WHAT ARE CHAIN REACTIONS? R. H. CRIST, COLUMBIA UNIVERSITY,NEWYORK CITY
Consecutive reactions that repeat their cycle many times after being initiated are called chain reactions. The termination of a chain occurs when one of the components of the set i s remmed permanently or suffers a n energy loss suficient to preerent its continued reaction. I n case the number of chains initiated per unit time is greater than those terminated the reaction m y increase to explosive proportions. Chainr may be initiated by a variety qf methods: photochemical, a-$article and electron collisions, and chemical. The photochemical equivalence law affords a means of estimating the number of chains started.
. . . . . .
Scientific curiosity was not long satisfied with knowing what substances result from chemical changes. It began quickly to delve into the nature of the process itself to see by which of a possible variety of paths the action may proceed. Certain simple organic and inorganic reactions were found to take "concurrently" a number of paths to the production of a single substance in one case, or, in another, of an equal variety of products. The path of the lead chamber process for sulfuric acid was fairly well indicated by the isolation of the intermediate compound. The rates of formation and decomposition of this compound determine the rate of formation of the final product. In the event the amount of the intermediate is insufficient for observation i t still determines the rate of the reaction. In the case of an unexplained mechanism a similar intermediate could be assumed and if the observations on the rate of formation of the final product were compatible with the assumption then we have "eluadated the mechanism of the reaction. Such mechanisms in which an essential component enters into the reaction yet remains constant by being regenerated are "catalytic" are in our present sense "chain" mechanisms. A reaction that has long been of interest is that of hydrogen and oxygen and it is also typical of those reactions that are so fast as to be explosive. Mixtures of hydrogen and oxygen a t room temperature are indifferent until a catalyst or local heating induces reaction after which the catalyst is unnecessary. The reaction proceeds throughout the mixture a t a rate which increases to a constant value. "Hot" molecules produced by the initial heating and by the heat evolved might be suggested as the induction mechanism. Another reaction of this type is the formation of hydrogen chloride. It can be initiated by a variety of different and fairly well understood methods which indicate that such simple formulations as
+ On = 2Hn0 + CL = 2HC1
2Hn Hn
are quite inadequate. Light has long been known to induce reaction in mixtures of hydrogen and chlorine, one light corpuscle being able to cause 504
VOL.8, NO.3
WHAT ARE CHAIN REACTIONS?
505
the reaction of a million molecules of chlorine. It is generally believed that the light corpuscle, or quantum, should be capable of causing just the one chlorine molecule to react by which it has been absorbed (the Einstein law of photochemical equivalence). It is of especial significance that the total change is proportional to the number of quanta absorbed, that is, a process of definite duration has occurred for each quantum. The chlorine molecule has become a catalyst whose activity is maintained until a million molecules have reacted. A closer examination has been made possible by the concept of chain mechanisms. This requires an initial process yielding an "active" substance that proceeds through a set of individually known or assumed consecutive reactions to the regeneration of the active product which repeats the process. The following set of reactions has been proposed: CI2 = 2C1 (initial light reaction) CI HZ+HCI H H Cln -+HCI C1 H HCI --+ H2 C1 H+H--+H2 CI CI +Clr H C1 --+ HCI
+ + +
+ + +
+ +
The most satisfactory example of a chain reaction is the thermal and photochemical formation of hydrogen bromide. The mechanism is similar to that above. Br* +2Br Br+H2+HBr+H H + Bn+HBr+ Br H HBr+H2 Br H Br --+ HBr HfH+H, Br Br +Br,
+ + +
+
(1) (2) (3) (4) (5) (6)
(7)
Each of these reactions can be realized separately. (1) and (7) simply represent the dissociation and association of bromine. Atomic hydrogen reacts readily with itself, with bromine, and with hydrogen bromide. (2) is the reverse of (3) and the probability of occurrence will depend upon the relative concentrations and the velocity constants. The chain would be terminated by (51, (B), and (7), and also on the walls if the pressure is so low that the atomic species will reach the walls before collision with reacting molecules. The intermediate products and processes cannot be isolated so that their plausibility must be determined from rate reactions. Analysis of the set of reactions (1) indicates that the rate of formation of hydrogen bromide should proceed as follows:
506
JOURNAL OF CHEMICAL EDUCATION
MARC&1931
The constants for the corresponding reactions can be consolidated for comparison with experiment. The experimental examination by Bodenstein and his students (2) resulted in an equation for both the thermal and photochemical rates that is identical with the theoretical equation, thus affording a strong basis for the mechanism. If this suggested mechanism is the true one then certain consequences should be observed as the temperature is changed. The initiation of chains in the thermal reaction is determinated by the bromine dissociation and in the photochemical reaction by absorbed quanta in addition. Their termination is the same in both. The readiness with which bromine atoms react with hydrogen molecules as well as the production of bromine atoms are greatly dependent upon the temperature, the reactions being endothermic. Absorption of light quanta by bromine molecules and their subsequent dissociation are practically independent of the temperature. From knowledge of the energies of activation and their established relation to the rate of the reaction* the effect of a temperature increase can he predicted. This predicted increase in the number of chains and their greater length, that is, increase in the reaction rate, has been verified by experiment thus further increasing our confidence in the proposed mechanism. The hydrogen chloride formation should proceed in a similar manner, yet over a century of persistent effort has not sufficed to give an adequate account of the reaction. I t is peculiarly sensitive to very small traces of different substances. For example, ammonia retards the rate initially, and oxygen permanently inversely as its concentration; the water vapor must he more than lo-' mm. for reaction to occur. As a consequence much contradictory and divergent experimental and theoretical work has been done. The thermal reaction is of little assistance, as few of its complications can he correlated with those of the photochemical reaction. Such varied findings have been explained by a similar variety of chain mechanisms. For instance, oxygen reacts with the chlorine or hydrogen atoms as follows: Cl C10,
+ 0~+CIO*
+ C1-+
C12
+ On
H H
+ O2 +HOr
+ HOz + + On H 2
resulting in a negative "catalytic" effect. Water is necessary in the first part of the chain so we have an attempted explanation in C1 OH H
+ H.0 +HCl + OH + Hz +H20 + H + Clz -+ HCl + CI
* The empirical relation of Arrhenius. d i n k / d T = A / R T 2 , where k is the velocity constant and A the heat of activation.
VOL.8. No. 3
WHAT ARE CHAIN REACTIONS?
507
where the water molecule is a positive catalyst. The initial stage of the reaction is also uncertain, it being difficult to decide whether the original reaction ,is* C1, + k. 4 2C1 C12
or
+ hv
4 CI's
Some other interesting methods of initiating chains in the hydrogen chlorine mixture have been investigated recently. If hydrogen is introduced into a reacting mixture of sodium vapor and chlorine, then hydrogen chloride and sodium result. It has been established that Na
+ Cb
4
NaCl
+ C1
and the C1 would produce a chain as previously outlined: The amount of hydrogen chloride formed was upward of two hundred times that of the sodium chloride which is about the same yield for the photochemical formation under the same conditions. Direct introduction of hydrogen atoms as from a discharge tube into a hydrogen chlorine mixture will accomplish the synthesis of hydrogen chloride thus, H
+
CIS +HC1
+
C1,
and the chain is started. It is difficult, however, to get quantitative information concerning the number and length of the chains in this case. A further interesting method of inducing reaction is by the action of a particles. The well-known primary result of the collision of an a particle with the gas molecules is ionization of the gas CIS--+ Clt+
+
r.
The fate of the electron can be represented by CIS+ CllC
+r +r
4 Clr 4 Cln-,
the probability of the second reactions occurring in this or other cases will depend upon the nature of the gas. In chlorine and oxygen, for example, one attachment results after more than a thousand collisions while the molecule HZ- is extremely improbable. In case other molecules are present the ionized products may undergo or may induce reaction In the hydrogen chlorine mixture the reaction is certainly induced. The number of ions produced by the passing of one a particle into the gas is known with considerable exactness and the number of hydrogen chloride molecules produced is found to he mauy times the number of original ions formed. The number in fact is about twice as mauy per ion pair as previously found per quantum. It has been found recently also that the effect of
* h is Planck's constant and v the frequency of light, their product representing the energy in one quantum.
508
JOURNAL OF CHEMICAL EDUCATION
MARCH,1931
the temperature on the photochemical and radiochemical reactions is the same. Since the primary acts are in each case not significantly affected by a change in temperature the same temperature coefficient strongly suggests a similar subsequent process and attempts have been made to show the generation of the previously suggested atomic species from the gas ions. This similarity of result with light quanta and or particles has also been found for the phosgene reaction CO
+ CIZ+COCI~,
which is also believed to have a chain mechanism. The reactions proceed in precisely the &me manner and with the same yield per quantum as per original ion pair. Now, if in a reacting mixture the number of chains being initiated is greater than the number terminated the reaction might develop into an explosion. This would be a chain mechanism of an explosion and an attempt has been made recently (3) to apply this view more closely. The reaction front in detonating gas mixtures increases in speed to a constant maximum, the velocity of the explosion wave, which is 1763 meters per second for the hydrogen chlorine mixture. This can be assumed to be the velocity of a chlorine atom in the direction of observation. Very satisfactory agreements have been found between this assumed velocity of the chlorine atom and that calculated from the thermochemical data. It is suggested that the OH molecule "carries" the wave in the hydrogen oxygen explosion:
+
HI O2 --i,2 0 H OH H* --i,H,O H+O.+H2--?,H~Of OH Hz -+ etc.
+
+
+H OH
In a number of oxidations atomic oxygen is assumed to be the "carrier." The idea of reaction chains has been extended to both thermal and photochemical reactions in solution in explanation of certain abnormal quantum yields and large positive or negative catalytic effects. Extremely small amounts of particular substances produce effects that are far out of proportion to their quantity. In the oxidation of sodium sulfite the retardation by alcohol is explained as a breaking of the chain by a permanent removal of the active component. In many cases the solvent effects seem di5cult to interpret. In conclusion i t might be observed that the idea of chain reactions has been a very useful instrument in conjunction with the law of photochemical equivalence which gives a good theoretical basis for the number of such chains initiated.
Literature Cited (1) CHRISTIANSEN, Danske. Vid. Math. Phys. Medd., 1 , 14 (1919); HERZPELD,Z. El&Irockm., 25, 301 (1919), Ann. Physik, 59, 635 (1919); POLANYI. Z. Elektrochem., 26, 50 (1920). Z. physik. Chem., 121, 127 (1926); BODENSTEIN (2) BonENsTErN and L~TKEMEYER, and LIND, ibid., 57, 168 (1907). B . , I.A m . Chem. Soc., 52,3120 (1930). (3) LEWIS,
