A.3.5 Slower Reaction Controls [C]
4.7 THE ACTIVATED STATE .1 a CtivatiOn e nergy
An alternate way to justify the Arrhenius equation is to use a thermodynamic approach and assume that only certain atoms or molecules have energies in excess of the activation energy, EA, and that they are in some activated state. For example, for the reaction of H2 and I2 to form HI the hydrogen and iodine molecules will collide with each other in the gas phase, so there will be Z such collisions per second (Figure 4.10). However, only some of these molecules will have enough energy to react, namely, those in an activated state, H2*
, for example. Assuming a first-order reaction in hydrogen for simplicity, the reaction rate could be written as
d H
dt2 Z H2
[ ]
= − ∗ (4.15)where H*2
is the concentration of hydrogen molecules that have enough energy to react or the concentration of hydrogen molecules in the “activated state.” There is an equilibrium between the molecules in the activated state and those in a normal state, determined by an activation Gibbs energy, ΔG*,
ΔG* = ΔH* − TΔS*
and an equilibrium constant can be written for the reaction H2H*2
H
H K
G RT
S R
H 2 RT
2
∗
∗ − −
= = =
∗ ∗ ∗
e e e
∆ ∆ ∆
(4.16) so that the rate of reaction becomes
d H
dt Z H Ze
S R
H RT
S R
H 2 RT
= − 2 = −
∗ ∗ ∗ ∗
− − −
e e e
∆ ∆ ∆ ∆
= −
= −
−
[H ]
k H k H
Q RT
2
0e 2 2 (4.17)
which means that the activation energy, Q, is the activation enthalpy, ΔH*, and k0=Zexp(∆S R∗/ ) in k k= 0exp(−Q RT/ ). The activation entropy, ΔS*, probably includes some orientation effects sug- gested in Figure 4.10, namely, the reacting molecules have to be oriented in a particular spatial rela- tion, or close to it, in order to react. Two possible orientations are shown at the bottom of the figure.
Possible collision configuration
Another possible collision configuration
Iodine, I2 Hydrogen, H2
(a)
(b) (c)
FIGURE 4.10 (a) Schematic representation of hydrogen and iodine molecules colliding in the gas phase to react to form 2 HI molecules. (b) Possible orientation configuration of the molecules when they collide.
(c) Another possible orientation on collision. Note that the bonds between the atoms are represented by springs giving rise to the vibrational energy of the diatomic molecules. However, the distances between molecules and the lengths of the spring are greatly exaggerated.
However, it should be noted that all of these diatomic molecules are rapidly rotating and vibrating that makes the details of their interaction rather complex.
Another way of representing this activated state is on a plot of the Gibbs energy as a function of the extent of the reaction or the reaction coordinate shown in Figure 4.11. ΔGo is the energy for the reaction, but for it to occur, molecules must be excited into the activated state having an energy ΔG*
above the energy of the reactants. Therefore, there is an activation energy or activation barrier, ΔG*, that must be overcome for the reaction to proceed.
4.7.2 r
OleOfaC
atalystIt is usually stated that the role of a catalyst—something that speeds up(usually) the rate of a reaction but does not enter the reaction—is to lower the activation energy for reaction. For example, platinum is used to speed up the reaction between oxygen in hydrogen in a proton exchange membrane (PEM) fuel cell.* Platinum is also used as a catalyst to speed up the combination of oxygen ions diffusing through ionically conducting zirconia, ZrO2, to form oxygen gas in automobile oxygen sensors and, of course, it is used in large quantities as the oxidation catalyst in vehicle catalytic converters to oxidize CO and any unburned hydrocarbons in exhaust gases.
However, catalysts usually play a more complex role than merely reducing the activation energy for a reaction. More generally, a catalyst provides an entirely different reaction pathway for a reac- tion to occur, most likely containing several different steps as shown schematically in Figure 4.12 (Haim 1989). As a result, to suggest that the primary role of a catalyst is to simply lower the activa- tion energy for reaction is too simplistic. Although the intent is not to spend a lot of time on the atomistic or molecular details of reactions at surfaces or interfaces, one illustration is given for the simple case of what is thought to occur at the surface of platinum when it catalyzes the simple reac- tion of (Dickerson and Geis 1976; Friend 1993)
H g2( )+D g2( )2HD g( )
where D stands for deuterium or 2H. Figure 4.13 attempts to show the five steps envisioned to occur at the surface of the platinum. Note that because these are series steps, the slowest will control the overall rate. The steps are the following: (1) H2 and D2 adsorb onto the surface of the platinum.
(2) The diatomic bonds in the H2 and D2 molecules are broken by the electronic attraction—and larger separation distance—of the electron orbitals of the platinum surface atoms. Eventually, most of the Pt sites on the surface are covered with single H or D atoms. When another molecule is absorbed to one of the few remaining empty sites, as in step 3, it can no longer be separated, but it is attracted to a neighboring H or D atom. The molecule can then exchange one of its atoms to the adsorbed
* A PEM fuel cell is called either a polymer electrolyte membrane or proton exchange membrane fuel cell.
Reactants
Products ΔG°
ΔG* Activated state
Reaction coordinate/reaction extent Activation energy
Gibbs energy, G (kJ/mole)
FIGURE 4.11 Free energies as a function of the extent of the reaction from reactants to products. In order to react, the reactants must reach some activated state or activation free energy, ΔG*.
atom forming another molecule—on the average, an HD molecule. The HD molecule is shown on the platinum surface in step 4. Finally, the HD molecule desorbs from the surface as shown in step 5 releasing this site for further reaction. In reality, the H and D atoms are probably diffusing around on the surface, so that the locations of the open sites are constantly changing.
Clearly, the electronic surface properties of the platinum are extremely important. There should be a sufficiently strong attraction between the Pt and the gas molecules to break the bond and sepa- rate the molecule into atoms, but not strong enough to form a permanent bond with either the diatomic molecule or a single atom at the surface. Understanding the details of the electronic struc- tures of surfaces and their roles in catalysis is an active area of surface physics and chemistry research.
It is very attractive to be able to tailor the electronic properties of an alloy or compound consisting of more readily available and cheaper materials than platinum or other noble metals. There have been instances in the past in which new catalyst compounds were thought to have been found only to have subsequent research show that the materials were contaminated with small platinum particles that were actually doing the catalysis.
H
H H H
D D D
D
D D D
H H H
H
H H
1 1
2 2
3
4
5 D
FIGURE 4.13 Schematic representation of the reaction H g D g2( )+ 2( )2HD g( ) on the surface of a noble metal such platinum: adsorption of H2 and D2 on the surface (1), breaking of the molecular bond and separation of the atoms on the surface (2), the molecule interacts with a surface atom forming an HD molecule (3), HD molecule attached to the surface (4), and desorption of HD from the surface (5).
Reactants
Products
Reaction coordinate/reaction extent Without
catalyst
ΔG* with catalyst
With catalyst Gibbs energy, G (kJ/mole) ΔG°
FIGURE 4.12 The effect of a catalyst on the reaction rate, activation energy, and activated state. The reality is that a catalyst frequently leads to a different pathway for the reaction that may show several steps, two in series are shown here, and not just lower the activation energy for the reaction.
Other good examples where catalysts provide more than just a decrease in activation energies are biological processes in which enzymes serve as catalysts. Take for example the oxidation of sucrose, sugar, C12H22O11. Sugar will burn in air being oxidized to
C H O s12 22 11( )+12O g2( )→12CO g2( )+11H O g2 ( ) (4.18) and the large enthalpy for the reaction will sustain combustion just like any SHS reaction. In fact, a mixture of sugar and a good oxidizer such as potassium nitrate, KNO3, makes a nice solid fuel model rocket propellant. However, in the human body, enzymes take the sugar molecules apart slowly piece by piece generating the energy necessary for life. Clearly, the overall reaction pathways for combus- tion and biological oxidation of sugar are very different, and the enzymes do much more than just lower the activation energy of the reaction.
Another example is the use of Ziegler–Natta catalysts (Claverie and Schaper 2013) on the polym- erization of olefins, unsaturated hydrocarbon molecules with one or more carbon double bonds such as ethylene, H C CH2 = 2. In this case, these catalysts—both homogeneous and heterogeneous—are designed to control, usually minimize, the branching of the polymer chain. As was seen in Chapter 3, radical polymerization is frequently used to make nominally linear polymers such as polyeth- ylene, [CH CH2 2]n. However, during polymerization, the radical may end up someplace along the chain, rather than at its end, forming a side branch and a branched polymer molecule. In contrast, Ziegler–Natta catalysts contain transition metal atoms, and the interaction of the monomers with the d- orbitals of these atoms adds additional monomers to the polymer molecule only at one site, essentially at the beginning of the molecule. As a result, these catalysts minimize branching. The lack of branching leads to better packing of the polymer molecules and a larger degree of crystallinity in polymers such as high density polyethylene, HDPE. These catalysts can also be designed to control the stereochemistry of the polymer chain, the tacticity, by determining how the various side groups arrange along the length of the polymer chain. Ziegler–Natta catalysts clearly demonstrate that the role of a catalyst is not merely to lower the activation energy for reaction but actually change the overall configuration of the polymer molecules.