1262
CONVUXICATIOSS TO THE EDITOR
ADDITIONS TO T H E ,1RTICLE “ X E L T I S G A\SD EVAPORATIOS RA4TEPROCESSES” (J. Phys. Colloid Chem. 62, 949 (1948))
.IS
It has been shonn in a recent discussion that the theory of absolute reaction rates leads to results for the isothermal rate of evaporation which are of the same order of magnitude as those obtained from the Knudsen equation (S. S. Penner: J. Phys. Colloid Chem. 62, 949 (1948)). This conclusion can be made more explicit by use of a relation betn-een free volume and vapor prebsure obtained by H. Eyring and J. 0. Hirschfelder (J. Phys. Chem. 41, 249 (1937)). The assumption that the activated state formed during evaporation is a gas-like molecule leads (S. S.Penner: loc. cit.)’ t o the folloning relation for the rate constant for evaporation, j p : je =
ek.jl;T 2nml1 ? ( r
2 3
e \ r p ( - U L lil)
1
(1)
where e is the base of the natural logniithnib, h is the transmission coefficient, is the Boltzmann constant, 1’ iq the ab-olute temperature, m is the mass per molecule, i“* = 1‘ is the volume per molecule in the condensed state, L , ic the corresponding free volume per molecule, R is tlie molar gas constant, and A H , is the molar heat of evaporation. In the derivation of equation 1 it TI as aisumed that the vibrational, rotational, and internal contributions t o the partition functions remain unaltered during evaporation. If the rate of loss of moleculec from a given volume V is - d72, dt and is assumed t o be proportional to the number of i n o l e d e s IZ, expnsed a t the surface nith the proportionality constant given by the rate conttant for evaporation ( S . S. Penner: lac. cit.), then -d,?, dt
=
je?lc
(2)
But 71, = nV and n , = n2’3Y. nhere n i h the number of molecules per unit volume and 5‘ is the surface mea. Therefore
G=
- (1 S)(dT7 d t i p = j t p
13)
IZ’*~
where p is the density of the evaporating compound and G is the rate of loss of molecules by evaporation from a given volume per unit surface area per unit time. Combining equations 1 and 3 leads to the result
G But
pv =
=
c k ( i ; T / 2 ~ ? n ) ~ ’ ?7(7 p* ’v3 ~ J’)(1
Lj)
exp(-AH,
RT)
(4)
m and (1
cj)
=
( p s k T ) exp(AH, R T )
(*3)
where p , is the saturated vapor pressure of the evaporating compound whose vapor is assumed to behave as a perfect gas. Equation 5 TTXS obtained by Eyring and Hirschfelder (loc. cit.), who noted that the Gibhs free energy of the evaporat1 T h e factor e n a b omitted i n t h e piececling discussion. sirice only order of m a g n i t u d e calculations were carried out
PHASE EQUILIBRIUSI DESCRIPTIOS
1263
in# bubbtance and of the gas n-ith which it is in equilibrium mush be equal to each other. From equations 4 and 5 it follows that
G
=
(6)
etip,(nz/2~kT)”~
since the product = 1. Equation G is of the same form as the I h i d s e n equation n-ith the accommodation coefficient of the Knudsen equation replaced by eK. It may also be noted that if evaporation is a rate process in which equilibrium betneen normal and activated molecu!cs is not established, and if the evaporating molecules move classically in the degree of freedom along which the molecules decompose with an average energy change of the order of kT between successive transfers of energy, then Hirschfelder’s correction factor (J. 0. Hirschfelder: J . Chem. Phys. 16, 22 11948)) of 0.387 should be introduced into equation 6, leading to the result : ( ~ 2 1 ) ~ ’ ~
G = ~ . O S K ~ , (27rkT)’i2 PL (7) It is evident that results calculated from equation ti Tvith eti = 1 should be identical u-ith results calculated from the Iinudsen equation with the accommodation coefficient set equal to unity. Therefore it appears likely that the discrepancies discussed previously (S. S. Penner: Zoc. cit.) svere introduced by an incomplete description of the physical state through partition functions c ~ l c u lated on the basis of the free volume model. The author wishes to express his appreciation to Professor J. G. KirLu ood for helpful discussion$.
s. s. PE:A\Ll{
Jet Propulsion Laboratory Californk Institute of Technology Pasadena, California July 12, 1948
PHASE EQUILIBRIUM DESCRIPTION Isosyst, a nelv word of Creek etymology, is proposed to describe a condition, or family, or curve of constant composition. This word has utility in descriptions of vapor-liquid phase equilibria, joining therein two words, isobar and isotherm, 11-hich have long been used. DISCUc3SIOS
In this laboratory’s work in phase equilibrium, a concise, descriptive, unique word was needed to describe the condition of the same composition throughout SL given experiment, or to label a curve of constant composition. The words “isobar” and “isotherm” have long been used t o label conditions of constant
