Intermolecular forces in air

Abstract

Th e in termol ecul ar force constants for a 6-12 Le nn ard-Jones potent ial model ha ve been co mpu ted [or a il' from second viri ai coeffici ents d erived from exp erimental pressure-volume-temperat ure m ea surements. Ni tro ge n : oxyge n intera ction second virial coeffi cie nts a nd in teraetion f01;ce constan ts have also been derived. The following symbols are used throughout the paper: Z = Compress ibili ty factor , P v/ RT, dimensionless. p = Absolu te press ure. V = Molar volume, cm3/ mole. R = Uni versa l gas cons ta nt, in uni ts of P v/T. T = Absolute te mperature. The t ri ple poin t of water is d efin ed as T = 273 .16°K. B = beco nd viri al coeffi cien t, em 3/ mole. C = Third virial coeffi cient, cmo/ mole 2. D = F our t h viria l coeffi cient, cm 9/ mo le 3. E = Fifth viria l coeffi cien t , cm 12/mole '. '0 = M ax imum energy of bin d in g between a pa il' o f molec ules wit h a L ennard-J ones po tent ia l. k = Boltz ma nn's co nsta nt. N , = Mo le fr action of t he ith component. _ b= Lenn ard-Jon es in teraction p ara mete r, ~ N7rd3, in uni ts of mola r volume. N = Avagadro's number. d = Collis ion di a meter of a pail' of molecules at ze ro e nergy of Lenn a rd-Jones in teraction. A = An gs tl'om units (= cm-8). • = P okl ntial energy of t wo interacting molec ules. 1' = Sepa rat ion be t wee n cen ter s of t wo inter actin g molec ules. ro = Coll is io n di a meter of a pail' of molec ules at max imum e ne rgy, '0, of Lenn ard-Jones in teraction. Compressibility factors for dry ail' have b een d et er mined exp erim en t ally and ar e r eported else-wher e [1 ].2 B~r fitting the P-v-T data to a K am er-lingh-Onnes vi rial equation of stat e the virial coefficients B , 0, D , and E wer e determined at various temp eratures in the r egion b etween the critical and 0° C. These are tabulat ed in t able 1. The second virial coefficients of nonpolar mixtures can b e d erived, to a good approximation, from the force constants of the pure components [2 , 3]. If we assume that the intermolecular forces of th e pure constitu ents of dry air (N 2 , O2, and A) can be described b y a L ennard-Jones model, then we may d efine pseudoforce constants for the air mixture: (2) I 'rhi s research wa.s supported , in part, b y the .A irborne Equ ipm ent Division o f the 1 av y Bureau of A ero nau tics. 2 Fi gul'es in brackets indicate t he literature references at the end of this paper. 4118 10-57-3 93 and If we assmne that th e ail' mixtUl'e has th e com-posit ion 78.2 p er cent of N 2 , 20.8 p ercen t of O2, and 1.0 p ercen t of A (d. [1 ]), and the N 2, O2, and .A can b e r epresented by a 6-12 L ennard-Jones intermolecu-lar poten t ial function with force const an ts: and (Eo/k) N~ = 95.93 0 , (E o/lc) O 2 = 118 .0 °, (d)N 2 = 3.6 9 A [3 , 4 ] (d)02= 3.46A [5] (d)A= 3 .42 A , [6 ] then , from eq (2) and (3), (Eo/k)a1r = 100.8° and ba1 r= 60.82 cm 3 /mole. These 6-12 L ennard-Jones pseudoforce constan ts can th en b e used to compu te th e valu es of th e second v irial coefficien ts for air at variou s temp eratures. The values thus compu ted ar e in good agr eem en t with the experimen t ally d et ermined second virial coefficien ts [1]. T able 2 compares th e calculated and exp erimen tal v alu es of B. The second virial coefficien t of a binar y gas mixture can b e expressed in terms of th e second virial coefficients of th e constitu en t gases and an interaction coefficient r elated to collisions of th e unlike molecules. B m1 x = 'L,'L,N iNjB tj • i j vVe may then write fo r air, not ing that BJ 2= B21' Rearranging: (4) Using t h e P-v-T dat a of Friedman et aI. , for Ba1r [1 ], of Friedman for B N2 [3 ], and th e t abulation of Hilsenrath et aI. , for B 02 [6], th e N 2 :0 2 interaction second vil'ial coefficients as a function of t empera-ture may b e calculat ed from eq (6). These ar e