If there is no experimental data available, are there any other methods of estimating thermochemical data?

Group Additivity

ab initio calculations

molecular mechanics calculations

Reasons for the Development of Estimation Techniques

1. To provide a value for the property when no experimental values are available

2. To provide a means of distinguishing between two or more discordant experimental values.

3. The parameters generated by the estimation technique may provide a handle to measure or understand some molecular property that can not be measured directly.

4. As a diagnostic tool to identify and sometimes quantify unusual interactions.

Question: Can thermochemical properties be subdivided into small increments so that the total molecular property in question can be calculated from the sum of its parts?

1. How small can the increments be?

2. Are these group increments interchangable so that they can be used to calculate similar properties of distinctively different molecules?

3. What properties are subject to this treatment?

Some Thermochemical properties that have been modeled by group additivity

1. Molecular weight

2. Atomic weight

3. Enthalpy of formation

4. Entropy of formation

4. Enthalpy of vaporization

5. Total phase change entropy

6. Heat capacity

7. Vapor pressure

Bond additivity

1. Bond Additivity: An assignment of a value associated with each type of bond.

Group additivity

2. Values are associated with a series of atom combinations is various structural environments.

Butane

C3H8 Hf(298) = 8 C-H + 2C-C

Hf(298) = [8(-3.83) + 2(2.73)]4.184

= -105.4 kJ mol-1

Hf(298)expt = -104.6 kJ mol-1

Bond Additivity

Butadiene

CH2=CH-CH=CH2

Hf(298) = 6 Cd-H + Cd-C

Hf(298) = [6(3.2) + 6.7]*4.184 = 109.4 kJ mol-1

Hf(298)expt = 110 kJ mol-1

Bond Additivity

Styrene

Hf(298) = 5 -H + -C +3 Cd-H

Hf(298) = 4.184[5(3.25) + 7.25 + 3(3.2)]

Hf(298) = 138.5 kJ mol-1

Hf(298)expt = 147.9 kJ mol-1

Bond Additivity

Benson’s Group Additivity

Values are assigned to groups based on their constitution and on their neighboring environment

Styrene

Hf(298) = 5 CB-(H) + CB-(Cd) + Cd-(Cd)(H)+ Cd-(H2)

Hf(298) = 4.184[5(3.3) + 5.68 + 6.78 + 6.26]

Hf(298) = 147.4 kJ mol-1

Hf(298)expt = 147.9 kJ mol-1

Group Additivity

Group Additivity

Butane

Hf(298) = 2 C-(H)3(C) + 2 C-(H)2(C)2

Hf(298) = 4.184[2(-10.2) +2(-4.93)]

Hf(298) = -126.6

Hf(298)expt = -125.5

Group Additivity

CyclobutaneHf(298) = 4 C-(H)2(C)2

Hf(298) = 4.184[4(-4.93)] = -82.5

Hf(298)expt = 28.4

Hf(298) = -82.5-28.4 = -111 kJ mol-1

CH2CH2

-CH2CH2CH2CH2- vs | | CH2CH2

Hf(298) = strain energy in cyclobutane

Cp(g)

Calculation of heat capacity follows the same rules as enthalpy.

What is the heat capacity of 2-methylhexane?

Cp(g)(298) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3

Cp(g)(298) = 4.184[3(6.19) + 3(5.5) +4.54]

Cp(g)(298) = 165.7 J mol-1K-1

Entropy: (S(298)(g)

The calculation of entropy follows the same rules as for enthalpy and heat capacity but has two additional corrections.

Correction terms: (1) symmetry (-Rln)

(2) mixing (-Riniln(ni))

where ni refers to the mol fraction and is the symmetry number. The symmetry number is the number of identical structures that can be obtained by a symmetry operation such as rotation.

What is the entropy of 2-methylhexane?

S(298) (g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections

S(298) (g) = 4.184[3(30.41)+3(9.42)-12.07] + corrections

S(298) (g) = 449.4

corrections = -3Rln(3) =-27.4

S(298) (g) = 449.4 - 27.4 = 422 J mol-1 K-1

S(298) (l)expt = 314.6, 315.1, 323.3

S(298) (g)

S(298)(g) = S(298)(l) + Cp(l)lnTB/298) + Hv/TB +Cp(g)ln(298/TB)

S(298)(l) = S(298)(g) - [Cp(l)lnTB/298) + Hv/TB+Cp(g)ln(298/TB)]

S(298)(l) = 422 -[222.9ln(363/298)+34900/363+165.7ln(298/363)]

S(298)(l) = 314.6 J mol-1K-1

S(298) (l)expt = 314.6, 315.1, 323.3

S(298) (l) TB=363 K; Cp(l)=222.9J mol-1K-1; Hv= 34.9 J mol-1K-1

What is the entropy of 3-methylhexane?

S(298) (g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections

S(298) (g) = 4.184[3(30.41)+3(9.42)-12.07] + corrections

S(298) (g) = 449.4

corrections = -3Rln(3) =-27.4; +Rln(2)

S(298) (g) = 449.4 - 27.4 +5.76 = 427 J mol-1 K-1

S(298) (l)expt = 309.6

S(298) (l) TB=364 K; Cp(l)=216.7J mol-1K-1; Hv= 35.1 J mol-1K-1

S(298)(g) = S(298)(l) + Cp(l)lnTB/298) + Hv/TB +Cp(g)ln(298/TB)

S(298)(l) = S(298)(g) - [Cp(l)lnTB/298) + Hv/TB+Cp(g)ln(298/TB)]

S(298)(l) = 427 -[216.7ln(364/298)+35100/364+165.7ln(298/364)]

S(298)(l) = 320.4 J mol-1K-1

S(298) (l)expt = 309.6 J mol-1K-1

What is the enthalpy of formation of 3-methylhexane?

Hf(298)(g) = 3 C-(H)3C+3 C-(H)2(C)2 +C-(H)(C)3 + corrections

Hf(298)(g) = 4.184[3(-10.2)+3(-4.93)-1.9] + corrections

Hf(298)(g) = -197.9 + corrections

correction = 0.8*4.184

Hf(298)(g) = -194.5 kJ mol-1

Hf(298)(g)expt = -191.3 1.3

H CH3

CH3

CH2

H2C

CH3

H H

1 gauche interaction

Summary on Using Benson Group Values

1. Identify the groups: Hf, Cp, S

2. Add non-bonded interactions: Hf, Cp, S

3. Add symmetry and chirality considerations: S