Rate chemical affinity

The fourth explanation for non-linear kinetics differs from the previous three in that it concerns the composition of the solution rather than any intrinsic property of the solid reactants or products. Changing solution composition can produce apparent or true parabolic dissolution kinetics either through the influence of changing pH and COj equilibria, or through the effect of chemical affinity and the reverse reaction rate. These phenomena have been discussed in detail by Helgeson and Murphy (V7) and Helgeson and others ( 1 8). 

For the purposes of this review, the key concept embedded in equation (1) is the chemical affinity term, which is expressed as 1 — Q/K. The chemical affinity of a system is related to the free energy of the reaction and is a measure of the degree of departure from equilibrium (i.e.,/(AG) = 1 — Q/K). The form of the chemical affinity term indicates that as the concentrations of dissolved elements build up in solution, the system approaches saturation in a rate-limiting solid and the overall dissolution reaction slows down, and, at equilibrium, the rate would be zero. In the case of glass dissolution, there are many circumstances, which are reviewed below, where the rate behaviour does not comply with these expectations. 

Over the last 20 years investigators have reported that predpitation of secondary phases can accelerate the corrosion rate of glass. This is because predpitation can cause a sudden drop in the activity of a key aqueous species. In other words, we hypothesize that the rate is affected through the chemical affinity of the system. 

Another difficulty presented by precipitation of secondary phases is that other aqueous species, such as those of Al, can be affected, as stated above. Under certain conditions the activity of Al(OH)4 in mildly alkaline solutions can drop to near zero due to precipitation of zeolite phases. The question is how to represent this change in aluminate activity using a rate equation based on chemical affinity concepts. For example, in equation (1), the activity of the... 

If the aluminate ion is a component in the chemical affinity term, then the activity of dissolved silica, by itself, cannot describe the change in rate with changes in chemistry of the contacting fluid. A number of attempts have been made to explicitly include Al activity in the chemical affinity term. Gin (1996) suggested that glass dissolution could be modelled using a mixed Si/Al term for the ion activity product ((2) ... 

Because adsorption isotherms are equilibrium equations, the rate at which the material is adsorbed has to be studied in terms of chemical affinities, pH, solubility, hydrophobicity, and many other physical and chemical characteristics. 

Solution Composition. Changing solution composition can also cause apparent or true parabolic dissolution kinetics through the influence of changing pH and C02 equilibria or through an effect on chemical affinity and reverse rate (Helgeson et al., 1984). 

The rate of lost work as a function of the chemical affinity (in dimensionless units see text). The solid line is Equation 4.37, whereas the dashed-dotted line is the parabolic asymptote for small A/RT0 and the dotted line is the linear asymptote for large A/RT0. 

Equations 4.42 and 4.43 present a possible explanation for the frequent occurrence in biochemical networks of sequential reactions with many steps n. For an overall reduced (dimensionless) chemical affinity of, let us say, A/RT0 = 5, the dimensionless chemical reaction rate vch/v is, according to Figure 4.3, close to 1, and the dimensionless lost work rate is the product 5 x 1 = 5, as shown in Figure 4.4. In Figure 4.3, this product is represented by the area left of the vertical axis at (A/RT0) = 5. 

However, if the total affinity A is spread over, let us say, n = 10 reaction steps, then each individual reaction step corresponds, on average, to a reduced chemical affinity of 0.1A/RT0 = 0.5, with a reduced chemical velocity of 0.4, according to Figure 4.3. So, the same chemical "distance" is now covered with a much smaller velocity and the corresponding lost work rate has been reduced accordingly. Point C in Figure 4.5. shows the reduced lost work per step, and Point C the total lost work for the multistep reaction. Point C in... 

The rate of lost work as a function of the chemical affinity (in dimensionless units see text). 

Feb. 22,1879, Varde, Denmark - Dec. 17,1947, Copenhagen, Denmark) Ph.D. Copenhagen 1908, since 1908 Professor of Chemistry (the 3rd chair, i.e., the chair of Physical Chemistry at the Univ. of Copenhagen). 1926/27 visiting Professor at Yale Univ., New Haven, Connecticut, USA. Famous for his work on chemical reaction kinetics, chemical affinity, indicators, and thermodynamics of solutions. He could explain the effect of activity coefficients on reaction rates in solutions. In 1923 he developed independently of - Lowry, and - Bjerrum a new -> acid-base theory, the so-called Bronsted acid-base theory. 

Mass flow, heat flow, and chemical reaction rate are some examples of the flows J,. The thermodynamic forces A of the chemical potential gradient, temperature gradients, and the chemical affinity cause the flows. The affinity A is... 

In a nonviscous fluid, where / chemical reactions take place, the dissipation functions are limited to the scalar chemical affinities A and chemical rates JT... 

If we expand the expression in brackets, and consider the case of a near-equilibrium state, which may be specified by the inequality Aj RT 1, then we have a linear relationship between the reaction rate and the chemical affinity... 

One of the conventional methods for establishing the existence of active transport is to analyze the effects of metabolic inhibitors. The second is to correlate the level or rate of metabolism with the extent of ion flow or the concentration ratio between the interior and exterior of cells. The third is to measure the current needed in a short-circuited system having similar solutions on each side of the membrane the measured flows contribute to the short-circuited current. Any net flows detected should be due to active transport, since the electrochemical gradients of all ions are zero (Ai// = 0, cD = c,). Experiments indicate that the level of sodium ions within the cells is low in comparison with potassium ions. The generalized force of chemical affinity shows the distance from equilibrium of the /th reaction... 

Gautier, J. M., Oelkers, E. H. Schott, J. (1994). Experimental study of K-feldspar dissolution rates as a function of chemical affinity at 150 °C and pH-9. Geochimica et Cosmochimica Acta, 58, 4549-60. 

This example illustrates the fundamental principle that if one describes coupled reactions in terms of a set of linearly independent steps, then sufficiently close to equilibrium the reaction rates may be described in terms of phenomenological equations involving the chemical affinities as driving forces. 

Thus, the rate of entropy production in a chemical stoichiometric trans formation is proportional to the product of the process driving force (chemical affinity of the reactions) and the reaction rate. At the same time, it is obvious that the rate of an elementary process ij is, by definition, the flux of the parameter chemical variable y d... 

This helps to establish a relationship between a purely thermodynamic parameter of the conjugate process—its chemical affinity—and the most important kinetic characteristic of the process—the reaction rate. The magnitude of ratio v 2Ar 2/vi iAr i can be treated as the energetic... 

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