (10.25), (10.26) and (10.27), we get
						(10.28)
Using (10.25), (10.26) and (10.28), we can rewrite (10.23) as follows: 

where k = Ct kS and Ke =KTKS / KB.

If the reverse surface reaction is neglected, we get
 
which can be written in linearized form as follows: 
			(10.29)

Exercise 10.3: Determine the rate-law parameters k, KB and KT using the data tabulated below:
Run	rS x 1010
(g mol/g cat. s)	PT
(atm)	PH2
(atm)	PB
(atm)	
3	41.6	1	1	1	
4	19.7	1	1	4	
6	17.1	1	1	5	
7	71.8	1	1	0	
9	284.0	1	4	0	
10	47.0	0.5	1	0	
12	117.0	5	1	0	
13	127.0	10	1	0	
14	131.0	15	1	0	
15	133.0	20	1	0	

Ref: Chapter 6 of H.S . Fogler, Elements of Reaction Engineering (2nd edition)