A CALCULATION OF HEATS OF CHEMISORPTION BY D. D. ELEY Received 3rd April, 1950 Heats of chemisorption are calculated by Pauling’s equation for covalent Quite good agreement is secured for hydrogen on tungsten, copper Calculations for oxygen on tungsten and ethylene on nickel enable bonds. and nickel. us t o rule out certain mechanisms of chemisorption. There are a number of good reasons for believing that in many cases the chemisorptive bond is of a covalent type.l* It is a matter of some interest that this hypothesis allows a calculation of heats of chemisorption. Consider, for example, the chemisorption of hydrogen on tungsten. We write this as The differential heat of chemisorption per mole of hydrogen, Qo, is to be calculated, when the fraction of surface covered 8 --f o and we may neglect effects due to neighbour interactions in the monolayer. The result may be obtained in terms of bond energies E, ZW + H2 -+ zW-H.Qo = 2E(W--H)-E(H-H) . - (1) Considerable success has attended the recent application of electron- pair theory to metal^.^ Therefore I shall assume that the energy of the surface W-H bond may be calculated from Pauling’s equation,4 (2) To evaluate eqn. ( 2 ) we first need to obtain E(W-W). We shall assume that each metal atom has 12 nearest neighbours. This result is true for face-centred cubic lattices, but not strictly for body-centred cubic lattices, where there are 8 nearest and 6 next nearest neighbours. In the latter case, however, no great error is involved in treating the lattice as one with 12 nearest neighbours. Since two atoms are involved in each bond we can write E(W-H) = &(E(W-W) + E(H-H)) + 23-06 (xw - x ~ ) ~ .E(W-W) = 2. s, I 2 where S is the sublimation energy of the metal, listed in Landolt-Born~tein.~ The term involving the difference in electronegativities xw - xH is estimated by Pauling’s approximate rule that it is equal to the dipole moment of the bond in debyes, p. If the measured contact potential of a complete monolayer is V volts, then we may write where C, is the number of sites per cm. of surface, taken here as the mean of the (110) and (100) surfaces, i.e. 1-2 x 1015 for W and 1-38 x 1015 for Ni. This value of p for an atom in a full layer can only be equated to p,, for a dilute layer if we assume depolarization effects to be small. Couper and Eley, this Discussion.Eley, Amer. Chem. SOC. Symposium, June, 1950 (to be published in J . Pauling, The Nature of the Chemical Bond ((New York, 1939). p = v/2ir3ooc,, Physic. Chem.). Pauling, Proc. Roy. Soc. A , 1949, 196, 343. 6 Landolt-Bornstein, Tabellen, Erg. IIIc, 2709. 34D. D. ELEY 35 The calculations have been made for systems where modern experi- mental data are available, and the results presented in the Table. The bond energy values used are due to Pitzer.6 For nitrogen and carbon bonds, two values are possible, " high " and " low " values, depending on the values chosen for the heats of atomization of carbon and nitrogen. The situation is well presented by Coates and Sutton.' Pitzer's values are high values, and for the -N=N- bond, we have also taken the high value given by Coates and Sutton.' The low values give the results which are very little different from those listed.In applying the equation t o multiple bonds, we are making a definite assumption, since the equation was deduced for single bonds. In par- ticular, it is not at all clear that the equation will give a correct estimate of the ionic term. Also, depolarization effects are probably more important for dipoles such as W = 0, 1-76 V contact potential, compared with W-H which has the smaller value of 1-04 V. v, Volts System p9 = x g l - x ~~ zNi+ H, +zNi-H zCu+ H, +zCU-H 2tv-0 +zW=O -- I- -0.34 D -- ? zNi+C,H, -+H,C--CH2 Ni FJi / \ -0.13 ? - 1-76 lo ~ _ _ _ - 1-38 lo ____ +0*83 -0-78 -0.61 -toe32 !?(M - M) kcal. 33.8 164 -- 13.6 2 x 33-8 3 x 33'8 16.4 C(A ~ A) kcal.103.2 103-2 103.2 Experi- mental Specimen Wire Film Powder Film Powder Powder Wire 1 ) ,I Wire Powder Film Discussion The agreement between calculation and experiment is good for W-H and Cu-H. For Ni-H, the calculated result is lower than the value of 31 kcal., which since it was obtained with an evaporated film is more likely to correspond to the true value for a clean surface than the value of 21 kcal. for a powder. The differences in electronegativities are what one might expect from Pauling's thermochemical values for similar bonds. 6 Pitzer, J . Amer. Chem. SOC., 1948, 70, 2140. Coates and Sutton, J . Chem. SOC., 1948, 1187. Bosworth, Proc. Camb. Phil. SOL, 1937, 33, 394. 9 Mignolet, this Discussion. lo Bosworth and Rideal, Physica, 1937, 4, 925.l1 Roberts, Proc. Roy. SOC. A , 1935, 152, 445. l2 Beeck, Rev. Mod. Physics, 1945. 17, 61. l3 Frankenburg, J . Amer. Chem. SOC., 1944, 66, 1827. l4 Eucken and Hunsmann, 2. physih. Chem. B, 1939, 44, 163. l5 Ward, Proc. Roy. SOC. A , 1931~ 133, 506. 16 Johnson and Vick, ibid., 1935, 151, 308. 17 Davies, Jr., J . Amer. Chem. SOC., 1946, 68, 1395.36 A CALCULATION OF HEATS OF CHEMISORPTION Thus for the nearest example, Al, xM = 1.5 and for H, X, = 2.1, so that x, - X, - - 0.6. For W=O and 2W=C,H4, the calculated values are markedly lower than the observed values. However, the calculations re- produce the general features of the observed results quite well, and the discrepancies may be associated with changes in hybridization and loss of resonance energy on adsorption at the surface. The experimental values for ethylene may be too high because of a certain amount of self-hydro- genation.12 The calculated oxygen value may be low because we have under-estimated the ionic term.Thus Pauling’s table 4 would give xAl - x,, = - 2.0 and one should not expect tungsten-oxygen to be very different . The nitrogen value is much higher than the preferred experimental value of 28 kcal. The relatively low stability of nitrogen films as com- pared with ethylene films has been qualitatively demonstrated by other methods,1* adding weight to the low values for Qexpt. This discrepancy may be connected with the relatively large ratio E(N = N) /E(N - K) compared with E(C = C) /E(C-C) .* Another possibility €or chemisorption is hT=h- 2W+N2-+d h but the calculated value is Qcalc.= - 38 kcal. which rules this out. Beeck has suggested that the chemisorbed film of ethylene consists mainly of acetylenic complexes. We have calculated three possible processes of formation, the third one being that favoured by Beeck. C H d H - (1) - ( 2 ) / \ 4Ni + C,H4 -+ Ni Ni + 2NiH Qcalc. = 25-2 kcal. . CH=CH / , \ 2Ni +.C,H4 --f Ni Ni +kHz Qcalc. = 8.0 kcal. CH=CH / 2Ni + 2C2H4 + Ni \ Ni + C2H, Qcalc. = 36-2 kcal.7 (3) The first process is a possible one energetically, although obviously not as likely as the associative adsorption calculated in the Table. How- ever, it is ruled out by the observation that hydrogen deuteride formation is inhibited by ethylene, so that there is no chemisorbed hydrogen in the film.19 The second process is clearly unlikely but the third process is a possible one.Finally, there is the process of dissociative chemisorption suggested by Farkas, 2o Ni + CZH4 + Ni-CH=CH, + &Hz Qcaic. = 4, which gives too small a heat. The associative process given in the Table yields the best value of Qcalc.. All the calculations for ethylene and nitrogen have been repeated using low values of the carbon and nitrogen bond energies concerned with very little difference in the calculated heat values. This is because the changes effect both the bonds disrupted and the bonds formed to metal in the same way. l8 Eley and Rideal, Proc. Roy. SOC. A , 1941, 178, 429. * It has been possible subsequently to solve this problem, cf. the following t 1.e.18.1 kcal. mole of ethylene. 19 Twigg and Rideal, Proc. Roy. SOC. A . , 1939, 171, 55. 2O Farkas, Trans. Faraday SOC., 1939, 35, 906. discussion.D. D. ELEY 37 In one of his later papers, Roberts 21 indicated a new view that possibly The only si mple alternative the oxygen film on tungsten is not atomic, to the process in the Table is 0-0 32 I7 68 36 39'7 Clearly this mechanism is ruled out because of its low heat value. It is hoped to improve this approach to chemisorption in future by a theoretical consideration of the type of bond involved, but even at its present stage, the method offers an approach to the heat of adsorption, which, while it is of great importance in chemical kinetics, is difficult to determine experimentally. The calculations support strongly the notion that the chemisorption bond is an electron pair bond, rather than a completely ionic bond.39 32 51 39 138 I should like gratefully to acknowledge that the two values for nickel contact potentials are taken from the paper by J. Mignolet (Li&ge),a2 and communicated personally to me beforehand. 44 I02 64 43 ADDENDuM.-It is possible to extend the calculations in my paper to all the new data reported by Beeck in his paper on Hydrogenation Catalysts. The Table compares calculated values (kcal./mole gas) with the values observed by Beeck. 15'7 34'7 39 I02 Gas H2 %d C2H4 Metal Jobs. calc. 1 obs. calc. Rh 28 23 50 42 50 Ni 31 I7 58 36 40 Fe 1 Ta The calculated values for C2H4 are for associative chemisorption, i.e. M-CH,-CH,-M. The heats of sublimation of Ta and Rh are not available, but I have found a good linear relation exists between sub- limation energy and melting point for the related metals, from which I have interpolated the values for Ta, S = 184 kcal., and Rh, S = 130 kcal.I have assumed the surface dipoles for H adsorption are the same for Rh, Fe and Ta as for Ni, and for CaH4 adsorption the same for Fe, Ta, W, Rh as for Ni. It seems likely that there will not be any large variations in the ionic term, for one gas with the range of metals, i.e. we should not expect very large variations in surface dipoles. Nevertheless, I would point out that this calculation strictly requires data on contact potentials at low surface coverings of gas, which are not available at present. The fundamental significance of the success of the calculation is this, that the surface M-H bond is closely similar to the M-M bond in the solid, i.e.it may be treated as a covalent bond, but of the metallic type, resonating below the surface of the metal with all the nearest neighbour metal atoms. It assumes that the hybrid orbitals are the same as in the bulk metal, essentially d3sp3 metal orbitals. This, of course, can only be an approximation and for the last two years, Mr. Crowne in my labor- atory has been building up the technique to test this hypothesis, by measuring the change, if any, in the surface paramagnetism of tungsten when hydrogen (and other gases) chemisorb. We know that when dimethyl 21 Roberts, Some Problems on Adsorption (Cambridge University Press, * 1.e. ignoring the possibility of a R bond.19391, PP: 88, 113. z2 This Discussion.38 A CALCULATION O F HEATS OF CHEMISORPTION sulphide is adsorbed on palladium, atomic d orbitals are pressed into service to form surface bonds, but in this case we have a co-ordinate link formed to the metal, rather than the simpler bond we are here considering. Calculations on the nitrogen data of Beeck, Cole and Wheeler enable us to give some quantitative support to views advanced by these authors, and originally by Taylor 23 as to the nature of these films. I give the arithmetic so that the method of calculation is clear. The value for N, on Ta observed is Q,, = 135 kcal. N, + eTa -+ eTa = N Now we calculate Just as for tungsten we calculate Qcalc. = 109 kcal. Qcaic. = 17 kcal. = 25 kcal.H, + 2Ta = N + 2Ta = N - H The steps are :. Ta = N --f Ta = N- The N-H bond is 92-2, the H-H, 103.2. :. Qcaic. = 2(92.2 - 31.9) - 103.2 = 17.4 kcal. The agreement here is such as to convince us that our models are probably right. The observed heats of N, on Fe (10 kcal.) and on W (28 kcal.) must be low because the chemisorption largely gives some species such as M=N-N=M, (for W=N-N=M, Qcalc. =- 3-1) and the pro- duction of the atomic nitrogen films may well be inhibited by an activ- ation energy as suggested by Taylor and Beeck. Finally may I refer to one way in which aromatic resonance energy may lower heats of chemisorption. For benzene Q = -31.9 kcal. To a first approximation where R, - R, is the diflerence in resonance energies between butadiene and benzene, i.e., -39 kcal. Thus Qcslc. = 36 - 39 =- 3 kcal. and benzene should be weakly chemisorbed, compared t o ethylene, in line with the different kinetic behaviour in exchange and hydrogenation ~ e a c t i o n s . ~ ~ Qca~c. = Qcalc.(C&a) + R4 - Re, Note added in proof.-Beeck in Advances in Catalysis, Vol I1 (New York, 1950), p. 183, gives for nitrogen on evaporated tungsten films Qo(expt.)=g5 kcal./mole. This is in good agreement with the calculated value for atomic nitrogen films, and is probably to be preferred to the value based on rates of desorption. The University, Bristol. 23 Joris and Taylor, J . Chem. Physics, 1939, 7, 893. 24 Eley, Quart. Rev., 1949, 3, 221.