Dissociation Ionization Constants of Weak Acids

The latter reaction can form long chain phosphates, where n is theoretically infinite. Being formed by heat treatments, these phosphates are excellent candidates for high-temperature ceramics and glasses. Because the subject of this volume is low-temperature ceramics, we will not discuss the condensed phosphates in detail, except in one case in Chapter 15, where cements for geothermal wells are discussed with sodium metaphosphate. However, bear in mind that CBPCs can be precursors to high temperature phosphates and glasses. For this reason, as we have seen in the literamre survey presented in Chapter 3, early interest in CBPCs was the formation of refractory shapes at room temperature, which were then fired to produce the final refractory components. 

Strong acids and bases react violently and produce heat and, hence, are not very useful in forming CBCs. Therefore, in the entire study of CBPCs, we will be dealing with phosphoric acid, which is a weak acid in that it dissolves in water slowly compared with strong acids such as hydrochloric acid. Acid phosphates such as KH2PO4 and A1(H2P04)3 and weak bases such as oxides of Mg and A1 dissolve slowly in water. To represent how slowly the weak acids or bases dissolve in water and to what extent, the term dissociation (ionization) constant is used. 

Dissociation constants, which are chemical equilibrium constants for dissolution of acids, are defined in a manner similar to the definition of pH in the case of water. As discussed before, a weak acid such as H3PO4 goes through step-by-step ionization in water given by Eqs. 4.7-4.9. In each step, the dissociation constant is experimentally found to be 

Note that, as customary, we have assumed that 1 mol of the acid is selected for the dissolution in each case. 

Similar analyses can be carried out for acidic or alkaline salts that are weakly soluble. One may define a dissociation constant, pK o, for a dissociation reaction of a dihydrogen phosphate of a w-valent metal, given by 

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