Chemical Processes - Isoconversional Kinetics of Thermally Stimulated Processes - page 208

PD H
RT

0 =− ∆ r

ln , (4.75)

where ∆ H is the enthalpy of reaction (4.73) and D is a constant. Equation 4.75 links
pressure and temperature at which all three phases, i.e., A s , B s , and C g , can coexist
in equilibrium.
A well-studied example of reversible decomposition is the thermal decomposi-
tion of calcium carbonate:

(4.76)

CaCO ⇔+ CaO O .

3(s) (s) 2(g)

A temperature dependence of the equilibrium pressure of carbon dioxide for the
decomposition of calcium carbonate [ 102 ] is presented in Fig. 4.34 . Fitting the de-
pendence to Eq. 4.75 yields the following equation:

20590

ln[ P ( Pa = )] 29 18 . − . (4.77)

0 , CO 2

T

The straight line set up by Eq. 4.77 correlates pressure and temperature at which
CaCO 3(s) , CaO (s) , and CO 2(g) are at equilibrium with each other. Above this line,
calcium carbonate remains thermally stable, whereas below it the compound would
decompose to calcium oxide and carbon dioxide. While largely simplified, this
thermodynamic model allows one to introduce an important notion of the equi-
librium temperature as the temperature, at which the equilibrium pressure of the
gaseous product rises above its partial pressure. For instance, according to the Keel-
ing curve [ 103 ], the concentration of carbon dioxide in atmospheric air has been
steadily growing over decades and currently is about 400 ppm that makes its partial
pressure at ambient conditions around 40 Pa. This is several orders of magnitude

Fig. 4.34 Temperature
dependence of the equilib-
rium pressure of CO 2 for
reaction 4.76. (Data from
Lide [ 102 ])

3D

7 .