5734 J. Phys. Chem. A 2008, 112, 5734–5741 Enthalpies of Formation of Hydrocarbons by Hydrogen Atom Counting. Theoretical Implications. Andreas A. Zavitsas, Nikita Matsunaga, and Donald W. Rogers* Department of Chemistry and Biochemistry, Long Island UniVersity, UniVersity Plaza, Brooklyn, New York 11201 ReceiVed: February 7, 2008; ReVised Manuscript ReceiVed: March 4, 2008 Standard enthalpies of formation at 298 K of unstrained alkanes, alkenes, alkynes, and alkylbenzenes can be expressed as a simple sum in which each term consists of the number of hydrogen atoms n of one of eight different types (n1-n8) multiplied by an associated coefficient (c1-c8) derived from the known enthalpy of formation of a typical molecule. Alkylbenzenes require one additive constant for each benzene ring, accounting for a possible ninth term in the sum. Terms are not needed to account for repulsive or attractive 1,3 interactions, hyperconjugation, or for protobranching, rendering them irrelevant. Conjugated eneynes and diynes show thermodynamic stabilizations much smaller than that observed for 1,3-butadiene, bringing into question the usual explanation for the thermodynamic stabilization of conjugated multiple bonds (p orbital overlap, π electron delocalization, etc.). ° ) - + - + - Introduction ∆f H (alkane) ( 3.345)n1 ( 2.490)n2 ( 1.590)n3 Certainly, there is no paucity of additive methods that 3 ° ) reproduce or predict the enthalpies of formation at 298 K, ∆fH , ∑ cini (1) of unstrained hydrocarbons to acceptable accuracy, generally t)1 within experimental error. Some are quite recent,1,2 whereas The coefficient c )-3.345 was obtained from the enthalpy others properly belong to the history of chemistry. We hope 1 of formation of 2,2-dimethylpropane,3 -40.14 kcal mol-1, that the understandably jaded reader will consider yet another divided by its 12 primary hydrogens; c2 was obtained from the method for achieving the same goal for three reasons: 3 1. The method is the simplest possible. enthalpy of formation of butane and the contribution of its six 2. The sum primary hydrogens divided by its 4 secondary hydrogens [-30.03 - (-3.345 × 6)]/4 )-2.490. The coefficient c3 was 3 9 obtained from the enthalpy of formation of 2,4-dimethylpentane ° ) and the contribution of six primary and two secondary hydrogens ∆f H ∑ cini i)1 divided by its two tertiary hydrogens [-48.30 - (-3.345 × 12) - (-2.490 × 2)]/2 )-1.590 kcal mol-1. There are many requires counting hydrogen atoms only and segregating them reference compounds that can be used in selecting parameters into eight categories. c -c (see Supporting Information for further discussion and 3.No global fitting is used. 1 9 our reasons for selecting the compounds that we did). Aside from simplicity and utility, the method offers new Alkenes. The process of counting hydrogens was extended insights into the whole process of group or bond enthalpy to unstrained and unconjugated alkenes by retaining the coef- summation. Explicit terms involving three- and four-center ficients of eq 1 for hydrogens connected to sp3 carbons and interactions are eliminated, along with hypothetical constructs that come with them, such as 1–3 attractions and repulsions, assigning values according to eq 2 for vinyl hydrogens, where hyperconjugation, and protobranching. n4 is the number of vinyl hydrogens and n5 is the number of 2 We present data for over 120 unstrained hydrocarbons in four hydrogens absent from sp carbons. classes: alkanes, alkenes, alkynes, and, by adding a term for each benzene ring, alkylbenzenes. Calculated values exhibit a 3 5 ° ) + + ) grand unsigned mean deviation from experiment of 0.37 kcal ∆f H (alkene) ∑ cini c4n4 c5n5 ∑ cini (2) ) ) mol-1. Where others find strain or conjugation energies by other i 1 i 1 methods, we find similar energies in amounts that agree with The coefficient c4 was obtained from the enthalpy of formation prior literature values. The energetic importance of conjugation of ethene,3 12.54 kcal mol-1, divided by the number of vinyl - in ene ynes is small, and for dialkynes, it is nearly zero. hydrogens, 12.54/4 ) 3.135, and c5 is from the enthalpy of 3 formation of trans-2-butene and the contributions of n1 and 2 Method n4, divided by the number of hydrogens absent from sp carbons, [-2.6 - (-3.345 × 6) - (3.135 × 2)]/2 ) 5.600. Alkanes. Enthalpies of formation of unstrained alkanes are Alkynes. Enthalpies of formation of unstrained and uncon- given by eq 1, where n is the number of primary hydrogens, 1 jugated alkynes were calculated by retaining the coefficients of n2 is the number of secondary hydrogens, and n3 is the number 3 - eq 1 for hydrogens on sp carbons and assigning coefficients of tertiary hydrogens. The units are kcal mol 1at 298 K. according to eq 3, where n6 indicates that there is at least one * To whom correspondence should be addressed. E-mail: bklynsci@ hydrogen on a triple bond (terminal alkyne) and n7 indicates aol.com. Fax: (718) 488-1465. the absence of any hydrogens on a triple bond (internal alkyne). 10.1021/jp801152t CCC: $40.75 2008 American Chemical Society Published on Web 05/30/2008 Enthalpies of Formation of Hydrocarbons J. Phys. Chem. A, Vol. 112, No. 25, 2008 5735 3 is methane. It is unique in having no carbon-carbon bonds, ° ) + + ∆f H (alkyne) ∑ cini c6n6 c7n7 (3) and it does not fit the pattern of the other alkanes. The average i)1 unsigned deviation between calculated and experimental values 3 -1 The coefficient c6 ) 54.42 was obtained from the experimental in Table 1 is 0.28 kcal mol for 36 typical unstrained alkanes ∆fH° of 1-butyne and the contributions of n1 and n2, [39.4 - and cycloalkanes. (-3.345 × 3) - (-2.490 × 2)]; similarly c7 ) 55.31 is the average Eq 1 makes no allowance for steric crowding, ring strain, or 3 of the experimental ∆f H° values of two internal alkynes, 2-butyne other “special effects.” It gives calculated values that are more and 2-pentyne, and the contributions of n1 and n2. negative than those of experimental enthalpies of formation in Alkylbenzenes. Enthalpies of formation of unstrained and such cases, indicating greater stability than actually exists. The unconjugated alkylbenzenes are given by eq 4, where n8 denotes difference between experimental enthalpies of formation and the number of aromatic hydrogens missing from the ring. The values calculated by eq 1 is a good measure of the extent of same coefficients c1-c3 were used as in eq 1. strain in the molecule, a positive value indicating strain. Table 2 shows some examples of strain energies along with literature 3 values, which were obtained by methods quite different and ∆ H°(alkylbenzene) ) ∑ c n + c n + ∆ H°(benzene) (4) f i i 8 8 f frequently much more complicated than eq 1. i)1 Alkenes. Table 3 lists ∆fH° for 39 typical unstrained alkenes ° 3 ) The coefficient c8 was obtained from ∆f H (toluene) 11.95, calculated by eq 2 along with experimental values from the ° 3 ) -1 n1, and ∆fH (benzene) 19.82 kcal mol as follows: [11.95 NIST Database No. 69,3 when available, or other sources, as - - - × ) -1 ° 19.82 ( 3.345 3)] 2.17 kcal mol . ∆fH (benzene) indicated. The average unsigned deviation between calculated is added for each benzene ring. values and 79 literature values in Table 3 is 0.48 kcal mol-1. A combination of eqs 1–4 permits estimation of conjugation Strained alkenes do not fit the pattern of eq 2 nor do alkenes stabilization in dienes, enynes, and diynes (vide infra). that are subject to the “special effect” of stabilization by conjugation. The difference between the experimental value and Results the value calculated by eq 2 is a measure of the magnitude of Alkanes. Table 1 lists ∆fH° calculated by eq 1 and experi- the effect, a positive value indicating strain and a negative value mental values from the NIST Database No. 69,3 supplemented indicating stabilization. Some typical strained alkenes are shown from other sources as indicated. Notably absent from Table 1 below the dashed line in Table 3. cis-Alkenes are more strained TABLE 1: Calculated by Equation 1 and Experimental Enthalpies of Formation of Unstrained Alkanes (kcal mol-1) a alkane n1 n2 n3 ∆fH°,eq1 ∆fH°, lit. ethane 6 0 0 -20.07 -20.04 ( 0.1 propane 6 2 0 -25.05 -25.02 ( 0.1 butane 6 4 0 -30.03 -30.03 ( 0.2 isobutaneb 901 -31.7 -32.1 ( 0.2 pentane 6 6 0 -35.0 -35.1 ( 0.1 isopentanec 921 -36.7 -36.7 ( 0.1 neopentaned 12 0 0 -40.1 -40.1 ( 0.2 cyclohexane 0 12 0 -29.9 -29.4 ( 0.2 hexane 6 8 0 -40.0 -40.0 ( 0.2 2,3-dimethylbutane 12 0 1 -41.7 -42.4 ( 0.3 2-methylpentane 9 4 1 -41.7 -41.7 ( 0.3 3-methylpentane 9 4 1 -41.7 -41.0 ( 0.2 heptane 6 10 0 -45.0 -44.9 ( 0.2 methylcyclohexane 3 10 1 -36.5 -37.0 ( 0.3 (Z)-1,2-dimethylcyclohexane 6 8 2 -43.2 -43.0 ( 0.4e ethylcyclohexane 3 12 1 -41.5 -41.1 ( 0.4 2,4-dimethylpentane 12 2 2 -48.3 -48.3 ( 0.2 octane 6 12 0 -50.0 -49.8 ( 0.2 2-methylheptane 9 8 1 -51.6 -51.5 ( 0.3 3-methylheptane 9 8 1 -51.6 -50.8 ( 0.3 4-methylheptane 9 8 1 -51.6 -50.7 ( 0.3 2,5-dimethylhexane 12 4 2 -53.3 -53.2 ( 0.4 propylcyclohexane 3 14 1 -46.5 -46.2 ( 0.3 nonane 6 14 0 -54.9 -54.5 ( 0.1e butylcyclohexane 3 16 1 -51.5 -50.9 ( 0.3 trans-decalinf 0162 -43.0 -43.5 ( 0.6 decane 6 16 0 -59.9 -59.7 ( 0.3 2-methylnonane 9 12 1 -61.6 -62.1 5-methylnonane 9 12 1 -61.6 -61.8 undecane 6 18 0 -64.9 -64.6 ( 0.3 dodecane 6 20 0 -69.9 -69.5 ( 0.3 bicyclohexylg 0202 -52.9 -52.2 ( 0.7 octylcyclohexane 3 24 1 -71.4 -70.7 ( 0.5 tetradecane 6 24 0 -79.8 -79.4 ( 0.4 hexadecane 6 28 0 -89.6 -89.6 octadecane 6 32 0 -99.7 -99.1 ( 0.6 a From ref 3, unless indicated otherwise.