Benson’s Group additivity of Cp is available for gases; what about for solid and liquid?

references:

“A Group Additivity Approach for the Estimation of Heat Capacities of Organic Liquids and Solids at 298 K,” Structural Chemistry 1993, 4, 261-269.

Heat Capacity Corrections to a Standard State: A Comparison of Some New and Literature Methods for Organic Liquids and Solids,” Structural Chemistry 1993, 4, 261-269.

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Application of Group Additivity to Estimate Cp(l) and Cp(c)

Protocol:

1. Group values are defined in terms of their hybridization and substitution pattern.

2. Primary, secondary, tertiary and quaternary carbons are defined in terms of the number of hydrogens attached, 3, 2, 1, 0.

3. Aromatic, aliphatic and cyclic carbons are treated separately.

4. Functional groups are treated separately.

Table I Group Values for Estimating Heat Capacities of Liquids and Solids at 298K

Group Valuesb,c

Cp(l) Cp(c)

Hydrocarbon Groups Benson Notationa

primary sp3 carbon C(H)3-(C) 34.9 36.6secondary sp3 carbon C(H)2-(C)2 31.9 26.9tertiary sp3 carbon C(H)-(C)3 22.4 9.0quaternary sp3 carbon C-(C)4 14.0 -4.98 secondary sp2 carbon Cd(H)2 25.8 [46.0]tertiary sp2 carbon Cd(H)-(C) 27.8 21.4 quaternary sp2 carbon Cd-(C)2 21.7 [6.86]tertiary sp carbon Ct(H) [34.3] [23.9]

quaternary sp carbon Ct-(C), and Ca 28.9 [15.2] tertiary aromatic sp2 carbon CB(H) 21.8 17.5quaternary aromatic sp2 carbon CBF(CB)2(CBF),

CBF(CB)(CBF)2, CB-(C) 15.3 8.49internal quaternary aromatic sp2 carbon CBFi(CBF)3 [16] [9.1] cyclic secondary sp3 carbon Cc(H)2-(Cc)2 25.9 24.6cyclic tertiary sp3 carbon Cc(H)-(Cc)2(C) 20.6 11.7cyclic quaternary sp3 carbon Cc-(Cc)2(C)2 18.0 6.1 cyclic tertiary sp2 carbon Ccd(H)-(Cc) 21.8 15.9cyclic quaternary sp2 carbon Ccd-(Cc)(C) 21.2 [4.73]

primary sp3 C

internal quaternary aromatic C

quaternary aromatic sp2 C

quaternary sp3 C

tertiary sp3 C

secondary sp2 C

tertiary sp2 C

quaternary sp2 C

tertiary sp C

quaternary sp C

CCH3

CH

CH3

CH

CH3CH3

CH2

secondary sp3 C

cyclic tertiary sp3 C

cyclic quaternary sp3 C

cyclic secondary sp3 C

cyclic tertiary sp2 C

Table II Functional Group Values for Estimating Heat Capacities of Liquids and Solids at298 K

Group ValuesbFunctional Group Benson Notationa Cp(l) Cp(c)hydroxyl (phenols) HO-(C) 53.1 23.5fluorine F-(C) 16.2 [24.8]chlorine Cl-(C) 30.8 28.7bromine Br-(C) 34.6 32.4iodines I-(C) 39.1 [27.9]nitrile NC-(C) 47.7 [42.3]carboxylic acid CO(OH)-(C) 87.4 53.1acid chloride CO(Cl)-(C) [62.8] [60.2]aldehyde CO(H)-(C) 57.7 [84.5]ketones CO-(C)2 51.5 [28.0]cyclic ketones CO-(Cc) [46.4] 34.3ester CO2-(C)2 63.2 40.3lactone CO2-(Cc)2 [67.4] [45.2]cyclic carbonates CO3-(Cc)2 [92.0] [68.2]cyclic anhydrides CO2CO-(Cc)2 [80.3] ether O-(C)2 29.8 49.8cyclic ether O-(Cc)2 24.6 9.71isocyanate OCN-(C) [58.2] [52.7]nitro group O2N-(C) [58.6] 56.1thiols HS-(C) 49.0 [51.9]primary sp3 nitrogen N(H)2-(C) 59.4 21.6secondary sp3 nitrogen N(H)-(C)2 [51.0] [-0.29]tertiary sp3 nitrogen N-(C)3 22.0 [31.5]tertiary sp2 nitrogen NI(H)-(Cd), NA(H)-(Cd) [44.4] 10.7

Table II Functional Group Values for Estimating Heat Capacities (continued) Functional Group Benson Notationa Cp(l) Cp(c)cyclic secondary sp3 nitrogenN(H)-(Cc)2 46.0 [23.9]cyclic tertiary sp3 nitrogen N-(Cc)2(C) [28.6] 1.21cyclic tertiary sp2 nitrogen Nd-(Ccd)(Cc), and

Nd-(CB)2 20.7 13.9primary amides CO(NH2)-(C) [41.0] [54.4]secondary amide CONH-(C)2 79.9 44.4tertiary amides CON-(C)3 [82.4]cyclic secondary amide CONH-(Cc)2 [92.0] 46.4cyclic tertiary amide CON-(Cc)2(C) [170] [52.7]carbamates NHCO2-(C)2 [76.1]cyclic imide NH(CO)2-(Cc)2 [74.1]mono substituted ureas NH2CONH-(C) [82.8]cyclic urea CO(NH)2-(Cc)2 [63.6]mono substituted guanidine group NH2(C=NH)NH-(C) [59.4]sulfides S-(C)2 40.3 [116]cyclic sulfides S-(Cc)2 33.8 18.2disulfides S2-(C)2 [74.5] [41.0]sulfoxides SO-(C)2 [83.7] [47.7]cyclic sulfoxides SO-(Cc)2 [31]sulfones SO2-(C)2 [52.4]cyclic sulfones SO2-(Cc)2 [38.7]sulfonamides SO2NH2-(C) [104]quaternary silicon Si-(C*)4 30.9 33.1tertiary aluminum Al-(C*)3 [46.9]quaternary tin Sn-(C*)4 [58.6] [77.4]quaternary germanium Ge-(C*)4 [48.1] [3.85]phosphine oxide PO-(C*)3 [28.5]aNI and NA refer to imino and azo nitrogens, respectively.bvalues in brackets are considered as tentative assignments only.cdue to insufficient experimental data, only the parameters listed in Table I can besubstituted for a C*.

Calculate the heat capacity of [2.2] spiropentane at T = 298.15 K.

Cp = quat sp3 C +4 sec sp3

Cp(l) = 18 + 4(25.9) = 121.6 J mol-1K-1

Cp(c) = 6.1 + 4(24.6) = 104.5 J mol-1K-1

Experimental value

Cp(l) = 134.5 J mol-1K-1

When are Cp(l) and Cp(c) values useful?

Hf (l)(T )

Hf (g)(T )

Hv (l)(T )

Hf (l)(298 K)

Hf (g)(298 K)

Hv (l)(298 K)

Cp (l)T

Cp (g)T

Hf (c)(T )

Hf (g)(T )

Hs (l)(T )

Hf (c)(298 K)

Hf (g)(298 K)

Hs (l)(298 K)

Cp (c)T

Cp (g)T

Suppose you measured Hv(325 K) of spiropentane and you wanted to correct the number to T = 298.15 K. How would you do it?

What do you do in the case where the group value or correction is not available?

1. Find data to identify a group value.

2. Look for another approach.

Calculated Cp(l) / J mol-1 K-1

0 200 400 600 800 1000 1200

Exp

erim

enta

l C

p(l)

- C

p(g)

/ J

mol

-1 K

-1

0

50

100

150

200

250

300

350

400

At T = 298.15 K

[Cp(l) - Cp(g)]expt = 10.26 + 0.26 Cp(l)calc(298)

Calculated Cp(c) /J mol-1 K-1

0 200 400 600 800 1000 1200

Exp

erim

enta

l Cp(

c) -

Cp(

g) /

J m

ol-1

K-1

-50

0

50

100

150

200

250

At T = 298.15 K

[Cp(c) - Cp(g)]expt = 0.71 + 0.15 Cp(c)calc(298)

Hf (c)(Tfus )

Hf (l)

Hfus (Tfus )

Hf (c)(298 K)

Hf (l)(298 K)

Hfus (298 K)

Cp (c)T

Cp (l)T (Tfus )

Hfus(298) = Cp(c) [Tfus-298] + Hfus(Tfus) + Cp(l)[298-T]

Hfus(298) = Hfus(Tfus) + [Cp(c) - Cp(l)][Tfus-298]

[Cp(l) - Cp(g)]expt = 10.26 + 0.26 Cp(l)calc (1)

[Cp(c) - Cp(g)]expt = 0.71 + 0.15 Cp(c)calc (2)

Eq (2) - Eq (1) =

[Cp(c) - Cp(l) ] = [0.15 Cp(c) - 0.26 Cp(l) - 9.83] (3)

Hfus(298) = Hfus(Tfus) + [Cp(c) - Cp(l)][Tfus-298]

Hfus(298)=Hfus(Tfus)+[0.15Cp(c) - 0.26Cp(l)-9.83][Tfus-298]

How accurate are eq. (1), (2), and (3)?

95 % confidence level = 2 standard deviations

For eq. (1): 30 J mol-1 K-1

For eq. (2): 1/3 the correction

Suppose you measured Hv(325 K) of spiropentane and you wanted to correct the number to T = 298.15 K. How would you do it?

Hv(298 K) = Hv(325 K) +[10.58 +.26Cp(l)][325-298]

Cp(l) = 14 + 4(31.9) = 141.6 J mol-1K-1

Hv(298 K) = Hv(325 K) +[4100 J mol-1]