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Analysis by computer of thermochemical data on boron compounds
J. C/I~UI. Tl?e~nlc,r!l,izantics1969, 1, 345-352
Analysis by computer of thermochemical data on boron compounds M. F. GUEST,
J. B. PEDLEY,
and (in part) M. HORN
School of Molecdar Sciences, University of Sussex Brighton, Sussex, U.K. (Received 28 November 1968; in revised form 23 December 1968) A computer programme has been developed which tabulates standard enthalpies of reaction at 298.15 K. Substances, and the reactions in which they are involved, can easily be located in the programme, and, by this method, all available enthalpies of reaction could eventually be compiled systematically. The data are analysed by a least squares procedure to find the enthalpies of formation of the substances. This paper reports the application of the method to substances containing boron.
1. Introduction There are several very useful tabulations of thermodynamic quantities, for example those in references 1,2, and 3. However, for the particular caseof standard enthalpies of formation at 298.15 K, these tabulations suffer from the four kinds of limitation outlined below. This paper presents a method of compiling the data, which overcomes these limitations. (i) Present compilations tend to be incomplete. For example, many organometallic substancesare omitted. There are some review articles on standard enthalpies of formation of particular kinds of substance,for example those in references4 and 5, but these appear very infrequently. In the method described here, standard enthalpies of reaction are punched on to cards, and a computer generatestables of self-consistent standard enthalpies of formation of the substancesinvolved. Eventually, all available data could be included and updated values of standard enthalpies of formation could be produced at frequent intervals. Enthalpies of reaction involving the elements B, Si, Ge, Sn, Pb, and S have been compiled so far, but this paper reports only the results for boron. (ii) The standard enthalpies of formation of most substancesdepend on the values for “key compounds”(6’ (for example, COz, H,O, halogen acids, and, in boron thermochemistry, those compounds listed in table 1). Some doubt has been expressedconcerning the standard enthalpy of formation of C02(‘) which affects the values for most organic compounds. Similarly, it has been suggested(8) that the value(‘) for HF(aq) is incorrect; and this castsdoubt on the values of the standard enthalpies of formation of many inorganic and organic fluorides. In the schemeproposed here, any changesin the values for “key” compounds would require only the alteration of a few cards, and the computer would automatically
346
M. F. GUEST,
J. B. PEDLEY,
AND
M. HORN
update the standard enthalpies of formation of those compounds affected by the changes. (iii) The various compilations do not always agree on the “best” values for the standard enthalpies of formation of “key” compounds, and there is a danger in the combination of data from two different sources. Table 1 lists the standard enthalpies of formation of some “key” boron compounds, quoted in references 1 and 2; the discrepancies arise because the two compilers have assigned different weights to the available experimental results. TABLE 1. Standard enthalpies of formation AH,” of some “key” boron compounds. Substance
B(g)
BCl,W - .-, ML(g) W&(4
H,BO&)
AH,“/kcal mol-l Reference (1) Reference (2) 134.5 -96.50 8.5
-304.20 -261.55
132.8 -96.31 9.8
-303.64 -261.47
It is not suggestedthat the standard enthalpies of formation obtained by the computer programme are any “better” than those in table 1. However, all the generated values are mutually self-consistent, and an important feature of the output is a clear indication of which results have been heavily weighted becausethey were regarded as reliable. Also, it is a trivial matter to reweight particular results in the light of more recent information, and to recalculate the standard enthalpies of formation. (iv) Results which cannot yet be used to obtain enthalpies of formation are included in the compilation. For example, if two substancesoccur in only one reaction, neither of their standard enthalpies of formation can be obtained. The computer sorts out these reactions, excludes them from the analysis, and prints out a list of the reactions. When sufficient results have been found and inserted, the reactions are automatically included, and the appropriate standard enthalpies of formation are generated. Full details of the computer programme will not be given in this paper, but the following sections deal with the general principles of the method of analysis, and its application to substancescontaining boron. 2. Method of Analysis The standard enthalpy AH; of a reaction at 298.15 K is given by the equation: AH3 = C Vi,jAH,q i,
(1)
where vi, j is the stoichiometric number (positive for products, negative for reactants) of the substance i in the reaction j and AH;, i is the standard enthalpy of formation of i at 298.15 K. Table 2 shows a hypothetical Vi,j matrix for a set of six substances involved in seven reactions, X indicating a non-zero matrix element. Three classesof reaction must be distinguished as follows. (a) “Key” compounds (substances 1,2, and 3 in table 2) usually occur in several reactions (reactions 1 to 5 in
THERMOCHEMICAL
DATA
ON BORON
COMPOUNDS
337
table 2) so that the simultaneous equations are over-determined and can be solved by the method of least squares by use of the equations: (2) T AH;, i 1 ri, j W&, j = c AH; Wfv,, j, j j where i and k denote substances and j the corresponding reactions. The weighting factors Wj will be discussed below. (b) When a substance k (substance 4 in table 2) occurs in only one reaction (reaction 6 in table 2), equations (2) reduce to the single equation : (3) vk, j AHi?. k = AH; - 1’ AH;, i \li, j, where c’ denotes summation over all substances except k. (c) For a few reactions (reaction 7 in table 2) two substances (substances 5 and 6 in table 2) occur in only one reaction. Then neither of the enthalpies of formation can be obtained. TABLE 2. Hypothetical
vi. j matrix
Substances 1
2
X x X
3
4
5
6
x
(4 (a) (4 (4 (a) (b) x (c)
X x X
x x
x x
x
x
The procedure used by the computer is as follows. I. The matrix J’ij is searched and sorted into substances and reactions of types (a), (b), and (c). 2. Substances and reactions of class (c) are listed as insoluble. 3. Reactions of type (a) are solved using the simultaneous equations (2) to give the standard enthalpies of formation of “key” compounds and of any other substances which occur in more than one reaction in the compilation. 4. The standard enthalpies of formation of the large number of substances occurring in reactions of class (b) are obtained by use of equation (3). 5. The “errors” Aj associated with each of the reactions of class (a) are computed from the expression : Aj = AH; - c vi, j AH;, i. (4) 1 The values Of Aj indicate the compatibility of the interdependent enthalpies of reaction.
3. Choice of weighting factors The precision of thermochemical results is very often in doubt, since systematic errors are sometimes difficult to trace. For this reason, three sets of computations were performed to investigate the precision and compatibility of the data. During the first set all measurements were given equal weight. If a given reaction was incompatible with the rest, this was indicated by a value of Aj for that reaction which might be large enough to justify removing it from the compilation.
B(amorphous) B(l) B(g) Mg) BO(g) BWg) J-MM9 B&(c) Bz03(amorphous) MM) BzW4 BWg) B&(g) BHdg) M-Mg) BJLdg) ML(g) BsHn(g) BsHdg) BmH~&) (HO)BO(c) (HOPOW H&(OH)(d HB(OW&) HzBOdc) H3B03.200H20(aq) H&Odd (WO)&h(c) (BOW&) ((HO)BO)&) BWg) B,C(g)
TABLE
0.53 5.26 134.09 197.63 18.35 -75.28 -108.13 -303.64 -299.33 -299.30 -199.17 108.24 45.71 23.80 8.39 15.51 17.54 24.34 22.17 7.09 - 190.57 - 134.05 -69.40 - 153.09 -261.29 -256.01 -236.98 -334.97 -290.02 -542.38 174.00 -11.25 0.00 0.00 134.09 197.63 18.35 -75.28 -108.13 0.00 0.00 0.00 -199.17 108.24 45.71 23.80 8.39 15.51 17.54 24.34 22.17 7.09 0.00 - 134.05 -69.40 - 153.09 0.00 0.00 -236.98 -314.97 -290.02 -542.38 174.00 -11.25
AHXg) kcalmol-l
AH,” kcalmol-l
enthalpies
0.00 0.00 0.00 70.57 175.31 328.50 495.45 0.00 0.00 0.00 646.05 77.96 192.59 266.60 572.41 1 041.89 1 121.86 1 219.26 1 303.43 2 063.31 0.00 439.37 419.36 562.61 0.00 0.00 706.06 1029.81 1 027.30 1 458.34 301.88 718.54
AH:, a. kcalmol-l
values of standard
3. Derived
:13(l)
of substances containing
Me20 ‘BF3(1) Et20 .BF,(l) BCKd BCMl) BCMg) WA(l) BOCW (BOCMd (BOCMg) HBCl& Bd&Cl&(l) B&CM-W Bu;BCl(l) PhBClz(1) (Me0)2BCl(l) (EtO)zBCl(l) (EtO)BCl,(l) CH,COCl.BC BLCk) BFCLCd BBrk) B%(l) Bu;BBr(l) PhBBr,(l) BMc) BMg) Bu;BI(l) Wd BWd J%ZMd &WC) MeaS. BH,(I)
of formation
-338.90 -354.30 36.01 -103.10 -97.50 -127.00 -75.97 -391.49 - 502.00 -60.52 -314.00 - 339.00 -98.91 -71.39 - 186.28 -204.92 -157.06 -168.20 -213.07 - 154.83 57.33 -57.01 -S4.21 -41.00 -2.49 12.99 -66.07 83.15 29.00 36.00 -57.50 -40.80
AH; kcalmol-l
boron.
0.00 0.00 36.01 0.00 -97.50 -118.97 -75.97 -391.49 - 502.00 -60.52 - 302.00 -339.00 --87.41 -63.29 - 179.28 - 195.62 - 148.66 0.00 -213.07 -154.83 57.33 -48.81 -72.11 - 30.50 0.00 12.99 -53.07 83.15 29.00 36.00 16.00 -30.50
AHW kcalmol-l
0.00 0.00 127.01 0.00 318.36 502.85 298.55 1 059.23 1 392.32 304.56 1 016.10 1 029.92 2 555.35 1 541.07 1 115.80 1 682.32 1002.44 0.00 413.81 365.63 103.51 263.13 2 537.87 1 503.92 0.00 197.73 2 517.63 116.63 236.46 363.56 449.24 1 040.96
AH,“, a kcalmol-l
,., +
j$)
BMeAl) BEtz(1) BPr;(l) BPr#) BBu;(l) BBu;(l) BBu;(l) Tri-n-pentylborane(1) Triphenylborane(c) Tricyclohexylborane(c) Tri-n-hexylborane(1) Tri-n-heptylborane(1) Tri-n-octylborane(1) Tri-set-octylborane(1) BH,CWd HB(OMe)dU B(OMe)dl) PWOHMc) HB(OP&(l) B(OW,(l) (HO)BBu;(l) B(OPr%(l) BiOBu” @‘h&),0(c) (PhWdc) Me,O’2B,H (c>) BF(g) ” = J%(g) BzFdg) BOW3 @OF),(c) @OFMg) HBF,(g) HBF,.14.67HF’58.72HZO(aq) (HO)zBF(g) tHO)BF,k) &KWH&) B303F2H(g)
- 34.04 -44.43 -66.26 -69.96 - 82.36 -78.16 -81.03 -108.17 11.87 -115.10 -116.00 -133.73 -152.21 -148.81 -26.58 -144.37 -223.07 -171.77 - 183.01 -250.02 -145.85 -271.21 -290.29 -83.58 -300.56 -30.00 -29.14 -271.59 -345.12 -143.10 -588.01 -566.53 - 176.59 -378.90 -249.21 ---260.65 -382.81 476.85
29.24 -35.63 -54.26 -57.96 -67.56 - 63.86 -67.23 -90.47 31.37 -95.60 -94.80 - 109.33 - 124.61 - 122.21 -26.58 - 138.23 -214.77 -151.77 -175.01 239.52 ~ 130.85 m--~259.41 -277.79 p-63.58 -269.06 ~ 30.00 -29.14 -271.59 --345.12 - 143.10 0.00 -566.53 - 176.59 0.00 --249.21 -~ 260.65 - 382.81 --- 476.85 1 134.91 1 976.57 2 820.47 2 824.17 3 659.04 3 655.34 3 658.71 4 507.22 3 960.25 5 025.02 5 336.82 6 176.62 7 017.17 7 014.77 547.43 1 097.93 1509.12 1 795.03 2 235.07 2 359.14 2 681.53 3 204.30 4 047.95 5 534.70 4 707.56 1 652.50 182.10 462.27 688.76 355.62 0.00 1204.09 400.51 0.00 625.49 544.13 1 086.85 1 147.65
?-Phcnyl-1 ,l,2-dithioborolan(1) ?-Phenyl-1,3,2-dithioborinan(l) B(SMeMU BWM) B(SPr”)3(1) B(SBu”M) B(S-n-pentyl)& NSPhMc) SF,.BF,(c) 2-Chloro-1,3,2-dithioborolan(1) 2-Chloro-1,3,2-dithioborinan(1) 2-Chloro-4-methyl-1,3,2dithioborolan(1) BNc) BN(g) (NH,), B&(c) B&H,(l) Diammonium decaborane(c) MeNH, BH,(c) Me,N BH3(c) Me3N. BH,(l) Me3B. NH,(l) MeNHz .BMea(c) Me,N.BH,(c) Me3N.BMes(c) EtzNH.BMej(c) BWMeddl) NH3 .B(OMe)s(c) NH, .BF,(c) Me,N BF3(g) B-Trichloroborazine(c) N-Trichloroborazine(c) (Me2N)BCldl) (Me,N),BCl(l) BP(c) Bd’a(c) 2PH3. B,H,(c) hleaP. BMea(c)
0.00 0.00 -36.91 ~ 67.92 -79.48 --93.74 110.19 45.60 0.00 1 0.00 0.00 0.00 0.00 154.84 0.00 22.20 0.00 0.00 0.00 p-20.26 --54.io -52.60 0.00 -- 52.60 h2.90 -64.06 0.00 0.00 -304.40 -237.08 -236.80 -97.72 -84.04 0.00 0.00 0.00 0.00
m-71.95 -36.54 m-49.84 -82.42 --- 100.28 ~~ 116.64 ~ 135.19 15.60 -484.00 -65.15 -72.64 -71.84 -59.46 154.84 -46.00 -129.30 -85.73 - 32.20 ~33.81 - 34.06 --67.90 -64.30 -38.10 -66.60 -m79.20 -75.26 -254.00 -323.60 - 304.40 -254.18 -255.00 - 106.62 -94.04 -19.00 -- 40.00 --27.00 m-81.80
0.00 0.00 92.26 0.00 1 176.10 0.00 0.00 0.00 1 405.23 1 439.07 1 712.66 0.00 2 262.84 2 548.23 2 500.30 0.00 0.00 1 589.65 1 221.44 1 221.16 1 057.04 1 781.82 0.00 0.00 0.00 0.00
0 00 0.00 1 3-19.65 2 205.90 3 042.13 3 882.26 4 723.98 4 143.06 0.00 0.00 0.00
LiBOa(c) LiBOJ)
BeJLOdc) BzMdc) B&MC)
PF, .BH,(g) Me3P. BF,(c) POCI, .BCl,(c) PH, . B’&(c) Me3As .BMea(c) Me,As . BF,(c) PbO.B,O,(c) PbO.B,O,(amorphous) PbO .2B,O,(c) PbO 2B203(amorphous) PbO .3Bz03(c) 2Pb0.5B203(c) BeMUz)
-204.10 - 327.40 -256.30 - 120.90 - 50.00 - 292.00 -378.78 -372.38 -682.53 -671.93 - 1 003.37 -1 672.36 -329.15 -743.18 -21.97 -25.12 -245.80 -241.33
_~--AH;--.kcal mol-1 -204.10 -312.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -329.15 0.00 0.00 0.00 -- 162.89 0.00
AH,“(g) kcalmol-’ -802.70 -791.89 -1 113.79 -1 413.63 -45.63 -233.82 -229.16 -783.19 -778.39 - 1 094.81 -44.73 -796.90 -786.10 -1 107.49 -1 420.98 -1 403.63 -53.84 -452.21
630.88 1 564.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 913.86 0.00 0.00 0.00 454.52 0.00 NaBH,(c) WUMc) &BkM1) K&Odc) K&O,,(c) &WAdU KBH,(c) KBFdc)
NaJLO,(l) NdMMc)
LiBH*(c) NaBO,(c) NaBO,(I) Na2&07(d
Li2B407k) Li2B40,(1) LiAOdc) Li2B80dc)
AH,” kcalmolml
3.-continued
AH;. a kcalmol-l
TABLE
0.00 0.00 0.00 0.00 0.00 435.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
- 156.82 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
AH:. a kcalmol-l
0.00 0.00 0.00 0.00 0.00
AH%3 kcalmol-l
THERMOCH!ZMICAL
DATA
ON BORON
COMPOUNDS
351
During the second set those measurements which were regarded by many authors as “reliable” were given a weight Wj of IO, and all other measurementswere given a weight of 1. Thus the error AI was forced to tend to zero for those measurementswhich at present are regarded as “reliable”. The third set involved using the equation: wj = l/lAjl, (5) where the jAj 1were the magnitudes of the errors found during the second set. Equation (5) has the effect of almost completely eliminating from the least squares procedure any reactions which are grossly incompatible with the rest. The above rather elaborate procedure is necessary, because a single inaccurate measurement can introduce appreciable errors into many of the standard enthalpies of formation. 4. Results for substances containing boron It would be impossible to process simultaneously all available enthalpies of reaction even in the largest available computer. The results are therefore subdivided into chemically significant sections; in this paper substances containing boron are considered. The standard enthalpies of formation of substancesin the compilation which do not contain boron were read in as “known”, having been taken for present purposes mainly from other compilations. It is hoped that, eventually, these data would be obtained from other sections of the complete compilation of all enthalpies of reaction. The contributions to the observed enthalpies of reaction, AH;, from these “known” standard enthalpies of formation, were subtracted from AH; to give a set of simultaneous equations for the standard enthalpies of formation of the boron-containing substances only, with modified enthalpies of reaction given by: AH;’ = AN; - c” ri, j AH;, i, (6) 1 where c” indicates summation over boron-free substancesonly. The iimultaneous equations were then solved as described in the previous section and the derived standard enthalpies of formation are listed in table 3. The filing order is a slight modification of the N.B.S. “finding number system”.(l) If the enthalpy of vaporization of a given substance was known, then the computer calculated the standard enthalpy of formation of the gaseoussubstance and the enthalpy of atomization -AH;, 3 using the following values of -AH;,./kcal moi-’ for the elements: 0 59.56;(9’ H, 52.10;‘9’ C, 170.89;‘9)F, 18.86;“) Cl, 28.92;(9) Br, 26.74;(9’ I, 25.54;‘“’ S,‘65.65;‘9’ N, 113.00;‘9’ P, 79.80;“’ As, 69.00;“’ Pb, 46.75;“’ B, 134.10 (this compilation). If the enthalpy of vaporization was not known or when it was not needed becausereactions involving the gaseousphase of the substance were already included in the compilation, then the enthalpy of formation of the gaseous substance and its enthalpy of atomization were arbitrarily set equal to zero. The enthalpies of atomization listed in table 3 could have been discussedin terms of various bond enthalpy schemes,and it would be possible, in this system of tabulation, to produce updated bond enthalpy terms at frequent intervals. However, it was in-
352
M. F. GUEST,
J. B. PEDLEY,
AND
M. HORN
tended in this paper only to establish the principles of a possible method of handling thermochemical data. The literature search for results on substancescontaining boron was not exhaustive, nor was the assignment of reliability unambiguous; but the authors would be pleased to send full details of the reactions in the compilation to anyone interested. Information concerning any omissions or possible modifications in the data would be welcomed, and the next generation of tables would then include the new information. The authors wish to thank the Sussex University Computing Centre for facilities, and the S.R.C. for a maintenance grant (to M. F. G.). REFERENCES 1. National Bureau of Standards Circular 500, 1952 and Technical Note 270. Washington, D.C. 1965. 2. JANAF Thermochemical Tables. Thermal Research Laboratory, Dow Chemical Company, Midland, Michigan. 3. Green, J. H. S. Quart. Rev. 1961, 15, 125. 4. Mackle, H.; O’Hare, P. A. G. Tetrahedron 1963, 19, 961. 5. Hartley, S. B.; Holmes, W. S.; Jacques, J. K.; Mole, M. F.; McCoubrey, J. C. Quart. Rev. 1963, 17,204. 6. Gunn, S. R. J. Phys. Chem. 1965, 69, 1010. 7. Hawtin, P.; Lewis, J. B.; Moul, N.; Phillips, R. H. Phil. Trans. Roy. Sot. Ser. A 1966, 261, 67. 8. Cox, J. D.; Harrop, D. Trans. Faraday Sot. 1965, 61, 1328. 9. Skinner, H. A.; Pilcher, G. Quart. Rev. 1963, 17, 264.
Analysis by computer of thermochemical data on boron compounds M. F. GUEST,
J. B. PEDLEY,
and (in part) M. HORN
School of Molecdar Sciences, University of Sussex Brighton, Sussex, U.K. (Received 28 November 1968; in revised form 23 December 1968) A computer programme has been developed which tabulates standard enthalpies of reaction at 298.15 K. Substances, and the reactions in which they are involved, can easily be located in the programme, and, by this method, all available enthalpies of reaction could eventually be compiled systematically. The data are analysed by a least squares procedure to find the enthalpies of formation of the substances. This paper reports the application of the method to substances containing boron.
1. Introduction There are several very useful tabulations of thermodynamic quantities, for example those in references 1,2, and 3. However, for the particular caseof standard enthalpies of formation at 298.15 K, these tabulations suffer from the four kinds of limitation outlined below. This paper presents a method of compiling the data, which overcomes these limitations. (i) Present compilations tend to be incomplete. For example, many organometallic substancesare omitted. There are some review articles on standard enthalpies of formation of particular kinds of substance,for example those in references4 and 5, but these appear very infrequently. In the method described here, standard enthalpies of reaction are punched on to cards, and a computer generatestables of self-consistent standard enthalpies of formation of the substancesinvolved. Eventually, all available data could be included and updated values of standard enthalpies of formation could be produced at frequent intervals. Enthalpies of reaction involving the elements B, Si, Ge, Sn, Pb, and S have been compiled so far, but this paper reports only the results for boron. (ii) The standard enthalpies of formation of most substancesdepend on the values for “key compounds”(6’ (for example, COz, H,O, halogen acids, and, in boron thermochemistry, those compounds listed in table 1). Some doubt has been expressedconcerning the standard enthalpy of formation of C02(‘) which affects the values for most organic compounds. Similarly, it has been suggested(8) that the value(‘) for HF(aq) is incorrect; and this castsdoubt on the values of the standard enthalpies of formation of many inorganic and organic fluorides. In the schemeproposed here, any changesin the values for “key” compounds would require only the alteration of a few cards, and the computer would automatically
346
M. F. GUEST,
J. B. PEDLEY,
AND
M. HORN
update the standard enthalpies of formation of those compounds affected by the changes. (iii) The various compilations do not always agree on the “best” values for the standard enthalpies of formation of “key” compounds, and there is a danger in the combination of data from two different sources. Table 1 lists the standard enthalpies of formation of some “key” boron compounds, quoted in references 1 and 2; the discrepancies arise because the two compilers have assigned different weights to the available experimental results. TABLE 1. Standard enthalpies of formation AH,” of some “key” boron compounds. Substance
B(g)
BCl,W - .-, ML(g) W&(4
H,BO&)
AH,“/kcal mol-l Reference (1) Reference (2) 134.5 -96.50 8.5
-304.20 -261.55
132.8 -96.31 9.8
-303.64 -261.47
It is not suggestedthat the standard enthalpies of formation obtained by the computer programme are any “better” than those in table 1. However, all the generated values are mutually self-consistent, and an important feature of the output is a clear indication of which results have been heavily weighted becausethey were regarded as reliable. Also, it is a trivial matter to reweight particular results in the light of more recent information, and to recalculate the standard enthalpies of formation. (iv) Results which cannot yet be used to obtain enthalpies of formation are included in the compilation. For example, if two substancesoccur in only one reaction, neither of their standard enthalpies of formation can be obtained. The computer sorts out these reactions, excludes them from the analysis, and prints out a list of the reactions. When sufficient results have been found and inserted, the reactions are automatically included, and the appropriate standard enthalpies of formation are generated. Full details of the computer programme will not be given in this paper, but the following sections deal with the general principles of the method of analysis, and its application to substancescontaining boron. 2. Method of Analysis The standard enthalpy AH; of a reaction at 298.15 K is given by the equation: AH3 = C Vi,jAH,q i,
(1)
where vi, j is the stoichiometric number (positive for products, negative for reactants) of the substance i in the reaction j and AH;, i is the standard enthalpy of formation of i at 298.15 K. Table 2 shows a hypothetical Vi,j matrix for a set of six substances involved in seven reactions, X indicating a non-zero matrix element. Three classesof reaction must be distinguished as follows. (a) “Key” compounds (substances 1,2, and 3 in table 2) usually occur in several reactions (reactions 1 to 5 in
THERMOCHEMICAL
DATA
ON BORON
COMPOUNDS
337
table 2) so that the simultaneous equations are over-determined and can be solved by the method of least squares by use of the equations: (2) T AH;, i 1 ri, j W&, j = c AH; Wfv,, j, j j where i and k denote substances and j the corresponding reactions. The weighting factors Wj will be discussed below. (b) When a substance k (substance 4 in table 2) occurs in only one reaction (reaction 6 in table 2), equations (2) reduce to the single equation : (3) vk, j AHi?. k = AH; - 1’ AH;, i \li, j, where c’ denotes summation over all substances except k. (c) For a few reactions (reaction 7 in table 2) two substances (substances 5 and 6 in table 2) occur in only one reaction. Then neither of the enthalpies of formation can be obtained. TABLE 2. Hypothetical
vi. j matrix
Substances 1
2
X x X
3
4
5
6
x
(4 (a) (4 (4 (a) (b) x (c)
X x X
x x
x x
x
x
The procedure used by the computer is as follows. I. The matrix J’ij is searched and sorted into substances and reactions of types (a), (b), and (c). 2. Substances and reactions of class (c) are listed as insoluble. 3. Reactions of type (a) are solved using the simultaneous equations (2) to give the standard enthalpies of formation of “key” compounds and of any other substances which occur in more than one reaction in the compilation. 4. The standard enthalpies of formation of the large number of substances occurring in reactions of class (b) are obtained by use of equation (3). 5. The “errors” Aj associated with each of the reactions of class (a) are computed from the expression : Aj = AH; - c vi, j AH;, i. (4) 1 The values Of Aj indicate the compatibility of the interdependent enthalpies of reaction.
3. Choice of weighting factors The precision of thermochemical results is very often in doubt, since systematic errors are sometimes difficult to trace. For this reason, three sets of computations were performed to investigate the precision and compatibility of the data. During the first set all measurements were given equal weight. If a given reaction was incompatible with the rest, this was indicated by a value of Aj for that reaction which might be large enough to justify removing it from the compilation.
B(amorphous) B(l) B(g) Mg) BO(g) BWg) J-MM9 B&(c) Bz03(amorphous) MM) BzW4 BWg) B&(g) BHdg) M-Mg) BJLdg) ML(g) BsHn(g) BsHdg) BmH~&) (HO)BO(c) (HOPOW H&(OH)(d HB(OW&) HzBOdc) H3B03.200H20(aq) H&Odd (WO)&h(c) (BOW&) ((HO)BO)&) BWg) B,C(g)
TABLE
0.53 5.26 134.09 197.63 18.35 -75.28 -108.13 -303.64 -299.33 -299.30 -199.17 108.24 45.71 23.80 8.39 15.51 17.54 24.34 22.17 7.09 - 190.57 - 134.05 -69.40 - 153.09 -261.29 -256.01 -236.98 -334.97 -290.02 -542.38 174.00 -11.25 0.00 0.00 134.09 197.63 18.35 -75.28 -108.13 0.00 0.00 0.00 -199.17 108.24 45.71 23.80 8.39 15.51 17.54 24.34 22.17 7.09 0.00 - 134.05 -69.40 - 153.09 0.00 0.00 -236.98 -314.97 -290.02 -542.38 174.00 -11.25
AHXg) kcalmol-l
AH,” kcalmol-l
enthalpies
0.00 0.00 0.00 70.57 175.31 328.50 495.45 0.00 0.00 0.00 646.05 77.96 192.59 266.60 572.41 1 041.89 1 121.86 1 219.26 1 303.43 2 063.31 0.00 439.37 419.36 562.61 0.00 0.00 706.06 1029.81 1 027.30 1 458.34 301.88 718.54
AH:, a. kcalmol-l
values of standard
3. Derived
:13(l)
of substances containing
Me20 ‘BF3(1) Et20 .BF,(l) BCKd BCMl) BCMg) WA(l) BOCW (BOCMd (BOCMg) HBCl& Bd&Cl&(l) B&CM-W Bu;BCl(l) PhBClz(1) (Me0)2BCl(l) (EtO)zBCl(l) (EtO)BCl,(l) CH,COCl.BC BLCk) BFCLCd BBrk) B%(l) Bu;BBr(l) PhBBr,(l) BMc) BMg) Bu;BI(l) Wd BWd J%ZMd &WC) MeaS. BH,(I)
of formation
-338.90 -354.30 36.01 -103.10 -97.50 -127.00 -75.97 -391.49 - 502.00 -60.52 -314.00 - 339.00 -98.91 -71.39 - 186.28 -204.92 -157.06 -168.20 -213.07 - 154.83 57.33 -57.01 -S4.21 -41.00 -2.49 12.99 -66.07 83.15 29.00 36.00 -57.50 -40.80
AH; kcalmol-l
boron.
0.00 0.00 36.01 0.00 -97.50 -118.97 -75.97 -391.49 - 502.00 -60.52 - 302.00 -339.00 --87.41 -63.29 - 179.28 - 195.62 - 148.66 0.00 -213.07 -154.83 57.33 -48.81 -72.11 - 30.50 0.00 12.99 -53.07 83.15 29.00 36.00 16.00 -30.50
AHW kcalmol-l
0.00 0.00 127.01 0.00 318.36 502.85 298.55 1 059.23 1 392.32 304.56 1 016.10 1 029.92 2 555.35 1 541.07 1 115.80 1 682.32 1002.44 0.00 413.81 365.63 103.51 263.13 2 537.87 1 503.92 0.00 197.73 2 517.63 116.63 236.46 363.56 449.24 1 040.96
AH,“, a kcalmol-l
,., +
j$)
BMeAl) BEtz(1) BPr;(l) BPr#) BBu;(l) BBu;(l) BBu;(l) Tri-n-pentylborane(1) Triphenylborane(c) Tricyclohexylborane(c) Tri-n-hexylborane(1) Tri-n-heptylborane(1) Tri-n-octylborane(1) Tri-set-octylborane(1) BH,CWd HB(OMe)dU B(OMe)dl) PWOHMc) HB(OP&(l) B(OW,(l) (HO)BBu;(l) B(OPr%(l) BiOBu” @‘h&),0(c) (PhWdc) Me,O’2B,H (c>) BF(g) ” = J%(g) BzFdg) BOW3 @OF),(c) @OFMg) HBF,(g) HBF,.14.67HF’58.72HZO(aq) (HO)zBF(g) tHO)BF,k) &KWH&) B303F2H(g)
- 34.04 -44.43 -66.26 -69.96 - 82.36 -78.16 -81.03 -108.17 11.87 -115.10 -116.00 -133.73 -152.21 -148.81 -26.58 -144.37 -223.07 -171.77 - 183.01 -250.02 -145.85 -271.21 -290.29 -83.58 -300.56 -30.00 -29.14 -271.59 -345.12 -143.10 -588.01 -566.53 - 176.59 -378.90 -249.21 ---260.65 -382.81 476.85
29.24 -35.63 -54.26 -57.96 -67.56 - 63.86 -67.23 -90.47 31.37 -95.60 -94.80 - 109.33 - 124.61 - 122.21 -26.58 - 138.23 -214.77 -151.77 -175.01 239.52 ~ 130.85 m--~259.41 -277.79 p-63.58 -269.06 ~ 30.00 -29.14 -271.59 --345.12 - 143.10 0.00 -566.53 - 176.59 0.00 --249.21 -~ 260.65 - 382.81 --- 476.85 1 134.91 1 976.57 2 820.47 2 824.17 3 659.04 3 655.34 3 658.71 4 507.22 3 960.25 5 025.02 5 336.82 6 176.62 7 017.17 7 014.77 547.43 1 097.93 1509.12 1 795.03 2 235.07 2 359.14 2 681.53 3 204.30 4 047.95 5 534.70 4 707.56 1 652.50 182.10 462.27 688.76 355.62 0.00 1204.09 400.51 0.00 625.49 544.13 1 086.85 1 147.65
?-Phcnyl-1 ,l,2-dithioborolan(1) ?-Phenyl-1,3,2-dithioborinan(l) B(SMeMU BWM) B(SPr”)3(1) B(SBu”M) B(S-n-pentyl)& NSPhMc) SF,.BF,(c) 2-Chloro-1,3,2-dithioborolan(1) 2-Chloro-1,3,2-dithioborinan(1) 2-Chloro-4-methyl-1,3,2dithioborolan(1) BNc) BN(g) (NH,), B&(c) B&H,(l) Diammonium decaborane(c) MeNH, BH,(c) Me,N BH3(c) Me3N. BH,(l) Me3B. NH,(l) MeNHz .BMea(c) Me,N.BH,(c) Me3N.BMes(c) EtzNH.BMej(c) BWMeddl) NH3 .B(OMe)s(c) NH, .BF,(c) Me,N BF3(g) B-Trichloroborazine(c) N-Trichloroborazine(c) (Me2N)BCldl) (Me,N),BCl(l) BP(c) Bd’a(c) 2PH3. B,H,(c) hleaP. BMea(c)
0.00 0.00 -36.91 ~ 67.92 -79.48 --93.74 110.19 45.60 0.00 1 0.00 0.00 0.00 0.00 154.84 0.00 22.20 0.00 0.00 0.00 p-20.26 --54.io -52.60 0.00 -- 52.60 h2.90 -64.06 0.00 0.00 -304.40 -237.08 -236.80 -97.72 -84.04 0.00 0.00 0.00 0.00
m-71.95 -36.54 m-49.84 -82.42 --- 100.28 ~~ 116.64 ~ 135.19 15.60 -484.00 -65.15 -72.64 -71.84 -59.46 154.84 -46.00 -129.30 -85.73 - 32.20 ~33.81 - 34.06 --67.90 -64.30 -38.10 -66.60 -m79.20 -75.26 -254.00 -323.60 - 304.40 -254.18 -255.00 - 106.62 -94.04 -19.00 -- 40.00 --27.00 m-81.80
0.00 0.00 92.26 0.00 1 176.10 0.00 0.00 0.00 1 405.23 1 439.07 1 712.66 0.00 2 262.84 2 548.23 2 500.30 0.00 0.00 1 589.65 1 221.44 1 221.16 1 057.04 1 781.82 0.00 0.00 0.00 0.00
0 00 0.00 1 3-19.65 2 205.90 3 042.13 3 882.26 4 723.98 4 143.06 0.00 0.00 0.00
LiBOa(c) LiBOJ)
BeJLOdc) BzMdc) B&MC)
PF, .BH,(g) Me3P. BF,(c) POCI, .BCl,(c) PH, . B’&(c) Me3As .BMea(c) Me,As . BF,(c) PbO.B,O,(c) PbO.B,O,(amorphous) PbO .2B,O,(c) PbO 2B203(amorphous) PbO .3Bz03(c) 2Pb0.5B203(c) BeMUz)
-204.10 - 327.40 -256.30 - 120.90 - 50.00 - 292.00 -378.78 -372.38 -682.53 -671.93 - 1 003.37 -1 672.36 -329.15 -743.18 -21.97 -25.12 -245.80 -241.33
_~--AH;--.kcal mol-1 -204.10 -312.60 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -329.15 0.00 0.00 0.00 -- 162.89 0.00
AH,“(g) kcalmol-’ -802.70 -791.89 -1 113.79 -1 413.63 -45.63 -233.82 -229.16 -783.19 -778.39 - 1 094.81 -44.73 -796.90 -786.10 -1 107.49 -1 420.98 -1 403.63 -53.84 -452.21
630.88 1 564.65 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 913.86 0.00 0.00 0.00 454.52 0.00 NaBH,(c) WUMc) &BkM1) K&Odc) K&O,,(c) &WAdU KBH,(c) KBFdc)
NaJLO,(l) NdMMc)
LiBH*(c) NaBO,(c) NaBO,(I) Na2&07(d
Li2B407k) Li2B40,(1) LiAOdc) Li2B80dc)
AH,” kcalmolml
3.-continued
AH;. a kcalmol-l
TABLE
0.00 0.00 0.00 0.00 0.00 435.80 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
- 156.82 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
AH:. a kcalmol-l
0.00 0.00 0.00 0.00 0.00
AH%3 kcalmol-l
THERMOCH!ZMICAL
DATA
ON BORON
COMPOUNDS
351
During the second set those measurements which were regarded by many authors as “reliable” were given a weight Wj of IO, and all other measurementswere given a weight of 1. Thus the error AI was forced to tend to zero for those measurementswhich at present are regarded as “reliable”. The third set involved using the equation: wj = l/lAjl, (5) where the jAj 1were the magnitudes of the errors found during the second set. Equation (5) has the effect of almost completely eliminating from the least squares procedure any reactions which are grossly incompatible with the rest. The above rather elaborate procedure is necessary, because a single inaccurate measurement can introduce appreciable errors into many of the standard enthalpies of formation. 4. Results for substances containing boron It would be impossible to process simultaneously all available enthalpies of reaction even in the largest available computer. The results are therefore subdivided into chemically significant sections; in this paper substances containing boron are considered. The standard enthalpies of formation of substancesin the compilation which do not contain boron were read in as “known”, having been taken for present purposes mainly from other compilations. It is hoped that, eventually, these data would be obtained from other sections of the complete compilation of all enthalpies of reaction. The contributions to the observed enthalpies of reaction, AH;, from these “known” standard enthalpies of formation, were subtracted from AH; to give a set of simultaneous equations for the standard enthalpies of formation of the boron-containing substances only, with modified enthalpies of reaction given by: AH;’ = AN; - c” ri, j AH;, i, (6) 1 where c” indicates summation over boron-free substancesonly. The iimultaneous equations were then solved as described in the previous section and the derived standard enthalpies of formation are listed in table 3. The filing order is a slight modification of the N.B.S. “finding number system”.(l) If the enthalpy of vaporization of a given substance was known, then the computer calculated the standard enthalpy of formation of the gaseoussubstance and the enthalpy of atomization -AH;, 3 using the following values of -AH;,./kcal moi-’ for the elements: 0 59.56;(9’ H, 52.10;‘9’ C, 170.89;‘9)F, 18.86;“) Cl, 28.92;(9) Br, 26.74;(9’ I, 25.54;‘“’ S,‘65.65;‘9’ N, 113.00;‘9’ P, 79.80;“’ As, 69.00;“’ Pb, 46.75;“’ B, 134.10 (this compilation). If the enthalpy of vaporization was not known or when it was not needed becausereactions involving the gaseousphase of the substance were already included in the compilation, then the enthalpy of formation of the gaseous substance and its enthalpy of atomization were arbitrarily set equal to zero. The enthalpies of atomization listed in table 3 could have been discussedin terms of various bond enthalpy schemes,and it would be possible, in this system of tabulation, to produce updated bond enthalpy terms at frequent intervals. However, it was in-
352
M. F. GUEST,
J. B. PEDLEY,
AND
M. HORN
tended in this paper only to establish the principles of a possible method of handling thermochemical data. The literature search for results on substancescontaining boron was not exhaustive, nor was the assignment of reliability unambiguous; but the authors would be pleased to send full details of the reactions in the compilation to anyone interested. Information concerning any omissions or possible modifications in the data would be welcomed, and the next generation of tables would then include the new information. The authors wish to thank the Sussex University Computing Centre for facilities, and the S.R.C. for a maintenance grant (to M. F. G.). REFERENCES 1. National Bureau of Standards Circular 500, 1952 and Technical Note 270. Washington, D.C. 1965. 2. JANAF Thermochemical Tables. Thermal Research Laboratory, Dow Chemical Company, Midland, Michigan. 3. Green, J. H. S. Quart. Rev. 1961, 15, 125. 4. Mackle, H.; O’Hare, P. A. G. Tetrahedron 1963, 19, 961. 5. Hartley, S. B.; Holmes, W. S.; Jacques, J. K.; Mole, M. F.; McCoubrey, J. C. Quart. Rev. 1963, 17,204. 6. Gunn, S. R. J. Phys. Chem. 1965, 69, 1010. 7. Hawtin, P.; Lewis, J. B.; Moul, N.; Phillips, R. H. Phil. Trans. Roy. Sot. Ser. A 1966, 261, 67. 8. Cox, J. D.; Harrop, D. Trans. Faraday Sot. 1965, 61, 1328. 9. Skinner, H. A.; Pilcher, G. Quart. Rev. 1963, 17, 264.