Adventures in Thermochemistry James S. Chickos * Department of Chemistry and Biochemistry University of Missouri-St. Louis Louis MO Eads Bridge

Based on the behavior observed in the melting temperatures of homologous series, we wondered how boiling temperatures varied as a function of size?

The plot of the boiling temperatures of the n-alkanes as a function of the number of repeat units. Number of repeat units, n TBTB Question: How do the boiling temperatures of the n-alkanes vary as a function of the number of repeat units?

Modeling boiling temperature Exponential functions have previously been used to model the behavior observed for the n-alkanes. 1. Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem , Partington, J. An Advanced Treatise on Physical Chemistry, Vol II, Properties of Liquids, Longmans, Green Co.: N. Y., 1949, p 301. Is there any basis for expecting the boiling temperature of an infinite alkane to be finite? M = molecular weight; , b = constants 1 T B = 138 C 1/2 ; C = number of carbons 2

A plot of  l g H m (T B ) versus  l g S m (T B ) at T = T B for the following: n-alkanes (C 3 to C 20 ): circles, n-alkylcyclopentanes (C 7 to C 21 ): triangles, n-alkylcyclohexanes (C 8 to C 24 ): squares.  l g S m (T B ) / J mol -1 K -1  l g H m (T B ) / J mol -1

If the relationship between  l g H m (T B ) and  l g S m (T B ) can be expressed in the form of an equation of a straight line:  l g H m (T B ) = m  l g S m (T B ) + C (1) Since at the boiling temperature,  l g G m (T B ) = 0;  l g S m (T B ) =  l g H m (T B )/T B Therefore  l g H m (T B ) = m  l g H m (T B )/ T B +C Solving for T B : T B = m  l g H m (T B )/(  l g H m (T B ) - C) (2) This is an equation of a hyperbola As  l g H m (T B )   ; T B  m

The Correlation Equations Obtained by Plotting  l g H m (T B ) Versus  l g S m (T B ) n-alkanes  l g H m (T B ) = (  22.6)  l g S m (T B ) – (  350); r 2 = n 1-alkenes  l g H m (T B ) = (  109.7)  l g S m (T B ) – (  951); r 2 = n-alkylbenzenes  l g H m (T B ) = (  37.3)  l g S m (T B ) – (  296); r 2 = n-alkylcyclopentanes  l g H m (T B ) = (  97.4)  l g S m (T B ) – (  926); r 2 = n-alkylcyclohexanes  l g H m (T B ) = (  87.3)  l g S m (T B ) – (  999); r 2 = n-alkanethiols  l g H m (T B ) = (  162.6)  l g S m (T B ) – (  1728); r 2 = T B (  ) ~ 3000 K

If T B approaches 3000 K in an ascending hyperbolic fashion, then a plot of 1/[1 – T B /T B (  )] versus n, the number of repeat units, should result in a straight line.

squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes A plot of 1/[1- T B /T B (  )] versus the number of methylene groups using a value of T B (  ) = 3000 K.

Use of T B (  ) = 3000 K did not result in straight lines as expected. Therefore: T B (  ) was treated as a variable and allowed to vary in  5 K increments until the best straight line was obtained by using a non-linear least squares program resulting in the following.

squares: phenylalkanes hexagons: alkylcyclopentanes circles: n-alkanes triangles: 1-alkenes 1/[1- T B /T B (  )] = aN + b

The Results Obtained by Treating T B of a Series of Homologous Compounds as Function of the Number of Repeat Units, N, and Allowing T B (  ) to Vary; a Bm, b Bm : Values of a B and b B Obtained by Using the Mean Value of T B (  ) = 1217 K Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkanes methyl-n-alkanes alkenes n-alkylcyclopentanes n-alkylcyclohexanes n-alkylbenzenes amino-n-alkanes chloro-n-alkanes bromo-n-alkanes fluoro-n-alkanes hydroxy-n-alkanes hydroxy-n-alkanes n-alkanals alkanones Using T B (  ) avg = 1217 K

Polyethylene Series T B (  )/K a B b B  /K a Bm b Bm  /K data points n-alkane-1-thiols n-dialkyl disulfides n-alkylnitriles n-alkanoic acids methyl n-alkanoates Mean Value of T B (  ) = (1217  246) K The results for T B (  ) for polyethylene are remarkably constant considering the use of data with finite values of n to evaluate T B (n) for n (  ). These results are also in good agreement with the values reported previously for the n-alkanes by Kreglewski and Zwolinski (T B (  ) = 1078 K), Somayajulu (T B (  ) = 1021 K), Stiel and Thodos ((T B (  ) = 1209) K. Kreglewski, A.; Zwolinski, B. J. J. Phys. Chem , Somayajulu, G. R. Internat. J. Thermophys. 1990, 11, Stiel, L. T.; Thodos, G. AIChE. J. 1962, 8,

A value of T B (  ) = (1217  246) K is considerably less than T B (  ) = 3000 K, the value obtained by assuming that  l g H m (T B )   as T B  . Why is T B (  ) = (1217  246) K, not ~3000 K? From the plot of  l g H m (T B ) vs  l g S m (T B ), shown earlier: T B = m  l g H m (T B )/(  l g H m (T B ) - C) Rearranging and solving for  l g H m (T B ) max using T B (  ) = 1217 results in:  l g H m (T B ) max = C (T B (  ))/(m - T B (  ))  l g H m (T B ) max =  18.5 kJ mol -1 A limiting value of  18.5 kJ mol -1 for  l g H m (T B ) max at T B is predicted where C and m are from plots of  l g H m (T B ) vs  l g H m (T B ) A limiting value for  l g H m (T B ) max suggests that this property may also be modeled effectively by a hyperbolic function

A plot of 1/[1-  l g H m (T B )/  l g H m (T B ) max ] against the number of repeat units, n 1-alkenes: circles n-alkylcyclohexanes: squares using a value of 154 kJ mol -1 for  l g H m (T B ) max.. Data from: Wilhoit, R. C.; Zwolinski B. J. Handbook of Vapor Pressures and Heats of Vaporization of Hydrocarbons and Related Compounds. TRC, Texas A&M Univ. College Station TX

Values of the Parameters of a H and b H Generated in Fitting  l g H m (T B ) of Several Homologous Series Using a Value of  l g H m (T B ) max =  18.5 kJ mol -1. a H b H  /kJ. mol -1 data points n-alkanes n-alkylbenzenes n-alkylcyclohexanes n-alkylcyclopentanes n-alk-1-enes n-alkane-1-thiols

At this point it might be useful to ponder why vaporization enthalpies may approach a limiting value. Consider what vaporization enthalpies measure: intermolecular forces As the size of a flexible molecule increases, what trend would be expected in the ratio of intermolecular/intramolecular interactions? In the limiting case, for a flexible molecule the ratio between intermolecular/intramolecular interactions might be expected to go as the ratio of the surface area of a sphere to its volume: 4  r 2 /4/3  r 3 ~ 1/r

Why do all of the series related to polyethylene converge to a value for  l g H m (T B ) max =  18.5 kJ mol -1 ?

Ambroses’ Equation T C = T B + T B /[c + d(n+2)] where c and d are constants and n refers to the number of methylene groups. This equation suggests that T C  T B as n  . Ambrose, D. "NPL Report Chemistry 92" (National Physical Laboratory, Teddington, Middlesex UK, 1978). How do critical temperatures of homologous series vary with n?

A plot of experimental critical temperatures versus n, the number of methylene groups for (from top to bottom): alkanoic acids: hexagons, 2-alkanones: diamonds, 1-alkanols: solid circles, 1-alkenes: triangles, and n-alkanes: circles. Experimental Critical Temperatures

According to Ambroses’ equation and the previous plots, the critical temperatures of series related to polyethylene appear to behave in an ascending hyperbolic fashion. This suggests that a plot of 1/[1- T C /T C (  )] versus the number of methylene groups n should also be a linear function provided a suitable value of T C (  ) was used. Treating T C (  ) as a variable in ± 5 K increments, a non linear least squares fit the data resulted in the following:

Number of CH 2 groups 1/[1-T c /T c (  )]  carboxylic acids  2-alkanones  n-alkanes

Results Obtained for the Constants a C and b C by plotting 1/[1-T C (n)/ T C (  ) as a Function of the Number of Repeat Units, N, and Allowing T C (  ) to Vary; a Cm, b Cm : Values of a C and b C Obtained by Using the Mean Value of T C = 1217 K Polyethylene data Series T C (  )/K a C b C  /K T C (  )/K a Cm  b Cm  /K points n-alkanes n-alkanals alkanoic acids alkanols alkanones alkanones alkenes methylalkanes

A plot of experimental critical temperatures versus n, the number of methylene groups for (from top to bottom): alkanoic acids: hexagons, 2-alkanones: diamonds, 1-alkanols: solid circles, 1-alkenes: triangles, and n-alkanes: circles. The lines were calculated using T C (  ) = 1217 K. Critical Temperatures vs n

What are the consequences if T B (  ) = T C (  )?

At T C,  l g H m (T C ) = 0 This explains why  l g H m (T B ) fails to continue to increase but may infact decrease as the size of the molecule get larger. What does  l g H m (T B ) measure? If vaporization enthalpies are a measure of intermolecular interactions, as the size of the molecule get larger, the ratio of intermolecular/intramolecular interactions  0 as n  .

Are there any additional consequences if T B (  ) = T C (  )? Since T B is the normal boiling temperature, If T C (  ) = T B (  ), then in the limit, P C (  ) = P B (  ) = kPa; 0.1 MPa. The critical pressure should decrease with increasing n asympotically approaching 0.1MPa as n  . Therefore a plot of 1/[1- P C (  )/P C (n)] versus n using P C (  ) = 0.1 MPa should result in a straight line.

n, number of CH 2 groups 1/[1-P c /P c (  )] A Plot of 1/[1-P c (  ) /P c ] vs n for carboxylic acids 1/[1-Pc (  ) /Pc] vs n

.A plot of the critical pressure versus the number of repeat units for the 1-alkanols: triangles, n-alkanes: circles, 2-methylalkanes: squares Critical Pressures vs n

What about other series?

How about the fluorocarbons?

n, number of CF 2 groups T B /K symbols: experimental T B / K lines: calculated T B / K circles: prefluoroalkanes squares: perfluorocarboxylic acids Boiling Temperatures Versus the Number of CF 2 Groups

Table 7. Values of the Parameters of a B and b B Generated in Fitting T B of Several Homologous Perfluorinated Series Using Equation 3 and Allowing T B (  ) to Vary in 5 K Increments; a Bm, b Bm : Values of a B and b B Using an Average Value of T B (  ) = 915 K T B = T B (  )[1-1/(1-a B N + b B )] (3) T B (  )/Ka B b B  /K T B (  )/K a Bm b Bm  /KN n-perfluoroalkanes n-perfluoroalkanoic acids methyl n-perfluoroalkanoates iodo-n-perfluoroalkanes

n, number of CF 2 groups T C /K symbols: experimental T C / K lines: calculated T C / K using T C = 915 K for the n- perfluoroalkanoic acids Critical Temperatures Versus the Number of CF 2 Groups

A plot of the critical pressure versus the number of repeat units using P C (  ) = (MPa) n, number of CF 2 groups Perfluoroalkanes P C (MPa)

Conclusions: 1. Boiling temperatures appear to converge to a finite limit. 2.Vaporization enthalpies are predicted to approach a limiting value and then decrease as the size of the homologous series increases. 3.Critical temperature and boiling temperatures appear to converge as a function of the number of repeat units. 4.Critical pressures appear to converge to some finite pressure (~1 atm) as the number of repeat units  . Can any of this be experimentally verified?