Reaction path model buffering

As we discussed in 6.2, the samples from the monitoring wells at the Bear Creek Uranium site are observed to fall into four fairly well defined pH zones (Figure 6.2). Compositional zones such as this are often produced by mineral buffering of the solutions. This process can be illustrated by using reaction path modeling. 

Fig. 2.1. Schematic diagram of a reaction model. The heart of the model is the equilibrium system, which contains an aqueous fluid and, optionally, one or more minerals. The system s constituents remain in chemical equilibrium throughout the calculation. Transfer of mass into or out of the system and variation in temperature drive the system to a series of new equilibria over the course of the reaction path. The system s composition may be buffered by equilibrium with an external gas reservoir, such as the atmosphere.

In this chapter we consider how to construct reaction models that are somewhat more sophisticated than those discussed in the previous chapter, including reaction paths over which temperature varies and those in which species activities and gas fugacities are buffered. The latter cases involve the transfer of mass between the equilibrium system and an external buffer. Mass transfer in these cases occurs at rates implicit in solving the governing equations, rather than at rates set explicitly by the modeler. In Chapter 16 we consider the use of kinetic rate laws, a final method for defining mass transfer in reaction models. 

Sliding activity and sliding fugacity paths are similar to fixed activity and fixed fugacity paths, except that the model varies the buffered activity or fugacity over the reaction path rather than holding it constant. Once the equilibrium state of the initial system is known, the model stores the initial activity a° or initial fugacity / / of the buffered species or gas. (The modeler could set this value as a constraint on the initial system, but this is not necessary.)... 

In fixed and sliding fugacity paths, the model transfers gas into and out of an external buffer to obtain the fugacity desired at each step along the path (see Chapter 12). The increment Anr is the change in the total mole number Mm of the gas component as it passes to and from the buffer (see Chapter 3). When gas passes from buffer to system (A ,. is positive), it is probably most logical to take its isotopic composition as the value in equilibrium with the initial system, at the start of the reaction path. Gas passing from system to buffer (i.e., Anr is... 

Busch et al. studied the applicability of CZE to the examination of hapten-antibody complex formation (11). The catalytic antibodies examined have been used to accelerate a Diels-Alder reaction. Association constants of two hapten-antibody complexes were investigated and compared to the ELISA method. The samples contained buffer, hapten, and antibody. The constants obtained with CZE are a factor of 3-5 larger than those found with the ELISA method. The free-hapten concentration is measured directly this allows confirmation of the stoichiometric model. Because of the poor concentration sensitivity of UV detection, the application of an extended optical path length such as a bubble cell is necessary to obtain reliable binding parameters. 

Rates of reduction were followed spectrometrically using a Hitachi model 220A spectrophotometer. The increase of reduced cytochrome c was followed at 550nm. All rates were determined using 3ml quartz cells with a 1cm light path, under anaerobic conditions. The reaction were carried out in pH 7.0( 0.01) phosphate buffer solutions at 25 C, and initiated by addition of 3-CD-NAH dissolved in DMF. All reagent were purchased from commercial suppliers and were used without further purification. 

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