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Chapter 4 Exercise
Material Equilibrium
Write the phase-equilibrium conditions for a crystal of NaCl in equilibrium with
an aqueous solution of NaCl. (Answer: m s m aq .)
NaCl NaCl

4.8 REACTION EQUILIBRIUM
We now apply the material-equilibrium condition to reaction equilibrium. Let the re-
action be
aA bA . . . S eA fA m 1 . . . (4.92)
1
2
m
where A , A , . . . are the reactants, A , A , . . . are the products, and a, b, . . ., e, f, ...
1 2 m m 1
are the coefficients. For example, for the reaction
2C H 15O S 12CO 6H O
6
6
2
2
2
A C H , A O , A CO , A H O and a 2, b 15, e 12, f 6. The sub-
1 6 6 2 2 3 2 4 2
stances in the reaction (4.92) need not all occur in the same phase, since the material-
equilibrium condition applies to several-phase systems.
We adopt the convention of transposing the reactants in (4.92) to the right side of
the equation to get
0 S aA bA . . . eA fA m 1 . . . (4.93)
2
1
m
We now let
n a, n b, . . . , n e, n m 1 f, . . .
1
m
2
and write (4.93) as
0 S n A n A . . . n A n m 1 A m 1 . . .
m
m
2
1
2
1
0 S a n A i (4.94)
i
i
where the stoichiometric numbers n (nu i) are negative for reactants and positive
i
for products. For example, the reaction 2C H 15O → 12CO 6H O becomes
6 6 2 2 2
0 → 2C H 15O 12CO 6H O, and the stoichiometric numbers are n
6 6 2 2 2 C 6 H 6
2, n 15, n 12, and n 6. The stoichiometric numbers (also called
O 2 CO 2 H 2 O
stoichiometric coefficients) are pure numbers with no units.
During a chemical reaction, the change n in the number of moles of each sub-
stance is proportional to its stoichiometric number n, where the proportionality con-
stant is the same for all species. This proportionality constant is called the extent of
reaction j (xi). For example, in the reaction N 3H → 2NH , suppose that 20
2 2 3
mol of N reacts. Then 60 mol of H will have reacted, and 40 mol of NH will have been
2 2 3
formed. We have n 20 mol 1(20 mol), n 60 mol 3(20 mol),
N 2 H 2
n 40 mol 2(20 mol), where the numbers 1, 3, and 2 are the stoichiomet-
NH 3
ric numbers. The extent of reaction here is j 20 mol. If x moles of N reacts, then
2
3x moles of H will react and 2x moles of NH will be formed; here j x mol and
2 3
n x mol, n 3x mol, n 2x mol.
N 2 H 2 NH 3
For the general chemical reaction 0 → n A [Eq. (4.94)] undergoing a definite
i i i
amount of reaction, the change in moles of species i, n , equals n multiplied by the
i i
proportionality constant j:
¢n n n n j (4.95)*
i,0
i
i
i