J. Chern. Soc., Faraduy Trans. I , 1988, 84(6), 1807-1816 The Association and Solvation of Formamide in Pyridine and Picolines Prem P. Singh Chemistry Department, Maharshi Dayanand University, Rohtak 124001, India Topological investigations of the volumetric and enthalpic effect in mixtures of formamide (A) and pyridine or a-, p- or y-picoline (B) have indicated that the state of association of (A) in an (A+B) mixture is dictated by the molecular entity B and that the magnitude of the attractive B-B interactions in the various picolines (B) varies in the order j? z y > 01. The energetics of the solution process characteristic of these (A-B) mixtures have also been investigated. The results obtained are rationalized by graph-theoretical arguments. Amides are compounds of considerable biological interest.' Spectroscopic and n.m.r.studies2 of the reactivity of the amide group have suggested that the unshared electron pairs of the carbonyl oxygen of the amide group are the positions of hydrogen bonding with other species. Further, in view of the two well known resonance structures of the arnide group3, it is reasonable to infer that the lower amides may exist, like alkan01s,~-~ as dimers, trimers or higher r-mers in the liquid state. However, Daviesg maintains that the association of amides in solution is limited to dimer formation. On the other hand, the nitrogen atom in pyridine is a n-electron acceptor," and is known" to be involved in a hydrogen- bonded interaction with chloroform. The addition of pyridine or picolines (B) to an amide, such as formamide (A), may thus cause rupture of the self-association in formamide, followed by its subsequent solvation in B.Further, since the electron density'(' at C,, C, and C, in pure pyridine is Iess than that in pure benzene, it is reasonable to infer that some kind of pyridine-pyridine or picoline-picoline interactions may characterize even the pure pyridine or picolines. Following Kier and Ha11,12 Singh et al. l3 have recently employed graph-theoretical arguments to investigate the association and solvation of A in A-B mixtures where A is ROH (R = CH, or C2H5) and B is CHX, (X = C1 or Br) or CH2Br2. Volumetric and enthalpic effects in A+B mixtures where A is formamide and B is pyridine or a-, p- or y-picoline may yield valuable information on the association and solvation of A in B in these (A+B) mixtures.Experimental Materials and Methods Formamide, pyridine and the a-, p- and y-picolines were purified by standard procedures. 14, l5 The purities of the purified samples were checked by measuring their densities at 298.15 kO.01 K, and these agreed to within 5 x g cm-' with their corresponding available literature Molar excess volumes, V E , were determined in a V-shaped dilatometer18 in a manner described elsewhere." The temperature of the water bath was controlled to within +0.01 K and the change in the liquid level of the dilatometer capillary was measured with a cathetometer that could read to & 1 mm. The uncertainty in the measured VE values is ca. 0.5%. Molar excess enthalpies, HE, for the various mixtures were measured at 298.15 K in 16, l7 as is shown in table 1.18071808 Solvation of Formamide in Pyridine and Picolines Table 1. Comparison of the measured densities at 298.15 & 0.010 K of the various compounds with their corresponding literature values density/g cm-3 compound this work literature ref. (1) formamide 1.12921 1.129 18 16 (3) a-picoline 0.939 80 0.939 82" 17 ( 5 ) y-picoline 0.95045 (2) pyridine 0.977 57 0.977 6 11 (4) Q-picoline 0.95248 - - - - a Evaluated from the density us. temperature plot. a flow microcalorimeter (LKB Broma, Sweden) in the manner described previo~sly.'~ The performance of the calorimeter was checkedl9 by measuring HE for benzene (A)-tetrachloromethane (B) mixtures, and these agreed to within the experimental uncertainties with the available literature values.The uncertainty in the measured HE values is ca. 1 YO. Results The measured VE and HE data recorded in tables 2 and 3 at 298.15 K for the various (A-B) mixtures were fitted to the expression 2 XE(X = Y or H ) = x, xB C x'")(2xA - I)" n-0 where (n = 0-2) are adjustable parameters and x, is the mole fraction of A in the (A-B) mixture. These parameters were evaluated by fitting XE ( X = V or H ) / x , xB to eqn (1) by the least-squares method and are recorded, together with the standard deviation of XE, a(XE), in table 4. The choice of n to have three distinct values (n = 0-2) was dictated by the consideration that the maximum deviation, am(XE), of XE [calculated from eqn (l)] from the corresponding experimental value satisfied the relation am(XE) < 2a(XE).Discussion We are unaware of any VE or HE data at 298.15 K for the present mixtures with which to compare our results. VE and HE are large and negative for all the present (A-B) mixtures, and for an equimolar mixture vary in the order pyridine > y-picoline > P-picoline > a-picoline. The increased negativities of VE and HE values when pyridine is replaced by picoline in their binary mixtures with formamide suggests' that in the competition between A-A and A-B interactions, the latter seem to be substantially favoured. This would then mean that as the introduction of pyridine or a-, p- or y- picoline (B) to formamide (A) would cause structural changes in A, so that it would be of interest to analyse VE data for the present (A-B) mixtures in terms of an approach20 that employs the graph-theoretical concept of molecular connectivity parameters of the third degree,12 35, of the constituents of these mixtures.According to this approach,20 VE for a binary mixture is given by 1 i=A, B i - A , BP. P. Singh 1809 Table 2. Measured VE values at 298.15 K for the various (A-B) mixtures as a function of the mole fraction xA of component A v'E/Cm3 VE/cm3 X A mol-1 X A mol-' formamide (Abpyridine (B) 0.0672 -0.054 0.5500 -0.1 16 0.0892 - 0.065 0.6001 - 0.108 0.1028 -0.072 0.6492 -0.097 0.1198 -0.081 0.7118 -0.082 0.1498 -0.098 0.7214 -0.080 0.2027 -0.115 0.7500 -0.074 0.2685 -0.130 0.8409 -0.051 0.3456 - 0.135 0.8804 -0.037 formamide (A)-a-picoline (B) 0.0648 -0.234 0.3803 -0.627 0.0752 -0.262 0.4923 -0.593 0.1249 -0.389 0.5568 -0.552 0.1864 -0.504 0.6536 - 0.475 0.2250 -0.556 0.6654 -0.465 0.2498 -0.575 0.6741 -0.455 0.2614 -0.588 0.8877 -0.194 0.3623 -0.627 0.9014 -0.173 formamide (A>-B-picoline (B) 0.0645 - 0.084 0.4569 -0.276 0.0851 -0.110 0.5148 -0.266 0.1 101 -0.136 0.6250 -0.230 0.1678 - 0.187 0.7227 - 0.182 0.2396 - 0.233 0.7550 - 0.162 0.4492 -0.276 0.8185 -0.126 formamide (A)-y-picoline (B) 0.0685 -0.101 0.5684 -0.220 0.0814 -0.118 0.6036 -0.206 0.1201 -0.158 0.6498 -0.187 0.2764 -0.253 0.6610 -0,180 0.3034 -0.260 0.7123 -0.154 0.3642 -0.267 0.7450 -0.140 0.4464 -0.259 0.7956 -0.112 0.5142 -0.240 0.8034 -0.107 0.5316 -0.235 where x, is the mole fraction of A and etc.are defined2' by In eqn (3) Sp etc. reflects21a explicitly the valency of the Zth etc.vertex in the molecular graph of A in forming bonds, and is related21* to the maximum valency, Z,, and the number of hydrogen atoms, h,, attached to the Zth etc. vertex by the equation Sy = Z , - h , . aAB in eqn (2) is a constant, characteristic of the (A-B) mixture. Since formamide (A) is expected to undergo structural changes in its binary mixtures1810 Solvation of Formamide in Pyridine and Picolines Table 3. Measured H E values at 298.15 K for the various (A-B) mixtures as a function of the mole fraction x, of component A x, HE/J mol-1 x, HE/J mol-l formamide (Akpyridine (B) 0.1635 -326.2 0.5128 -847.8 0.2815 -557.6 0.6785 -815.4 0.3055 -581.9 0.8003 -629.0 0.4470 -798.5 0.8191 -586.9 0.4686 - 817.2 0.8523 - 503.9 0.4980 - 839.0 0.9103 - 332.4 formamide (A)-a-picoline (B) 0.1678 -909.2 0.5479 - 1536.4 0.2917 - 1338.0 0.7233 - 1131.0 0.3122 - 1390.2 0.8310 -781.2 0.4979 - 1570.0 0.8616 -651.9 0.5 104 - 1566.4 0.8664 - 632.7 0.5206 - 1558.8 formamide (A)-/?-picoline (B) 0.1659 - 564.3 0.5446 - 1148.6 0.2889 -904.4 0.7206 - 892.4 0.3093 -951.8 0.8291 -590.4 0.4949 - 1 160.0 0.8324 - 58 1.6 0.5071 - 1160.3 0.8600 -491.6 0.5173 - 1159.3 0.8648 -475.4 formamide (A)-y-picoline (B) 0.1915 -660.9 0.7023 -955.8 0.3220 -938.1 0.8234 -690.3 0.3477 -976.6 0.8459 -620.8 0.5166 - 1097.4 0.8662 -558.4 0.5458 - 1094.9 0.9248 - 341.5 0.5605 - 1090.7 0.9292 - 323.6 with pyridine (B) or the picolines (B), '<A of A in an (A-B) mixture will not be the same as that in the pure state. Consequently, eqn (2) may be expressed1' in the form 1 (4) i-A, B where and 'ti denote, respectively, the 'c value of i in the mixture and in the pure state. Again, as the degree of association in pure A is not known with certainty and as no theoretical method is available to evaluate of A in the (A-B) mixture, we regarded and 'lB as adjustable parameters and evaluated them by fitting the experimental VE values to eqn (4).Only those and 'ti values were retained that best reproduced the experimental VE data, i.e. for which the variance of fit, p, defined by where ( q - p ) is the number of degrees of freedom, was a minimum. Such ('ti, i = A or B) values, together with the VE values calculated in this manner at various x,, are (3cB)m, P = c ( E p t l - e l c d 2 / ( q - P )P.P. Singh 181 1 Table 4. Comparison of V" and HE values [calculated from eqn (4), (19) and (21), (see text)] with their corresponding experimental values at 298.15 K for the various (A-B) mixtures as a function of the mole fraction of A, xA; also included are the interaction energies xiB, ;s and the parameters Fn) (X = V or H, n = 0-2) of eqn (1) together with the standard deviation a(XE) of XE property" 0.1 0.2 0.3 0.7 0.8 0.9 formamide (A)-pyridine (B) I/ (calcd) -0.089 -0.114 -0.133 -0.122 -0.086 -0.030 I' (exptl)" -0.080 -0.1 16 -0.132 -0.080 -0.060 -0.030 If (calcd) -178.7 -385.0 -581.3 -802.9 -643.1 -377.6 If (exptl)b -200.0 -400.0 -581.0 -810.0 -637.0 -360.0 V0) = -0.496, V(I) = 0.2798, V2) = -0.1293; a(V") = 0.001 cm3 mole', aAB = 0.5619; WO) = - 3360.0, H ( l ) = - 1197.9, Hc2) = 392.4; a(H") = 0.8 J mol-'; (3<A)m = 0.32, = 0.33; (:3rR)m = 0.64, 3(B = 0.60; xi, = -746.1 J mol-'; x = - 7422.1 J mol-'. formamide (Aka-picoline (B) V (calcd) -0.503 -0.551 -0.583 -0.490 -0.384 -0.225 F.' (exptl)" -0.375 -0.535 -0.610 -0.430 -0.310 -0.175 H (calcd) -641.4 - 1100.5 - 1397.9 - 1254.1 -934.1 -514.0 H (exptl)b -600.0 - 1020.0 - 1360.0 - 1240.0 -920.0 -500.0 V(O) = -2.360, V ( l ) = 1.0715, VC2) = -0.7263; a( V") = 0.002 cm3 mol-', aAR = 2.655; W0) = -6280.0, H(') = 714.29, H ( 2 ) = 559.53; a(HE) = 1.07 J mol-l; (3cA)m = 0.60, = 0.602; (3'5R)m = 1.2; 3(r, = 1.0; xir, = - 3704.72 J mol-'; x = - 1927.8 J mol-I.formamide (A)-p-picoline (B) V (calcd) -0.139 -0.229 -0.253 -0.230 -0.127 -0.106 V (exptl)" -0.115 -0.210 -0.258 -0.196 -0.133 -0.067 H (calcd) -386.6 -704.5 -944.6 - 1006.4 -775.7 -440.9 V (exptl)" -340.0 -660.0 -940.0 -980.0 -720.0 -400.0 V0) = - 1.080, (3(R)m = 1.1, 3cB = 1.0; xiB = -2087.24 J mol-'; x = -4077.7 J mol-'.Vcl) = 0.3869, Vc2) = - 0.0208 ; = 1172.63 ; a(HE) = 0.87 J mol-'; (3cA)m = 0.60, a( V") = 0.001 cm3 mol-' ; aAB = 1.7213 ; = 0.603; = -4640.0, H ( l ) = 59.53, formamide (A)-y-picoline (B) V (calcd) -0.180 -0.214 -0.238 -0.180 -0.113 -0.048 V (exptl)" -0.127 -0.210 -0.258 -0.160 -0.110 -0.055 H (calcd) -369.8 -670.9 -896.2 -943.3 -725.6 -411.7 H (exptl)b - 340.0 - 660.0 - 900.0 - 960.0 - 760.0 -430.0 Vco) = -0.980, Vcl) = 0.5893, V2) = -0.1399; a(VE) = 0.001 cm3 mol-'; aAB = 1.8018; H(O) = -4379.99, = -357.16, W2) = -303.53; a(H") = 1.1 J mol-'; (3(A)m = 0.60, = 0.63 ; (3<B)m = 1.2, 3(R = 1.1 ; xiB = - 2005.5 J mol-'; x = - 4039.0 J mol-'.a Y and H denote V" and H E , respectively. are in J mol-'. Read from XE (X = V or H) us. x, plots. Vn) (n = 0-2) are in cm3 mol-l; while H(n) (n = 0-2) recorded in table 4. Since the agreement between the experimental and calculated VE values is reasonably good, the present 34 and (3<i)m values can be relied upon to yield meaningful information about the state of A and/or B in these (A-B) mixtures. Such an analysis13 of VE data for mixtures where A is ROH (R = CH, or C,H,) and B is CHX, (X = Cl or Br) or CH,Br2 in terms of eqn (4) has yielded information about the state of aggregation and solvation of A that is consistent with the information provided by an independent study2, based on an ideal associated approach for their HE and ac tivit y-coefficien t data. 60 FAR 11812 Solvation of Formamide in Pyridine and Picolines # but also that (,tB), # 3<B in all these (A-B) mixtures.Since ,< values of a constituent depend on the 6" values of the various vertices of its molecular graph, the present analysis suggests that both A and B are undergoing some kind of changes in their topology. An examination of the (3<)m values in table 4 shows not only that In our analysis we assumed that formamide in the pure liquid state exists as H\3.0 5.5 3.0,c=o- -- H 1.5 \A5 3.0 N - H-N \ . 5.5 3.0/ "o=c I H ( I ) or or 3.0~05.5 3.0, I HzN c,H In states (I) and (111) the oxygen atom of the carbonyl group is involved in hydrogen- bonded interactions.In the absence of a hydrogen-bonded interaction the four non- bonded electrons and the two on the =O fragment of the carbonyl group of formamide require21b that the maximum value of 6' (0) is 6. This means that 6" (0) (= 2- h) in (I), (11) and (111) must be between 5 and 6. Similarly, the 6" for the hydrogen atom involved in this hydrogen-bonded interaction would lie between 1 and 2. Following our earlier work', we arbitrarily assigned 6" (0) = 5.5 and 6" (H) = 1.5 to those oxygen and hydrogen atoms that are involved in the hydrogen-bonded interaction. The dotted line in (11) denotes that there is charge delocalization between the N and 0 atoms (which is consistent with spectroscopic studies2,, 24 on amides) spilling over onto the hydrogen atoms of the -NH, group.The 6" value for the carbon atom in the ECH configuration was taken21 to be 3. The values of various vertices in the formamide backbone are shown in (1)-(111). The ('ti), values for configurations (I)-(111) of A were then calculated [from eqn (3)] to be 0.58, 0.312 and 0.434, respectively. As the value of in formamide (A)-a-, or p- or y-picoline (B) mixtures is close to 0.6 (table 4), the values of (I), (11) and (111) suggest that in all these mixtures formamide in the pure state exists mainly as cyclic dimers (I), with perhaps a proportion of configuration (11). On the other hand, a (3tA)m value of 0.33 (table 4) for formamide (A) in pyridine mixtures suggests that here formamide exists mainly as monomer (11) [with Further ab-initio molecular-orbital calculations" on the structural, energetic and electronic properties of p- and y-R-pyridines (R = CH,, NH,, OH, F etc.) have SuggestedlO that the n-electron density at the C,, C, and C, positions in pyridine is less than that in benzene.This suggests that either one, or two or all three electron-deficient carbon centres in one pyridine molecule are involved in weak interactions with the n-electron cloud of the other pyridine molecule. We next assumed that the electron- deficient C, centre in one pyridine molecule is involved in interaction with the n-electron system of the other pyridine molecule, and then evaluated ,<' for pyridine for configuration (IV) assuming that P(n) = 1. Such a procedure yielded ('<;), = 0.706 for configuration (IV) of pyridine.[The 6" values of the various vertices are also shown in (IV) and the 6" value for the nitrogen atom of pyridine was calculated in the manner suggested by Kier.21] This value for pyridine is very close to the value (3c5B)m = 0.6 (table 4) obtained from an analysis of VE data of formamide (A)-pyridine (B) mixtures in terms of eqn (4). Further, as the equilibrium geometry of the pyridine ring has been shownlO to be independent of the nature and position of the substituents, it follows that a similar scheme of molecular interactions should also characterize picolines. Consequently, we next evaluated ('<;), configuration values for (V), (VI) and (VII) configurations of = 0.3121.P. P. Singh 1813 3.0 3.0 5.0 5.0 3 . 0 0 ‘ 0 3.0u N 4 o 1.0 3.ou N- < I N5.0 3.0 Is-.’ 3.0 3.0 ‘.-el 3.0 3.0 \--‘ 4.0 ‘-O ‘,-, , 3.5 I3.5 13.5 ’.O 3.0 ,3.5 I I I I 5.0 I I I Ip P m a, D- and y-picoline, respectively, again utilizing P(n) = 1.This yielded ( 3 c 3 m values of 1.012, 1.371 and 0.933 for a-, p- and y-picoline, respectively, These (3(& values are close to the corresponding (3c& values of 1.0, 1.0 and 1.1 (table 4) obtained from an analysis of their VE data with formamide in terms of eqn (4). in formamide (Aka-, p- or y-picoline (B) mixtures, and since formamide has been postulated to exist in configuration (I) and/or (11), it is reasonable to assume that only a small part of the configuration of (A) contributes to the 3tB value of B in all these (A-B) mixtures. If it is now postulated2 that the hydrogen atom attached to the -C=O group of (A) is involved in hydrogen bonding with the nitrogen atom of pyridine (B) or picoline (B), then the molecular entity that should determine the ’( value of B in all these (A-B) mixtures should be (VIII), (IX) or (X) with R = H or CH,.Postulating molecular entity (VIII) in these mixtures would then yield (3~&, values of 0.783, 1.085, 1.200 and 1.079 for pyridine and a-, p- and y-picoline, respectively. On the other hand, (3(b)m values for pyridine and a-, p- and y-picoline (B) would be 1.375, 1.775, 2.057 and 2.105 for the molecular entity (IX) and 1.296, 1.850, 1.631 and 1.459 for the molecular entity (X). It is thus evident that the (3&Jm values evaluated for pyridine and a-, 8- and y-picoline (B) are very close to the corresponding (315B)m values of 0.6, 1.200, 1.100 and 1.20 (table 4) for the molecular entity (VIII) only.The present analysis thus suggests that all these mixtures are characterized by the presence of molecular entities having the configuration (VIII). We next undertook a study of the energetics of the various interactions characterizing these mixtures. If we assume what has been stated above to be reasonable, then the process of the present (A-B) mixture formation would require (a) a mixing of (A) with (B) to establish (A)-(B) contacts with an interaction energy xAB per mole of (AHB) contacts. (b) these (A)-(B) contacts between (A) and (B) would then cause rupture of (i) the intramolecular association in A to yield monomers and (ii) the intermolecular interactions in B to yield ‘free’ B molecular entities.(c) The monomers of A would then undergo solvation in ‘free’ B molecules to form AB molecular entities. Consequently, if AH, is the molar enthalpy change due to process (a) then the enthalpy change AHl due to process (a) would be given13 by In addition, since (3cA)m = AH1 = XA xAB S B ( 5 ) where SB is the surface f r a c t i ~ n ~ ~ , ~ ~ of B, defined by so that (7) On the other hand, if xAA is the energy per mole required to cause rupture of the self- association in A, and xBB is the corresponding energy per mole required to cause rupture 60-21814 Solvation of Formamide in Pyridine and Picolines R R R Ix of intermolecular interactions (B-B) in pure B, then the enthalpy changes AH2 and AH, due to processes (b) (i) and (b) (ii) would be given13 by an expression identical to expression ( 5 ) , i.e.by (8) (9) AH2 = XA xAA SL AH3 = XA xBB s;3 where S;3 is the surface fraction of B that brings about changes in A. Evidently Sb would depend13 on the mole fraction of A and also on the surface of B in the (A-B) mixture, so that sk x, S B (10) or Hence and where k and k' are constants. On the other hand, if x12 is the interaction energy per mole for process (c), resulting in the formation of AB molecular entities, then the enthalpy change, AHq, due to this process should be expressed18 by where k" is another constant of proportionality. The total enthalpy change, HE, due to processes (a), (b) and (c), resulting in the formation of the (A-B) mixture from pure A and B would then be given by 4 HE(T, xA) = C AHi i-1 = LxA xB 'B/ c (xi y)] k AR + kXAA xA + k'XBB xA +kNX12 xB)* (' 5, i - A , B Now [taking account of configurations (I) and (VIII)] ifP.P. Singh 1815 then eqn (1 5) yields H E ( T, However, VA/VB has been xA) = Ex, xR 'B/ c (xi %)I (2xaB + x A X ) (18) i = A , B taken13 equal to ( 3 c A / 3 r B ) , so that eqn (18) reduces to Evaluation of xiB and x (and hence xAB, xI2, xBB and x,,) would then require a knowledge of H E data for the (A-B) mixture at two mole fractions. For the present analysis we utilized H "( T, x, = 0.4 and 0.5) data for the (A-B) mixture to evaluate xiB and x [from eqn (19)] and these were subsequently employed to calculate HE data for the (A-B) mixture at another value of x,. Since processes (a), (b) and (c) of (A-B) mixture formation would apply [in view of configurations (I) (V) and (VIII)] strictly to formamide (A)-a- or p- or y-picoline (B) mixtures, we evaluated [from eqn (1 9)] HE data for these mixtures at various x,.Such H E data are recorded in table 4 and are also compared with their corresponding experimental values. Also recorded in table 4 are xiB and x interaction energies characteristic of the various formamide (A)-picoline (B) mixtures. Again, as formamide in formamide (Akpyridine (B) mixtures has been postulated to exist as a monomer [configuration (11)], the solution process for this mixture would involve process (a), (b) (i) and that stated above. Consequently, H E for this particular mixture would be given by which in view of eqn (7), (13), (14), (17) and (18) yields H E = AH, -I- AH3 -k AH4 (20) Evaluation of H E data [from eqn (21)] for formamide (Appyridine (B) mixtures would then, of necessity, require that H E data at two compositions be known.For the present analysis we utilized HE(T, x, = 0.4 and 0.5) data to evaluate xiB and x, which were subsequently employed to evaluate H E for the mixture at any x,. Such H E values at various x, along with xiB and x values characteristic of this mixture, are recorded in table 4. Examination of table 4 clearly shows that the HE data calculated from eqn (19) for formamide (A)-a-, a- or y-picoline (B) mixtures and from eqn (21) for formamide (A)-pyridine (B) mixtures compare well with their corresponding experimental values. Further, since xiB = kxAA = k"XIz = xAB [eqn (16)] and x = k'x,, [eqn (17)], and if it is assumed that k' is the same for all three picolines (B) in the present (A-B) mixtures, then the xBB values in table 4 show that B-B interactions among the various picolines are attractive and that their strength increases in the order p x y > a.This is understandable : since the B-B interactions in configurations (V)-(VIII) of the various picolines are due to charge rearrangements their magnitudes should be determined by the hyper- conjugative effect of the methyl group within the molecule. It is known2' that the magnitude of the hyperconjugative effect of the methyl substituent in a-, p- and y- picoline (B) varies in the order a > y x p, so that the B-B interaction should be largest in a-picoline and smallest in a-picoline.This would further require that the boiling points of these picolines should vary in the order x y > a ; their actual boiling points28 support such a conclusion. Again, as the introduction of a methyl substituent into the pyridine molecule should increase the availability of the lone-pair electrons on the nitrogen atom (owing to the inductive effect of the methyl group] and as the base strength of pyridine and a-, p- and y-picoline increases27 in the order pyridine1816 Solvation of Formamide in Pyridine and PicoIines < y- c p- < a-picoline, it follows that the energy released when pyridine or a-, p- or y-picoline forms hydrogen-bonded entities (VIII) with formamide should vary in the order pyridine < y- < p- c a-picoline.If k” in eqn (16) is assumed to be the same for pyridine and a-, a- and y-picoline, then the xiB values for the various (A-B) mixtures in table 4 clearly show that this is true. The present study thus has indicated that the state of association of a formamide in forrnamide (A)-pyridine or a-, p- or y-picoline (B) mixtures is determined by the molecular entity B and that the volumetric and enthalpic effects in (A-B) mixtures can be rationalized by graph-theoretical arguments to yield information that is consistent with the more involved ab-initio molecular-orbital calculations. It has provided an insight into the energetics of the formation of A-B solution from the pure components A and B. I thank the Head of the Chemistry Department, and the authorities of Maharshi Dayanand University, Rohtak for providing the necessary research facilities.References 1 P. Assarsson, N. Y. Chen and F. R. Eirich, in Colloidal Dispersions and Micellar Behaviour, ed. K. L. 2 C . C. Costain and J. M. Dowling, J . Chem. Phys., 1960, 32, 158. 3 L. Pauling, in The Nature ofthe Chemical Bond (Cornell University Press, 3rd edn, 1960), p. 281. 4 F. Franks and D. J. G. Ives, Q. Rev. 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