Page 64 - Chemical equilibria Volume 4

40 Chemical Equilibria
By way of example, we shall examine the search for independent
reactions in a system containing the following species:
– Gas: NH 3;
+
+
-
-
+
2+
– Aqueous solution: Ag , Cl +, H 3O , OH , NH4 , [Ag 2(NH 3) 3] , H 2O,
NH 3(aqu);
– Solid: AgCl.
Let us write the weak-acid–weak-base equilibria within the solution:
+
−
HO + OH = 2H O
3
2
+
+
2+
+
+
3H O 2Ag + 3NH = Ag (NH ) + 3H O
2
3 3
3
4
2
+
NH + H O = NH (aqu + 3 +
) H O
3
4
2
We verify the independence of these three equilibrium states. Indeed, on
the basis of the matrix of the algebraic stoichiometric coefficients, which is
written as:
− 1 − 1 2 0 0 0 0
3 0 − 3 − 2 − 3 1 0
0 − 1 0 0 − 1 0 1
we can deduce a non-null determinant of rank 3 (Jouguet criterion), such as:
− 1 − 1 2
3
3 0 −= ≠
4 0
0 − 1 0
In addition, we can verify that any other reaction written solely with
components of the solution can be deduced from the above three equilibria.
Such is the case, for instance, with the reaction:

+
+
3NH (aqu ) 2Ag = Ag (NH ) 2+
3
2
3 3