ChemBytes - Chapter 14

Chemical Kinetics

CHEMByte 30: He Was Called "Kisty."
George B. Kistiakowsky, known to all his students and colleagues as "Kisty," was born in Kiev (Russia) in 1900. It was a time of revolution, and as a young man he fought in the White Russian Army. Studying chemistry in Germany, Kistiakowsky obtained his doctorate in 1926, the year he came to the United States. For more than 40 years afterwards, he was professor of chemistry at Harvard University, receiving many awards, including the Priestley Medal for his research in chemical kinetics, and was recognized for his work by three Presidents of the United States (Truman, Eisenhower, and Kennedy). Kistiakowsky was Eisenhower's Assistant for Science and Technology and Chairman of the Science Advisory Committee from 1957-1963 (under Eisenhower and Kennedy). Besides his benchmark studies on rates of chemical reactions, he was an authority on explosives, and as a key member of the Manhattan Project, designed the triggering mechanism for the first atomic bomb, which was tested at Alamagordo, New Mexico in July of 1945. Though he ranked high among those who developed the bomb (being Director of the Los Alamos Laboratory at the time), he almost immediately sensed the extraordinary potential of atomic weapons for destruction and became an advocate for severely limiting, and then preventing, their use. He resigned from the Pentagon in 1967 and returned to full time teaching and research at Harvard. Summarizing his opinions on nuclear weapons in the last year of his life (1982), he wrote that the world could well explode unless an unprecedented mass movement for peace could be created to halt the threat of nuclear annihilation.

Among his classic studies on chemical kinetics in the 1930s is the dimerization, or coupling, of butadiene (C4H6), an important example of a second order process involving one reacting species:
2 C4H6 (g) C8H12 (g)
Introducing butadiene into an empty flask at 600 K, dimerization begins at time t=0, and the progress of the coupling reaction can be followed by observing the pressure, which decreases as each pair of molecules of butadiene monomer becomes one molecule of dimer. Kistiakowsky's data support the following rate law:
rate = -D[C4H6] / 2Dt = k[C4H6]2
In the reaction, partial pressures are recorded rather than concentrations. Therefore, the equation for the second order process takes the form, 1/p = k + 1/po , where po and p refer to the partial pressure of C4H6. For a value of elapsed time, the partial pressure p of C4H6 is calculated using the reaction stoichiometry and the observed total pressure. By substituting that partial pressure of C4H6 at time t and the initial pressure of C4H6 into the equation for the second order process, the value of the specific rate constant could be calculated. The rate law is consistent with the data since the same value of the specific rate constant is calculated for each value of t within reasonable limits of error. Here is how the partial pressure of C4H6 is calculated from the total pressure:
Letting x = p(C8H12)

2 C4H6 C8H12
Initial po 0
Final po - 2x x
Thus,

ptotal = (po - 2x) + x = po - x
x = po - ptotal
p(C4H6) = po - 2x = po - 2 (po - ptotal) = 2 ptotal - po
In an experiment where po = 632.0 torr and ptotal = 606.6 torr at t = 367 s, the second order rate law predicts
1/p - 1/po = kt
1/581.2 - 1/632.0 = k(367)
k = 3.77 x 10-7 torr-1·s-1
Similar computations for the other times yield consistent values of k and confirm that the reaction is second order.

CHEMByte 31: "The Theory of Rate Processes."
Until the beginning of the 20th century, what was known about chemical kinetics all came from the results of experiments. There were no accepted theories tying experiments together. Little was understood about rates of reactions in terms of the behavior of molecules and chemical bonds. Arrhenius had published his monumental paper on activation energies (1889) which contained the idea of an energy barrier impeding or blocking the progress of a chemical reaction as it proceeded from reactants to products but it was hardly given the attention it deserved. However, with the half-century long career of Henry Eyring, that all changed.

The year 1901 was remarkable for chemistry, being the birth year of Linus Pauling, Enrico Fermi, and Henry Eyring. Born in Mexico of German-English descent, Eyring was trained and educated in engineering -- as a mining engineer at the University of Arizona and received a masters degree in metallurgy in 1924. On graduation, he worked briefly for the Inspiration Copper Company but became quickly disillusioned with the industry because of the poor safety practices at that time. During one short period of time, Eyring witnessed the accidental deaths of three miners. Returning to university to study chemistry, he received his Ph.D. from the University of California (Berkeley) in 1927. As a young instructor at the University of Wisconsin, Eyring came under the influence of Farrington Daniels, stimulating research interests in chemical kinetics that lasted to the end of his long and successful career.
In 1946 Eyring moved to the University of Utah as Professor of Chemistry and Dean of the Graduate School and remained there until his death in 1981. He was a devout, practicing Mormon and an elder of the Mormon Church.
With the publication of his 1934 paper on "The Activated Complex in Chemical Reactions," Eyring firmly established a line of research that profoundly influenced the direction of theoretical chemistry to the present day, connecting the new quantum theory with emerging ideas on the nature of the chemical bond and the understanding of the rates of chemical reactions. His several books and many scientific papers are testaments to his success as a teacher, especially "The Theory of Rate Processes," published in 1941, in which he presented a systematic account of transition state theory which is still in use today. His last book, on rate processes in medicine and biology, was published posthumously in 1984. To many, the surprise of his career is the absence of the Nobel Prize in Chemistry.

CHEMByte 32: Jons Jacob Berzelius Out of the Stockholm laboratory of Jons Berzelius (1779-1848), one of the early 19th century giants of chemistry, came significant discoveries and contributions to inorganic and organic chemistry, chemical analysis and theoretical chemistry such as atomic weights, chemical combination, molecular geometry.... and catalysis. His laboratory could count among its disciples the great Friedrich Wöhler who in turn trained and educated the generation of chemists that contributed so much to the rise of chemistry in America in the second half of the 19th century. Berzelius was also a master of literary style and classroom scholarship. His Lehrbuch der Chemie (Textbook of Chemistry) contained the entire body of chemical knowledge known at that time in 6 volumes and comprising over 4000 pages.

CHEMByte 33: Inexpensive, Catalytic Hydrogenation. Paul Sabatier (1854-1941) spent his professional lifetime studying catalysts, for which he was eventually awarded the Nobel Prize. But it was a failed experiment that he conducted in 1897 at the University of Toulouse that got him started on that line of research. Sabatier was fascinated by the fact that nickel could form a volatile compound named nickel carbonyl on reaction with carbon monoxide:

Ni(s) + CO(g) Ni(CO)4(g)       Preparation of nickel carbonyl
What so interested him was the extraordinary fact that a metal could form stable compounds that vaporized at relatively low temperatures. He reasoned that since ethylene has a multiple bond as has carbon monoxide, perhaps it too could form a volatile compound with nickel. But when ethylene was added to the carbon monoxide gas stream being passed over his heated nickel catalyst, no volatile compound of nickel and ethylene could be found. Fortunately, Sabatier and his young graduate student saved what gases did form and to their surprise, found ethane. Apparently nickel had catalyzed the addition of hydrogen to ethylene, forming ethane:
CH2=CH2(g) + H2 (g)    (Ni catalyst) CH3CH3(g)        Nickel-catalyzed hydrogenation
Until the work of Sabatier and his students, catalytic hydrogenation required very expensive materials such as platinum and palladium, precluding widespread, economical use on an industrial scale. Nickel catalysis made it possible to perform such reactions as producing solid fats such as margarine and shortenings from vegetable oils.
Sabatier, of course, in investigating his failed experiment, asked himself where the hydrogen had come from that added to the double bond in ethylene bringing about the catalyzed hydrogenation reaction. He quickly realized. The carbon monoxide was prepared by his student from the reaction of methane and steam and used directly:
CH4(g) + H2O(steam) CO(g) + H2(g)
Stoichiometric quantities of hydrogen were present. And as they say, "The rest is history."

CHEMByte 34: Free Radical Chemistry in a Flash. The fact that light produces chemical reactions has been known for a long time. Light fades colors and causes changes in silver salts that makes it possible for us to create photographic images. For light to produce a chemical reaction, it has to be absorbed by a molecule which then gets so excited that it reacts. In chemistry, excited means raised to a higher and less stable level of potential energy. The excited molecule must dissociate and then recombine into a new arrangement. The time intervals required for light-induced or photochemical excitation are very short. For the very fastest photochemical reactions, the times required are on the order of ten thousandths of a millionth of a second, speeds approaching picoseconds. To estimate what that means, thinks of that small time interval in terms of seconds and years. One ten thousandth of a millionth of a second is the same order of magnitude compared to one second as one second is to hundreds of years. Check it out. Its fast! Until very recently, immeasurably fast.

The realization that free radicals and atoms take part in fast photochemical reactions has proved to be of great practical importance. In the geochemistry of the upper atmosphere, for example, we have been witness to the destruction of the ozone layer for more than a quarter-century. But it was the exothermic synthesis of hydrogen chloride from its elements that first led to the conclusion that the primary reaction indeed involved the photolysis of the reactant molecules into atoms, followed by the well known chain reaction:
Cl2 + hn Cl· + ·Cl      dissociation into atoms
H2 + Cl2 2 HCl + heat       net result of the chain reaction
The early work was done by giants of the period, Bodenstein, Warburg, Nernst, Polanyi.... and no less a chemist than Einstein.
It is possible to demonstrate the elegant simplicity of the photochemical process and, at the same time, the dramatic qualities of fast reactions involving unpaired electrons brought about by propagating chain mechanisms in a now classic lecture demonstration. A heavy-walled, clear glass bottle from a carbonated beverage will do just fine. Fill it 50-50% by volume with hydrogen and chlorine, stopper with a well-fitted cork, mount on a ring stand behind a polycarbonate shield with the stopper aimed to the ceiling, and directly expose the bottle (through the shield) to an intense pulse of light from a powerful flash as is easily obtained from a strobe-like camera flash attachment. The photoflash causes enough chlorine molecules to dissociate to initiate the chain reaction.... and blow the stopper sky-high.... perhaps 30-60 feet up.

CHEMByte 35: The Catalytic Converter It is well known that automobile exhaust is a major air pollutant, containing a variety of incomplete fuel combustion products such as carbon monoxide and various lower molecular weight hydrocarbons as well as combustion by-products such as assorted oxides of nitrogen and sulfur. In the United States and the rest of the industrialized world, catalytic converters are fitted onto automobile exhaust systems to convert combustion products to carbon dioxide and water and the nitrogen oxides back to nitrogen and oxygen. Three-way converters that can handle both those tasks have been installed as original equipment on automobiles since 1980 in the United States. Manufacturing these converters is a billion dollar a year business. Newer designs that meet the more stringent 1991 Clean Air Act requirements have electrical pre-heaters since the greatest amount of pollutants is produced during the first ten minutes of engine operation when it is essentially running cold.

CHEMBytes: Additional Problems on Chemical Kinetics
  1. Articles found in the Lascaux Caves in France have a C14 disintegrqation rate of 2.25 disintegrations per minute per gram of carbon. How old are these articles?
  2. The decomposition of gaseous nitrogen pentoxide occurs according to the following reaction:
    N2O5(g) 2 NO2(g) + 1/2 O2(g)
    The experimental rate law is
    - d[N2O5] / dt = k[N2O5] And the reaction mechanism is believed to be
    N2O5 <=> NO2 + NO3       (K, fast equilibrium)
    NO2 + NO3 NO2 + O2 + NO       (k2, slow step)
    NO + NO3 2 NO2      (k3, fast step)
    (a) Show that this mechanism is consistent with the rate law, and express the experimental rate constant in terms of the rate constant for the elementary processes.
    (b) If k = 5 X 10-4s, how long does it take before the concentration of N2O falls to one-tenth its original value?
  3. Consider the set of reactions
    A + B <=> C + D        (k1 = k-1)
    C + E F        (k2)
    proceeding in a situation where all concentrations are approximately equal. What relationships between the magnitudes of k1, k-1, and k2 will lead to the following rate laws?
    (a) d[f] / dt = k[A][B][C] / [D](b) dF / dt = k'[A]{B]