Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

FINDING (^) fH^298 OF METHANOL 335
If we knew the energy released when C, O, and H atoms are formed from their
subatomic particles, and the energy released when an appropriate number of C, O,
and H atoms combine to form C(graphite), O 2 (g), and H 2 (g), all in the standard state
at 0 K, we could find the energy of formation of CH 3 OH(g) at 0 K.
C(gr)+^12 O 2 (g)+2H 2 (g)→CH 3 OH(g)
(^) fH^298 (methanol)=H^298 (methanol(g))
−

[

H^298 (C(gr))+^12 H^298 (O 2 (g))+ 2 H^298 (H 2 (g))

]

The numbers in square brackets have been established both by computation and by

experiment. They are shown at the left of Fig. 20.7.

There are six downward steps shown on the left of Fig. 20.7. Three are large steps

given in hartrees. Their sum –114.78647Ehrepresents the addition of a requisite

number of electrons to a carbon nucleus, four hydrogen nuclei, and an oxygen

nucleus to produce the gaseous atoms C, H, and O. The bottom three steps on the

left represent the enthalpy in kcal mol−^1 obtained when a mole of C atoms, two

moles of H 2 molecules, and^12 mole of O 2 molecules, all in their standard states,

are formed from the gaseous atoms. The elements in their standard states have an

enthalpyH^298 =− 115. 471973 Ehat the short solid line.

The enthalpy change from nuclei and electrons to the methanol molecule in its

standard state is given by the long vertical line on the right-hand side of Fig. 20.7.

The difference between the calculated enthalpy of the molecule in the standard state

and that of the composite elements in their standard states is the enthalpy difference

we seek, (^) fH^298. Thus the whole argument depends on the length of the vertical line
on the right-hand side of Fig. 20.7. Notice that (^) fH^298 has the opposite sign from
-37.78934 h
4(-.50184) h
-74.98977 h
-169.73
4(-50.62)
-57.95
H^298 (methanol)
FIGURE 20.7 The G3(MP2) thermochemical cycle for determination of (^) fH^298 of
methanol. Step sizes are not to scale. Values not designated h (hartrees) are in units of
kcal mol−^1.