Concise Physical Chemistry

c04 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

VA R I AT I O N O F
HWITHT 65

Hence the bond energy is the energy of the final state (the molecule) minus the

energy of the initial state (the two atoms):

E(H H)− 2 E(H·)

=− 1. 1630 −(2×− 0 .4998)=− 0. 1630 Eh=− 102 .3 kcal mol−^1 =−428 kJ mol−^1

as compared to the experimental value of−431 kJ mol−^1. The bond energy is

negative because the molecule is more stable than the isolated atoms (energy

goes downhill). Thus our first molecular orbital calculation comes to within about

1% of the experimental value. The conversions 1.0Eh=627.51 kcal mol−^1 and

1 .0 kcal mol−^1 ≡ 4 .184 kJ mol−^1 have been used. This calculation can be carried out

on much more complicated molecules, ions, and free radicals, some of which will be

described in later chapters The advent of these powerful computer programs and the

hardware to run them has made it possible to study reactions that are not accessible

by experimental means. Computational thermochemistry is an active research area at

present.

4.9 VARIATION OF
HWITHT

The definition of the heat capacity at constant pressureCp=(∂H/∂T)Pleads to the

infinitesimal enthalpy change with temperature of a pure substancedH=CPdT.

Over a reasonably short temperature interval
T, the equation
H=CP
Tis

approximately true. The heat capacity of a mixture is the sum of the molar heat

capacities of its components multiplied by the number of moles of each component

present. When a chemical reaction takes place, the number of moles of the reactants

decreases and the number of moles of products appears with different heat capacities.

The difference in heat capacities between the reactant state and the product state is

CP=

∑

CP(products)−

∑

CP(reactants)

Applying the definition ofCpto all of the component species of a chemical reaction,

we get

Cp=

(

∂
H

∂T

)

P

Selecting the hydrogenation of ethene to ethane for simplicity, experimen-

tal values (webbook.nist.gov) areCp= 42 .90 J K−^1 mol−^1 for ethene andCp=

52 .49 J K−^1 mol−^1 for ethane; and taking an experimental value (Atkins, 1994) of

Cp= 28 .87 J K−^1 mol−^1 for hydrogen, we obtain

Cp= 52. 49 − 42. 90 − 28. 87 =− 19 .28 J K−^1 mol−^1