Minerals Beneficiation - Hydrolytic and Ion Pair Absorption Models for Collectors in Flotation

Sutherland used an ion-pair adsorption model to derive the author's hy-drolytic pee-acid) adsorption equation for the contact bubble curves of Wark and Cox. To do so it was necessary to postulate that the sum of coverages of surface anion sites by the collector and depressant anions is practically unity. It is here shown that the free energy of Sutherland's postulated collector ion (x-)-depressant ion (OH-) exchange reaction (for no other than the OH- to compete with X-), namely EX + (OH-) Z SOH- + X-, is in some cases positive and X- should not even adsorb. Also, in many cases the (OH-) adsorption must be quite negligible even though the collector covers only about a sixth of the mineral surface at the threshold of air bubble contact. This, however, contradicts the postulate that permits one to derive the correct bubble contact eqwztion for the ion-pair model. Furthermore, the requirement for charge neutrality leads in the ion-pair model to the (impossible) constancy of the ratio @+)/(OH-) along a contact bubble curve in which pH may change by more than seven units. HYDROLYTIC ADSORPTION EQUATION Hydrolytic (free-acid or free-base) and ion-pair (H', X-, or R', OH-) adsorption models of the collector in metal sulfide and similar flotation systems are superficially alike and somewhat difficult to differentiate. This is because they yield, under seemingly valid assumptions, equivalent forms of the equations describing the distribution of the collector between the aqueous solution and the mineral surface. This has been discussed by the author and associates1-4 and more recently by Sutherland,' both for simple collector-mineral and for more complicated collector-depressant-mineral systems. In the hydrolytic adsorption model the equations describing the contact bubble curves of Wark and coxeJ7 are as follows :2 Here X is the collector anion, D- the depressant anion, 9, and On are the fractions of the free-acid sites S on the surface of the mineral covered by collector and depressant free acids, respectively, and @ is the fraction of uncovered sites. Kx is the free-acid collector dissociation equilibrium con- stant, K1 that for the free-acid collector adsorption, KD that for the free-acid depressant dissociation, and K2 the equilibrium constant for the free-acid depressant adsorption. Eqs. 1 to 5 yield upon simultaneous solution the result is the critical free-acid concentration for bubble contact in the absence of depressant-free acid. Eq. 8 expresses the conditions along a simple collector-mineral contact bubble curve for the case HD = 0, or V = 0. Last and Cook showed that Eq. 6 applies generally and with good accuracy in the collector-depressant-metal sulfide mineral systems. Inci-dentally, it has been shown by infrared absorption studies that in some cases the free-acid adsorption process splits out water.' In this case, Eq. 2 might be written SHOH + HX Z SHX + H20, with a similar equation replacing Eq. 4 for depressant-free acid-water exchange. This possibility does not change, however, the basic equations or considerations of the hydrolytic adsorption model. Indeed, this type of free acid-water exchange reaction was predicted for fluorite and iron ore flotation by oleic acid in the dry grinding and boiling processes.410