Mutual Equilibrium Research Articles

Carbonate equilibria in the open ocean and their bearing on the interpretation of ancient carbonate rocks

A model of steady-state equilibrium deposition of carbonates in the open sea, where exchange of material between the sediment and the water is permitted, is studied from the phase-equilibrium point of view. Allowing for the possibility of arbitrary variations in temperature, pressure and activity of CO 2 in the system, in general only one-carbonate deposits, either calcite or dolomite, should result. The contact between calcite beds and dolomite beds should be sharp although the two carbonates should be in mutual equilibrium. Changes in hydrographie conditions may result in onlap-offlap relations in the deposits and apparent interbedding of the strata. Experimental results in the literature on the solubility of dolomite in water are not all internally consistent, although they do indicate that, under atmospheric conditions, the solution relations are sensitive to the value of the CO 2 activity. Increases in total pressure (depth) favour the precipitation of dolomite. Available thermochemical data indicate that dolomite may be the carbonate phase in equilibrium with many sea-water compositions. Modern carbonate deposits are either calcite or aragonite at the surface, but may change over, abruptly, to dolomite at depth. Two-carbonate deposits, where carefully studied, show evidence of incomplete reaction. The prevalence of one-carbonate deposits thus accord with theoretical considerations although the nature of the surface deposit is at variance with thermochemical data. In the sedimentary record, carbonate rocks with nearly equal amounts of calcite and dolomite are not uncommon; these beds cannot be due to direct chemical precipitation in the open sea.

Energy Transfer from Differentiation in a Differential Pressure System under Non-Equilibrium Conditions: A Discussion of "Partial Quantities"

If a rock whose minerals are in mutual equilibrium at hydrostatic pressure and given temperature is affected by additional pressure differences, then free-energy gradients are created parallel to the pressure gradients. Provided diffusion is a permissible process in the system, the high-pressure regions will then function as sources and the low-pressure, or tension, regions will function as sinks for fluxes of matter which tend to iron out the free-energy differences. These diffusive flows of matter also generally carry heat from highto low-pressure sites. (Compare the Dufour effect in diffusion through homogeneous phases [Denbigh, 1951, p. 9]). These elementary thermodynamic and kinetic principles were applied to petrogenesis in 1944 by the author and have since then attracted in-

Sedimentation and electrophoresis of interacting substances. I. Idealized boundary shape for a single substance aggregating reversibly

The effect of differential transport on the gradient of concentration across a boundary is calculated for a substance existing in solution as a series of aggregates in mutual equilibrium. General equations are derived which are then used to construct schlieren patterns for a model system in order to illustrate the types of pattern to which aggregation can give rise. It is shown that in electrophoresis experiments the boundary in one limb is diffuse, and in the other hyper-sharp. In sedimentation the boundary is diffuse in general, but may have a hypersharp leading edge if there is a strong dependence o f the sedimentation velocity of the individual species on solute concentration. Although it is not possible for true resolution to occur at the boundary of a system in which equilibrium is maintained, the shapes of the schlieren patterns of the diffuse boundaries can be such as to give the impression that partial resolution is occurring. It means then that aggregates composed of more than two molecules are present and that at least one type of higher aggregate is strongly accentuated.

Ternary liquid equilibria systems:n‐propanol‐water‐esters

AbstractMutual solubility and tie‐line data are presented for five ternary‐liquid systems containingn‐propanol, water and the estersn‐propyl acetate,n‐butyl acetate, amyl acetate, ethyl propionate and ethyl butyrate. Equilibrium distribution data for the systemn‐propanol‐water‐ethyl acetate at 20° reported in the literature have been plotted for comparison on the mutual solubility and equilibrium distribution diagrams. The tie‐line data for all the systems are correlated well by the methods of Hand and Othmer‐Tobias and the plait points are located by the method of Treybalet al.From the equilibrium distribution diagram, it is seen that in all the above systems,n‐propanol prefers the ester layer unlike methanol which favours the aqueous phase. Esters seem to be better suited for the extraction ofn‐propanol than of methanol from water.

Ternary liquid equilibria: Systems: acetone - water - esters

Mutual solubility and tie-line data are presented for six ternary liquid-liquid systems containing acetone, water, and the esters methyl acetate, ethyl acetate, propyl acetate, amyl acetate, ethyl propionate and ethyl butyrate at 30°C. For comparison, equilibrium data for the system acetone—water— n-butyl acetate reported in literature has been plotted on the mutual solubility, equilibrium distribution and selectivity diagrams. The tie-line data for the six systems have been correlated satisfactorily by the methods of H and and O thmer and T obias and the plait points are located by the method of T reybal, W eber and D aley. From the comparative plot of the distribution of acetone between the ester and aqueous layers for the various systems, it is found that acetone favours the ester layer in all the cases. The system, propyl acetate—acetone-water is observed to exhibit solutropy. Among the various esters studied, amyl acetate is observed to be the most selective of all the solvents.