T H E RADIATION HYPOTHESIS O F CHEMICAL REACTIONS AND T H E CONCEPT O F THRESHOLD WAVELENGTH BY G . GOPALA R.40 A S D S .
R. DHAR
The rapid increase of velocity of a thermal reaction with temperature is one of the outstanding difficulties in the theoretical treatment of chemical dynamics on the basis that there are active and inactive molecules in any system at a given temperature, and increase in the velocity of a reaction with temperature is due mainly to the increase in the proportion of active molecules. Arrhenius' first derived an equation showing the relation between temperature and reaction velocity. This relation can be written as
Subsequently, Marcelin* and Rice3 arrived at a similar relation on the basis of statistical mechanics. According to them E is the energy of activation, that is the energy necessary to convert I mole of normal molecules into the active state. I t becomes obvious, therefore, that the theory of activation and the idea of critical energy increment arc necessary to account for the influence of temperature on chemical reactions. Arrhenius, Marcelin and Rice have not however suggested any mechanism by which molecules become activated. How does a molecule receive the critical energy increment before it reacts? These are fundamental questions, and an answer to this was provided in the general radiation theory of chemical change, put forward originally in an obscure form by Trautz4 and considerably developed by W.C. McLenis5and Perrin.6 Briefly stated, the hypothesis is, that the increase in internal energy, which a molecule must receive before it is capable of reacting, (that is the critical energy increment E) is communicated to it by infrared radiant energy present in the system by virtue of its temperature; the addition of energy being made in terms of quanta of the absorbable type. The velocity of a reaction is therefore determined by the intensity of that radiation and depends only on the temperature in the measure that the intensity depends upon it. In the activation of molecules a narrow band of infrared frequencies was assumed to be operative. If the molecules are activated by more or less monochromatic radiation, then the frequency for the effective radiation can be calculated from the relation E = Nhv 'Arrhenius: Z. physik. Chem., 4,226 (1889). Compt. rend., 157, 1419 (1913);158, 116,407 (1914);Ann. Phys., (9) 3,
* Marcelin: 120 ( 1 9 1 5 ) .
Rice: Brit. Ass. Rep., 387 (1915). Traute: Z. wiss. Phot., 4, I60 (1906);Z.physik. Chem., 76, 129 (1911). W. C. McLewis: J. Chem. SOC.,109, 796 (1916);111, 387, 457, 1087 (1917); Phil. Mag., 39, 26 (1920). Perrin: Ann. Phys., (9) 11, 5 (1919). a
RADIATION HYPOTHESIS OF CHEMICAL REACTIOSS
637
E is the energy of activation, the value of which can be obtained from the temperature coefficient of the reaction, N is Avogadro's number and v is Planck's constant. Thus, the radiation hypothesis represents an extension of Einstein's law of photochemical equivalence. There are three consequences of the radiation hypothesis which should serve as a test for its validity. ( I ) Firstly the frequencycalculated fromE must correspond to a wavelength in the observed absorption band. ( 2 ) The reaction must be greatlyaccelerated by light of the calculated wavelength, and (3) thirdly thr total amount of energy corresponding to this wavelength in the dark must be sufficient to activate the requisite number of molecules so as to account for the dark reaction. Kow let us consider the evidence on these three heads. Lewis and coworkers have shown that in a large number of cases the observed and calculated frequencies do agree. Ethylsulphonium bromide has been shown by von Halban to decompose into ethyl bromide and diethyl sulphide in a unimolecular manner in various solvents. Taylor and Lewis have shown that in this case the calculated and observed absorption lines show a remnrkable agreement in the case of eight solvents studied. Similar coincidence was obtained in the case of the inversion of sucrose (Moran and Taylor') in the conversion of y-hydroxybutyric acid into the lactone (Garret and Taylor') and in the hydrolysis of acetamide (Meehan?). A further case is the transformation of fused maleic acid into fumaric acid; of course, there are some cases of disagreement also (Cf. Langmuir3). Furthermore, Lewis on the basis of certain calculations made with the help of the radiation theory, predicted in 1918 that ozone should be decomposed by visible light. Griffith and Shuttl shoized that ozone is decomposed by light of wavelength larger than 6700 A near the red end of the spectrum. On the other hand, Lindemann has pointed out that the inversion of sucrose (which has a temperature coefficient of 3.13 corresponding to wavelength 10j80 A) must be greatly accelerated by sunlight which contains a large proportion of this wavelength; and reported that such indeed is not the case. Dhar,j however, has shown that the reaction is greatly accelerated by sunlight. Furthermore, Daniels and Johnston, working with nitrogen pentoxide decomposition, and Framegot, studying the reduction of ceric salts by acetaldehyde in acid solution, have reported that insolation with appropriate wavelength does not lead to increased reaction velocity. There appears to be some contradiction, therefore, on the second point. The hypothesis as originally put forward by Lewis, fails more completely when we consider the third deduction:-it has been shown by Langmuir (loc. cit.) that the radiation theory cannot account quantitatively for the observed rate of dissociation of phosphine. Similar calculations made by Christianren and Kramers6 in the case of nitrogm pentoxide decomposition l
J. Am. Chem. SOC.,44,2886 (1921).
* "A
System of Physical Chemistry," 3, 2 2 6 . (1924). Langmuir: J. Am. Chem. SOC., 42, 2090 (1920). 4Griffith and Shutt: J. Chem. SOC.,119, 1948 (1921). N. R. Dhar: 2. anorg. allgem. Chem., 119, 177 i1921). 'Christiansen and Kramers: 2. physik. Chem., 104, 451 (1923).
648
G. GOPALA RAO AND N . R. DHAR
show that, if activation by monochromatic radiation is assumed, it is not possible to account for the observed rate of decomposition. I t appears that if activation by a more or less continuous band of frequencies of some considerable width is assumed then there would be sufficient absorption in unit time to account for the number of molecules transformed. Nevertheless there is a considerable body of opinion in favour of some form of radiation hypothesis. The acceleration of many reactions by light shows that there is nothing improbable in principle about the supposition that molecules are activated by ordinary temperature radiation. Without some form
70
FIG.I Potassium Oxalate and Bromine
of radiation hypothesis, it appears difficult to account for the occurrence of unimolecular gaseous reactions e.g. decomposition of nitrogen pentoxide [the alternate activation mechanisms put forward by Lindemann (assuming a time lag between activation by collision and chemical change) and by Christiansen and Kramers (reaction chain mechanism) have been shown to be inadequate. Cf. Hinshelwood’]. In view of this one of us2 has put forward the conception that the wavelength calculated from the critical energy increment may be regarded as the threshold limit, No acceleration of the chemical change is possible with radiations of wavelengths longer than the threshold limit, while wavelengths shorter than the threshold wavelength will accelerate the chemical change, provided they are absorbed. The main difference between this conception 1
Hinshelwood: “Kinetics of Chemical Changes in Gaseous Systems,” 126-129 (1926). Chem., 33, 850 (1929); J. Indian Chem. SOC.,6,451 (1929).
* Dhar: J. Phys.
RADIATION HYPOTHESIS O F CHEMICAL REACTIONS
649
and the Perrin-Lewis radiation hypothesis is that according to the latter view the wavelength calculated from the temperature coefficient of the reaction should bring about the maximum speed of the reaction in question, whilst according to the conception now put forward, the threshold frequency is the minimum frequency necessary for carrying out the reaction. Now we have devised a new method of arriving at this threshold wavelength from altogether independent lines. A number of photochemical reactions have been studied in this laboratory in radiations of different wavelengths. It is fouud in general that the quantum yield of any one reaction, that is the number of molecules reacting per quantum of light absorbed, decreases with increase in the wavelength of the light. 4
P
,/
;PI1 --
P
$ FIG.2 Citric Acid and Chromic Acid
The following table illustrates this point of view:Reaction
Quantum yield in wavelength
4725 -4
Citric acid and chromic acid ( 2 1 ' )
3.6
Pot. oxalate and Sromine (zoo)
7.9
Inversicm of cane sugar 35"
8.41 X
Sodium cobaltinitrite (20')
3.75
Sodium cobaltinitrite (40')
Quantum yield in wavelength 56jo A
I.j
2.7
x
Quantum yield in wavelzngth 7304 A
6.66 X
IO
5 . 4 1 X IO
IO*
7.32 X
IO?
1.43
1.1
9.60
6.0
8 jOO
A
1.1
IO
2.23
Quantum yield in waveleFgth
x
IO2
2.82
0.92
X
IO?
G . GOPALA RAO A N D N . R. DHAR
650
If now we plot the quantum yields against the wavelengths and extrapolate the curve to zero quantum yield, we can get the wavelength with which there should be no acceleration of the chemical change, that is the threshold limit referred to above. Now all these reactions take place in the dark also, so that the threshold limit can be obtained from the temperature coefficient of the dark reaction. The close agreement between the values of the threshold wavelength obtained by the two methods lends great support to our conception.
Reaction
Threshold wavelength Threshold wavelengt h obtained from the calculated from the temperature coefficient of graph the dark reaction
A
12,200
A
Sodium cobaltinitrite
13000 k
13,500
A
Inversion of cane sugar
10580
10,600 A
Citric acid and chromic acid
I2000
Potassium oxalate and bromine
See Graphs
I
to 3.
RADIATION HTPOTHESIS O F CHEMICAL REACTIONS
651
Summary Some sort of radiation hypothesis appears to be necessary. I t is well known that the hypothesis as originally put forward by Lewis and Perrin is untenable. A modified view of the radiation hypothesis is pu, forward. Xccording to this new conception, the wavelength calculated from the temperature coefficient of the dark reaction, represents the threshold limit. Kavelengths longer than this will have no action, whereas wavelengths shorter than this limiting value will accelerate the reaction, provided they are absorbed. 2. A second method of obtaining this threshold wavelength is described. Many photochemical reactions have been studied in our laboratory in different wavelengths. I t is found that the quantum yield in any reaction generally decreases with increasing wavelength. We have plotted the wavelengths against the quantum yield; and by extrapolation of the curve to zero quantum yield, the threshold wavelength is obtained. This can also be obtained from a knowledge of the temperature coefficient of the dark reaction. 3. The close agreement between the values of the threshold wavelength obtained by the two methods lends support to the new conception of the radiation hypothesis put forward. I.
Chemical Laboratory, Cnzversity of Allahabad, Allahabad, Indaa, tfarch 19, 1.981.
