CHAPTER 7 – Pressure Effect on Equilibrium Reactions

Pressure Acting on Homogeneous Equilibria

Pressure Acting on Heterogeneous Equilibria


Pressure Acting on Homogeneous Equilibria

The effect of pressure on equilibrium constants is of paramount importance; sinking down into the depths of the oceans, pressure increases by 1 atm with every 10 meters. As the intermolecular distances between water molecules decrease slightly, the density of liquid water increases accordingly. Therefore, interionic interaction and equilibrium constants become progressively altered in relation to the pressure itself. The effects become noticeable when pressure reaches hundreds of bars; pH and solubility of calcium carbonate alter to such an extent that aragonite oversaturation, and calcite at greater depths, disappear and, if formed, these salt readily re-dissolve.

As discussed in Section 4.4 on water density, we recall that water pressure is measured in 'bars' (1 atm = 1.01325 bar; 1 bar = 0.1 Mpa), and that the surface pressure of the sea is assumed to be zero.

The effect of pressure on equilibrium constants can be calculated (Millero 1995) according to a second order polynomial expression of the natural logarithm of the ratio between Ki,P (the value of i-esimal constant at pressure P) and Ki,0 (the value of i-esimal constant at reference zero pressure P)

The constant value R1 is given by R1 = 83.131 cm3 bar mol-1 K-1, whereas ΔVi is the molal volume change, and Δki the compressibility change. They are in turn deconvoluted in terms of a second order polynomial which, strictly speaking, is only valid for Salinity = 35.

ΔVi = a0 + a1·Tc + a2·Tc2

Δki = b0 + b1·Tc + b2·Tc2

The values for the a and b parameters are taken from Millero 1979 and Millero 1995 and are reported here for each of the reactions, where Tc indicates the temperature in °C, P the pressure in bar, and T the absolute temperature (T = Tc + 273.15) and finally R1 = 83.131. In the formulas, LnKi,0 indicates the natural logarithm of Ki at P=0, while LnKi,P the natural logarithm of the same equilibrium constants at pressure P>0(in bars). The same applies for every equilibrium constant. Fig... resumes all the expressions used.

The effect of pressure alters the values for every equilibrium constant, and must therefore be properly accounted for in the program flow. Greater detail on this will be given in Chapter 8

In the appendix, code 002.bas is the general routine for the complete and simultaneous set of calculations. It can be simply downloaded from my web-site ( and is ready to run. It requires a text file input (SeaWaterCalc.txt) from which all starting parameters are read, but the reader is strongly recommended to read the lines and the comments related to the pressure effects.

Pressure Acting on Heterogeneous Equilibria

Generally speaking, in heterogeneous reactions, reactants are in different phases, like solids, liquid solutions or gaseous mixtures. One of the most relevant of such reactions is the formation or dissolution of calcium carbonate (solid/solution), according to its oversaturation value, indicated by Ω and discussed in Section 6.5.

Once formed biologically by calcifying organisms or by inorganic route, and with a density greater than 1, it eventually sinks into the dark abyss. Due to increasingly high pressure, solid CaCO3 begins to dissolve below a certain depth, referred to as the saturation horizon where Ω is exactly equal to 1. Dissolution of the solid is not instantaneous, and the downward flux continues to a depth where the solid particles of calcium carbonate are completely dissolved. This depth is called the carbonate compensation depth. If the sea bottom does not reach such a depth, it becomes undissolved carbonate sediment. The two crystallographic forms of CaCO3, calcite and aragonite, have different solubility products, the former being less soluble. Therefore, the saturation horizon and the compensation depth for aragonite are at a higher level compared to calcite. Most calcifying organisms (e.g. Coccolithophores) produce calcite, whilst coral reefs are made of aragonite.

Solving the equilibria involved in CaCO3 formation with the algorithm described in the preceding sections of this book, (whose usage will be comprehensively described in Chapter 8) the oversaturation profiles at different depths can be calculated. Some of the results can be seen in the graph in Fig. 7.1. The curious reader, intent on modifying input parameters and looking for new results (in a “see what happens” procedure) is directed to Chapter 8.

Fig. 1 Oversaturation for calcite at different ppmCO
2 versus pressure

In Fig. 1 oversaturation Ω, is plotted against pressure being temperature fixed at 4°C, which is the overall temperature for the ocean's depths below the thermocline (about 300 meters). The four colored curves correspond to four concentrations of CO2 values (red = 280 pre-industrial value; cyan = 345; blue = 410 present day value; green = 475 ppm). The full line indicates calcite and the dashed line, aragonite. Below Ω=1 (light blue area) carbonates begin their dissolution process.

One topic frequently debated today is the potential hazard for coralline reefs of the rising concentrations of CO2, through the reduction of ocean pH and carbonate ion concentration. The effect of this, evident from Fig.2. is however compensated for by an increase in oversaturation in warmer areas of oceans, where calcifying organisms and coral reefs prosper. Global warming, estimated at about 1°C from the beginning of the twentieth century to the present day, also favours oversaturation and thereby counteracts the effects of increasing CO2 content by anthropogenic emissions. Therefore the two figures... should be considered together to gain a complete picture.

Fig. 7.2 Oversaturation for calcite at 1 atm. versus temperature of seawater