Feb.,
1933
THERMAL EQUILIBRIUM BETWEEN OXYGEN MOLECULES AND ATOMS 507
the film was stationary, measured back from the new auxiliary spark line made with film in motion, located the point on the film a t which the light point was when the spark passed in the bomb.
Summary A diaphragm indicator for measuring the pressures developed in explosions is described. Its essential advantages are sensitivity, freedom from hysteresis for the deflections employed, and constancy. A method of calibrating dynamically, without removing the diaphragm from the explosion chamber, is described in which pressures are released against the diaphragm in a time interval of the same order as in explosions. It is shown that for this type of diaphragm the observed deflections for a given range of pressures investigated are the same for dynamic as for static calibration. PITTSBURGH.
RECEIVED AUGUST4 , 1 9 3 2 PUBLISHED FEBRUARY 9,1933
PENNSYLVANIA
u.s.
[(:ONTRXBUTION FROM THE PITTSBURGH EXPERIMENT STATION, BUREAU OF AND THE COBB CHEMICAL LABORATORY, UNIVERSITY OF VIRGINIA]
MINES,
Thermal Equilibrium between Oxygen Molecules and Atoms’ BY GUENTHER VON EL BE^
AND
BERNARD LEWIS^
During the course of experiments carried out a t the Pittsburgh Experiment Station of the U. S. Bureau of Mines on the direct determination of the specific heat of oxygen a t high temperatures by exploding mixtures of ozone and oxygen,4 it was necessary to know the degree of dissociation in order to obtain accurate values of the specific heats. Since this information is not available in the literature, we have set up an equation for the 0 2 expressed as equilibrium constant of the reaction 2 0
One commences with the well-known fundamental thermodynamic equation AF = AH
- TAS
For the condition of equilibrium between atoms and molecules of oxygen AF = 0, and therefore 0 = ( A H / T ) - AS (3 1 The entropy per mole of each participant in the reaction is given by S
= C ,. In T
+ f”% dT - R In p + Ri + Cp,
where C,, is the constant part of the specific heat a t the temperature T, (1) Published by permission of the Director, U. S. Bureau of Mines. (Not subject to copyright.) (2) Research associate, Univefsity of Virginia. ‘3) Physical chemist, U. S. Bureau of Mines, Pittsburgh Experiment Station, Pittsburgh, Pa. 14) L e a k and von Elbe, THIS TOT’RNAI., 111. 511 (1933:
508
GUENTHER VON ELBEAND BERNARD LEWIS
Vol. 55
i. e., due to translation and rotation;
Cvib. is the specific heat due to vibrations of the molecule, p is the partial pressure of each constituent a t equilibrium, i is the chemical constant of each constituent. Equation 4 includes the Sackur equation for translational entropy and also the rotational entropy for the case that rotation is fully excited. This may be shown by comparison with the statistical formulas St,,,,. = 6 , / ~InR T - R In p 8/2R In m R In [ ( 2 ~ ) ~ / 3 K % / h ~R] In g 6 / ~ R(3a)
+
S,,,
=
2/ZR In T
+
+
- R In (symmetry number)
h2
+
+ 2/2R
- R In WIk
(3b)
Adding 3a and 3b results in equation 3, less the vibrational part, vi2, Strans.+rot. = i/2R In T
- R In P + Ri +
i/2R
(34
Giauque and Johnston6 have calculated the entropy of molecular oxygen + rot. + f imol.) where from 0°K. to 298'K. which includes (Stran,, imol. is the chemical constant of the oxygen molecule. Their value for this at one atmosphere pressure is 49.03 entropy units which we shall employ. Equation 3 transforms to AH 0 T - [2&.
- (smo1.1&
+ 4Q.o3)]
(5)
where Sa, represents the entropy of the oxygen atom and Smol./& is the part of the entropy of the oxygen molecule between 298°K. and TOK. This expands to
Substituting for the entropy, equation 4,one obtains
lg8 %
dT - In 1
The expression
298
(cvib,/T)
+ + 7/2
&,.I.
(7)
d T is negligibly small. Transposing, divid-
ing by R and changing to logs to the base 10
lP t.= log s PUlC.1.
5 + 5 log T + 2i.t - 2.3RT 3+ 32.3'- 3.5 log T + 3.5 log 298 2.3
A€& is the heat of dissociation at absolute zero which is equal to 117,300 calories per mole.6 This value is for dissociation from the 32 state of the (5) Giauque and Johnston, THISJOURNAL, 61, 2300 (1929). (6) Paschen, Nafurwloisscnschaffcn,84, 752 (1930); Sommer, ibid., 34, 752 (1930): Frerichs, P h y s . Rev., 36, 398 (1930).
Feb., 1933
THERMAL EQUILIBRIUM BETWEEN OXYGEN MOLECULES AND ATOMS 509
oxygen molecule to the 3P2 state of the atom (see below). The expression T (Cvib./T)
d T can be evaluated by Einstein functions ( F
- FO)/T.’
There is practically no difference between the values so derived and the values derived from the spectroscopic vibrational-rotational levels of the molecule. This is known by a comparison of such calculation^.^ This also makes it unnecessary to account for the change of the moment of inertia I in imol. for higher rotational levels (compare equation 3b). Using the value of 1556.4 cm.-’ for the separation of the first vibrational level of the oxygen molecule*we obtain
Y = -2229 T
T
from which ( F - Fo)/T can be evaluated. well-known equationg
iat./2.3
is expressed by the
2.3 = - 1 . 5 8 7 + 1 . 5 l o g M + l o g g
(9)
where M is the atomic weight of the oxygen atom and g is the statistical weight of the atomic state. The value of g is derived in the following way. The ground level of the 3P1and 3 P ~ oxygen atom is a triplet state in which the three terms 3Pz, are separated by small energy differences: 3P2 = 447 calories, 3E’z - 3P0= 635 calories. The multiplicity of the separate terms can be obtained from measurements of magnetic susceptibility made by Kurt and Phipps.’O They find a multiplicity of 5 for the 3Pzterm, 3 for 3P1and 1 for 3 P ~ . The statistical weight g of the atomic state is given by the sum of the 3P1 and 3P0and the probaproducts of the multiplicity of the terms sP~, bility of the atoms being in each of these states, referred to the lowest state 3Pz. Then g = j + 3e-447/RT + e-GI/RT (101 The complete equation for log K , is log K , =
-117300 + 1.5 log T - ( ‘ I S F I T ; BvIT = 2 2 2 9 / T ) -o.104 4.571T 4.571 2 log (5
+ 3e-447/RT +
+ e--635/RT)
(11)
However, equation 11 must be revised by the addition of another term relating to the oxygen molecule, for the following reasons. In our experimental determination of the specific heat of oxygen up to 2500°K.,the results show that the experimental values of the specific heats are always higher than those calculated from the vibrational-rotational levels of the normal state of the molecule4in the temperature range investi(7) Landolt and BGrnstein, Supplementary Vol.1, p. 702. (8) Mecke and Buumann, Z . Physik, 73,139 (1931); Babcock and Hoge, Phys. Rev., 39, 550 (1932) (9) See, for example, A. Eucken, “Lehrbuch der chemischen Physik,” Leipzig, 1930, pp. 246247: or the constant part of equation 3a above. (10) Kurt and Phipps. Phys. Rev., SC, 1357 (1929).
510
GUENTHER VON ELBEAND BPRNARD LEWIS
Vol. 5
