Thermodynamics and Chemistry

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES

11.3 MOLARREACTIONENTHALPY 320

system is independent of the path and is equal to the sum ofÅHvalues for any sequence
of changes whose net result is the given change. (We may apply the same principle to a
change ofanystate function.)
For example, the following combustion reactions can be carried out experimentally in a
bomb calorimeter (Sec.11.5.2), yielding the values shown below of standard molar reaction
enthalpies (atTD298:15K,pDpD 1 bar):

C(s, graphite)CO 2 (g)!CO 2 .g/ ÅrHD393:51kJ mol^1

CO(g)C^12 O 2 (g)!CO 2 .g/ ÅrHD282:98kJ mol^1

(Note that the first reaction, in addition to being the combustion reaction of graphite, is
also the formation reaction of carbon dioxide.) The change resulting from the first reaction
followed by the reverse of the second reaction is the formation reaction of carbon monoxide:

C(s, graphite)C^12 O 2 (g)! CO(g)

It would not be practical to measure the molar enthalpy of this last reaction by allowing
graphite to react with oxygen in a calorimeter, because it would be difficult to prevent the
formation of some CO 2. From Hess’s law, the standard molar enthalpy of formation of CO
is the sum of the standard molar enthalpies of the reactions that have the formation reaction
as the net result:

ÅfH(CO, g,298:15K)D.393:51C282:98/kJ mol^1

D110:53kJ mol^1 (11.3.2)

This value is one of the many standard molar enthalpies of formation to be found in
compilations of thermodynamic properties of individual substances, such as the table in
AppendixH. We may use the tabulated values to evaluate the standard molar reaction en-
thalpyÅrHof a reaction using a formula based on Hess’s law. Imagine the reaction to take
place in two steps: First each reactant in its standard state changes to the constituent ele-
ments in their reference states (the reverse of a formation reaction), and then these elements
form the products in their standard states. The resulting formula is

ÅrHD

X

i

iÅfH.i/ (11.3.3)

(Hess’s law)

whereÅfH.i/is the standard molar enthalpy of formation of substancei. Recall that the
stoichiometric numberiof each reactant is negative and that of each product is positive, so
according to Hess’s law the standard molar reaction enthalpy is the sum of the standard mo-
lar enthalpies of formation of the products minus the sum of the standard molar enthalpies
of formation of the reactants. Each term is multiplied by the appropriate stoichiometric
coefficient from the reaction equation.
A standard molar enthalpy of formation can be defined for asolute in solutionto use in
Eq.11.3.3. For instance, the formation reaction of aqueous sucrose is

12 C(s, graphite)C11 H 2 (g)C^112 O 2 (g)!C 12 H 22 O 11 (aq)

andÅfHfor C 12 H 22 O 11 (aq) is the enthalpy change per amount of sucrose formed when
the reactants and product are in their standard states. Note that this formation reaction does