Out of equilibrium with the

In this chapter we consider the problem of the kinetics of the heterogeneous reactions by which minerals dissolve and precipitate. This topic has received a considerable amount of attention in geochemistry, primarily because of the slow rates at which many minerals react and the resulting tendency of waters, especially at low temperature, to be out of equilibrium with the minerals they contact. We first discuss how rate laws for heterogeneous reactions can be integrated into reaction models and then calculate some simple kinetic reaction paths. In Chapter 26, we explore a number of examples in which we apply heterogeneous kinetics to problems of geochemical interest. 

Observations from deep-water sediment traps have demonstrated that PIC is present in waters that are undersaturated with respect to this mineral. Thus, thermodynamic considerations are not a perfect predictor of the presence of PIC. In other words, some PIC is present out of equilibrium with the seawater it is in. This is largely a result of kinetics in which dissolution is slow enough to enable PIC to persist for some time. Much effort has been applied to determining the factors that control the rate of PIC dissolution. Marine scientists have reached agreement that the rate law for CaC03 dissolution in undersaturated waters (H < 1) can be represented as ... 

The most exotic materials in CP IDPs are particles of glass with embedded metal and sulfides, identified by the acronym GEMS (Fig. 12.8d). Although GEMS are commonly described as having chondritic bulk compositions, that description applies only for aggregates of these submicron particles. The nanometer-sized FeNi metal (kamacite) inclusions and pyrrhotite are clearly out of equilibrium with the magnesium-rich silicate... 

Slopes (mr) of these plots derived from ambient air sampling data are often different from the expected value of -1 (Equation 8) possibly because of kinetic limitations and/or sampling artifacts or thermodynamic factors (Pankow and Bidleman, 1992). Goss and Schwartzenbach (1998) and Simcik et al. (1998) argued that slopes differing from -1 do not necessarily mean that the aerosols are out of equilibrium with the gas phase. In these situations, the intercept (br) partly depends on the slope and cannot be used to estimate 0 (Pankow and Bidleman, 1992). Table 10.2 lists reported values of these parameters. 

We turn to Figure 6.2, which shows a specific mass, let us say 1 mol, of air that is out of equilibrium with the environment only with respect to its temperature T, which has been chosen to be larger than T0, the temperature of the environment. As has been shown before in this chapter, Equation 6.11, thermodynamics allows us to calculate the minimum amount of work required to bring this mass out of equilibrium with the environment Weired Weired... 

Physical exergy out of equilibrium with the environment in temperature. 

Laage, Burghardt Hynes present and discuss analytic dielectric continuum nonequilibrium solvation treatments of chemical reactions in solution involving conical intersections. Their analysis shows that theories of the rates of mechanisms of the chemical reaction in solution have to incorporate the fact that the solvent can be out of equilibrium with the instantaneous charge distribution of the reacting solutes(s). 

These discrepancies could be due to experimental problems in the measurement of the potentials, or to the existence of micro-circuits out of equilibrium with the bulk phases. These would possess a significant resistance between the localized proton circuit and the bulk phase. The respiratory chain would see the localized... 

As described above, if this electrochemical reaction is driven out of equilibrium with the thermodynamic force ry, a current / will flow. One of the great successes of electrochemistry is its ability to provide a quantitative description of the charge transfer current characteristics. Max Volmer (1885—1965) and John Alfred Valentine Butler (1899—1977) proposed the following relation, which is known today as the Butler—Volmer equation, between the over potential 7j and the current density j (Fig. 3.4) ... 

This process is irreversible because the reverse process is not the exact opposite of the forward process. This is because the gas is out of equilibrium with the surroundings (that is, Pext P) during the expansion (compression). 

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