Altering the mechanism of a reaction so that the activation energyThe energy barrier over which a reaction must progress in order for reactants to form products; the minimum energy that reactants must have if they are to be converted to products. is lower is the second major way to speed up the reaction. A catalystA substance that increases the rate of a chemical reaction but that undergoes no net change during the reaction. can do this by participating in the activated complexIn the mechanism of a reaction, a species that lies at an energy peak and that can change either into products or into reactants; also called a transition state. for the rate-limiting stepThe step in a reaction mechanism that by its relatively slow rate limits the overall rate of a reaction; also called rate-determining step., even though the catalyst itself is neither a reactantA substance consumed by a chemical reaction. nor a productA substance produced by a chemical reaction. in the overall stoichiometric equation.
A good example of catalysisThe increase in rate of a reaction due to the presence of a substance that undergoes no net change during the reaction. is provided by the effect of I2 on the rate of isomerization of cisDescribes the relationship between two atoms or groups of atoms, each attached to one of two doubly bonded carbon atoms and located on the same side of the double bond. Also refers to groups located adjacent to each other in an octahedral or square planar coordination complex.-2-butene. You will recall from the section on rate equations that the rate lawAn equation which describes the rate of a reaction as a function of the rate constant and the concentrations of reactants (and any other substances that affect the rate, such as products or catalysts); also called rate equation. for the catalyzed reaction involves the concentrationA measure of the ratio of the quantity of a substance to the quantity of solvent, solution, or ore. Also, the process of making something more concentrated. of I2 raised to the one-half power. This implies that half a moleculeA set of atoms joined by covalent bonds and having no net charge. of I2 (that is, an I atom) is involved in the activated complex, which probably has the structure
Since there is no double bondAttraction between two atoms (nuclei and core electrons) that results from sharing two pairs of electrons between the atoms; a bond with bond order = 2. between the two central C atomsThe smallest particle of an element that can be involved in chemical combination with another element; an atom consists of protons and neutrons in a tiny, very dense nucleus, surrounded by electrons, which occupy most of its volume., one end of the activated complex can readily twist around the other.
The currently accepted mechanism for this catalyzed reaction involves three steps:
½ I2 I
I + cis-C4H8 → C4H8I‡ → transDescribes the relationship between two atoms or groups of atoms, each attached to one of two doubly bonded carbon atoms and located on the opposite side of the double bond. Also refers to groups located opposite to each other in an octahedral or square planar coordination complex.-C4H8 + I
I ½ I2
The first and last steps have coefficients of one-half associated with I2 because each I2 molecule that dissociates produces two I atoms, only one of which is needed to help a given cis-2-butene molecule to read. Note also that for every I2 molecule which dissociates in the first step of the mechanism, an I2 molecule is eventually regenerated by the last step. As a result, the concentration of I2 after the reaction remains exactly the same as before.
If we consider the energetics of each step in the proposed mechanism, we find that much less than the 262 kJ mol–1 activation energy of the uncatalyzed reaction is required. A complete energy profile for the catalyzed process is compared with that of the uncatalyzed one in Fig. 1. The bond enthalpyThe change in enthalpy when a mole of chemical bonds of a particular type are broken; the molecules whose bonds are broken must be in the gas phase. Closely related to bond energy. is 151 kJ mol–1 (from Table 1 in the bond enthalpy section), and so 75.5 kJ mol–1 will be required for formation of the I atom in the first step. An additional increase in energy occurs as the I atom collides with cis-2-butene and bonds with it. Then about 12 kJ mol–1 is required for twisting around the C—C single bondAttraction between two atoms (nuclei and core electrons) that results from sharing a single pair of electrons between the atoms; a bond with bond order = 1. in the activated complex. All told 115 kJ mol–1 is required to go from the initial molecules to the activated complex. When rotation to a trans structure is complete, the I atom dissociates fromtrans-2-buten and eventually reacts with another I atom to form I2. These last two processes involve an overall decrease in energy which is nearly the same as the increase required to achieve the activated complex.
The reductionThat part of a chemical reaction in which a reactant gains electrons; simultaneous oxidation of a reactant must occur. in activation energy illustrated in Fig. 1 is the chief factor in speeding up the catalyzed reaction.
EXAMPLE Based on activation energies given, how many times larger would the rate constantIn a differential rate equation, the proportionality constant that relates the rate with the concentrations of reactants and other species that affect the rate. The rate constant is the rate of reaction when all concentrations are 1 M. be for the catalyzed rather than for the uncatalyzed isomerization of cis-2-butene at a temperatureA physical property that indicates whether one object can transfer thermal energy to another object. of 500 K?
SolutionA mixture of one or more substances dissolved in a solvent to give a homogeneous mixture. The fraction of molecules which have sufficient energy to achieve the activated complex can he calculated using equation 1 from the section on the effect of temperature on catalysis:
- Fraction (catalyzed) = 10–115 kJ mol–1/(2.303 × 8.314 J K–1 mol–1 × 500K) = 10–12.0 = 1 × 10–12
- Fraction (uncatalyzed) = 10–262 kJ mol–1/(2.303 × 8.314 J K–1 mol–1 × 500K) = 10–27.4 = 4 × 10–28
Since the respective rate constants should be proportional to these fractions,
- = = 2.5 × 1015
Thus at unitA particular measure of a physical quantity that is used to express the magnitude of the physical quantity; for example, the meter is the unit of the physical quantity, length. concentrations of cis-2-butene and iodine, the catalyzed reaction will be more than 1015 times faster.
Another example of catalysis is involved in the reaction between H2O2 and the I– ion. In discussing this reaction in example 2 in the rate equation section we noted that it is first order in H2O2 and first order in I– ion between pH = 3 and pH = 5. At lower pH values, however, a different mechanism takes over, and the rate law becomes
- Rate = k(cH2O2)(cI–)(cH+)
This indicates that the activated complex contains an additional protonThe positively charged particle in an atomic nucleus; its mass is similar to the mass of a hydrogen atom. when compared with the uncatalyzed case. This proton apparently adds to the H2O2 molecule, forming H3O2+. Because of the positive charge, less energy increase occurs as an I– ion approaches H3O2+ and the reaction
- H3O2+ + I– → H2O + HOI
has a lower activation energy than
- H2O2 + I– → OH– + HOI
The latter is the rate-limiting step in the mechanism at higher pH (Eqs. (1a), (1b), and (1c) in the reaction mechanisms section), and so protonating H2O2 results in a faster overall reaction. Measurements over a range of temperatures show that the activation energy is lowered from 56 to 43.6 kJ mol–1 by this change of mechanism.
The peroxide-iodide reaction is one example of a great many acidIn Arrhenius theory, a substance that produces hydrogen ions (hydronium ions) in aqueous solution. In Bronsted-Lowry theory, a hydrogen-ion (proton) donor. In Lewis theory, a species that accepts a pair of electrons to form a covalent bond.-catalyzed reactions. In most of these the hydrogen ion concentration appears in the rate law, indicating that the activated complex contains an extra proton. The positive charge of this proton allows negative ions to combine more readily with the protonated species. The proton may also shift electronA negatively charged, sub-atomic particle with charge of 1.602 x 10-19 coulombs and mass of9.109 x 1023 kilograms; electrons have both wave and particle properties; electrons occupy most of the volume of an atom but represent only a tiny fraction of an atom's mass. densityThe ratio of the mass of a sample of a material to its volume. toward itself and away from some other site in the protonated molecule, allowing a negative species to bond to that site more readily. The net result is a lower activation energy and a more rapid reaction. The preceding examples are illustrative of the three main features of catalysis:
1 The catalyst allows the reaction to proceed via an alternative mechanism.
2 The catalyst is directly involved in this mechanism, but for every step in which a catalyst molecule is a reactant, there is another step where the catalyst appears as a product. Thus there is no net consumption of the catalyst.
3 The catalyzed mechanism results in a faster reaction, usually because the overall activation energy is lowered.