Equilibrium equilibrium concentration

Multimedia models can describe the distribution of a chemical between environmental compartments in a state of equilibrium. Equilibrium concentrations in different environmental compartments following the release of defined quantities of pollutant may be estimated by using distribution coefficients such as and H s (see Section 3.1). An alternative approach is to use fugacity (f) as a descriptor of chemical quantity (Mackay 1991). Fugacity has been defined as fhe fendency of a chemical to escape from one phase to another, and has the same units as pressure. When a chemical reaches equilibrium in a multimedia system, all phases should have the same fugacity. It is usually linearly related to concentration (C) as follows ... 

Water and methanol can form strong hydrogen bonds in solutions. These kinds of solvent-solvent interactions have a pronounced effect in the NIR spectral region. For example, in pure methanol solutions it is possible to have dimers, trimers, and other intermolecular hydrogen-bonded species in equilibrium. Equilibrium concentrations of these species are very sensitive to impurity concentrations and temperature changes. 

Position of the dissociation (ionization) equilibrium Equilibrium concentration of H compared with original concentration of HA Strength of conjugate base compared with that of water... 

However, when carboxylic acids are present in a mixture, fugacity coefficients must be calculated using the chemical theory. Chemical theory leads to a fugacity coefficient dependent on true equilibrium concentrations, as shown by Equation (3-13). ... 

Irreversible adsorption discussed in Section XI-3 poses a paradox. Consider, for example, curve 1 of Fig. XI-8, and for a particular system let the equilibrium concentration be 0.025 g/lOO cm, corresponding to a coverage, 6 of about 0.5. If the adsorption is irreversible, no desorption would occur on a small dilution on the other hand, more adsorption would occur if the concentration were increased. If adsorption is possible but not desorption, why does the adsorption stop at 6 = 0.5 instead of continuing up to 0 = 1 Comment on this paradox and on possible explanations. 

With equilibrium concentrations the (small) deviation from equilibrium is given by... 

Figure B2.5.7 shows the absorption traces of the methyl radical absorption as a fiinction of tune. At the time resolution considered, the appearance of CFt is practically instantaneous. Subsequently, CFl disappears by recombination (equation B2.5.28). At temperatures below 1500 K, the equilibrium concentration of CFt is negligible compared witli (left-hand trace) the recombination is complete. At temperatures above 1500 K (right-hand trace) the equilibrium concentration of CFt is appreciable, and thus the teclmique allows the detennination of botli the equilibrium constant and the recombination rate [54, M]. This experiment resolved a famous controversy on the temperature dependence of the recombination rate of methyl radicals. Wliile standard RRKM theories [, ] predicted an increase of the high-pressure recombination rate coefficient /r (7) by a factor of 10-30 between 300 K and 1400 K, the statistical-adiabatic-chaunel model predicts a...

The ortho- and meto-isomers are bulkier than the para-iaomer and diffuse less readily in the zeolite pores. The transport restriction favours their conversion into the /lara-isomer, which is fonned in excess of the equilibrium concentration. Because the selectivity is transport influenced, it is dependent on the path length for transport, which is the length of the zeolite crystallites. 

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

The distributions of excess, or injected, carriers are indicated in band diagrams by so-called quasi-Fenni levels for electrons or holes (Afp). These functions describe steady state concentrations of excess carriers in the same fonn as the equilibrium concentration. In equilibrium we have... 

If the equilibrium concentrations for A, B and C are a, b and c, respectively, the concentration changes resulting from the application of the perturbation will be... 

The equilibrium constant K, the rate constants and and the dependences of all these quantities on temperature were determined. In the absence of added acetic acid, the conversion of nitric acid into acetyl nitrate is almost quantitative. Therefore, to obtain at equilibrium a concentration of free nitric acid sufficiently high for accurate analysis, media were studied which contained appreciable concentrations (c. 4 mol 1 ) of acetic acid. 

These equations, relating to oi,s, and E t,g to Egy, show that 3od can be calculated for a reaction proceeding through the equilibrium concentration of a free base if the thermodynamic quantities relating to the ionisation of the base, and the appropriate acidity function and its temperature coefficient are known (or alternatively, if the ionisation ratio and its temperature coefficient are known under the appropriate conditions for the base. )... 

Because of these difficulties, special mechanisms were proposed for the 4-nitrations of 2,6-lutidine i-oxide and quinoline i-oxide, and for the nitration of the weakly basic anilines.However, recent remeasurements of the temperature coefficient of Hq, and use of the new values in the above calculations reconciles experimental and calculated activation parameters and so removes difficulties in the way of accepting the mechanisms of nitration as involving the very small equilibrium concentrations of the free bases. Despite this resolution of the difficulty some problems about these reactions do remain, especially when the very short life times of the molecules of unprotonated amines in nitration solutions are considered... 

For the nitration of the very weak base, acetophenone, there is reasonable agreement between observed and calculated activation parameters, and there is no doubt that nitration of the free base occurs at acidities below that of maximum rate. In this case the equilibrium concentration of free base is much greater than in the examples just discussed and there is no question of reaction upon encounter. ... 

Since the first-order rate constant for nitration is proportional to y, the equilibrium concentration of nitronium ion, the above equations show the way in which the rate constant will vary with x, the stoichiometric concentration of dinitrogen tetroxide, in the two media. An adequate fit between theory and experiment was thus obtained. A significant feature of this analysis is that the weak anticatalysis in pure nitric acid, and the substantially stronger anticatalysis in partly aqueous nitric acid, do not require separate interpretations, as have been given for the similar observations concerning nitration in organic solvents. 

Substituting the equilibrium concentrations into the solubility product expression (equation 6.33)... 

How might we solve equation 6.34 if we do not have access to a computer One possibility is that we can apply our understanding of chemistry to simpKfy the algebra. From Le Chatelier s principle, we expect that the large initial concentration of Pb will significantly decrease the solubility of Pb(I03)2. In this case we can reasonably expect the equiKbrium concentration of Pb to be very close to its initial concentration thus, the following approximation for the equilibrium concentration of Pb seems reasonable... 

Before accepting this answer, we check to see if our approximation was reasonable. In this case the approximation 0.10 -l-x 0.10 seems reasonable since the difference between the two values is negligible. The equilibrium concentrations of Pb3+ and IO3-, therefore, are... 

Letting x equal the change in the concentration of Pb +, the equilibrium concentrations are... 

Chaston, S. Calculating Complex Equilibrium Concentrations by a Next Guess Factor Method, /. Chem. Educ. 1993, 70, 622-624. 

The solubility of AgCl, therefore, is the sum of the equilibrium concentrations for all soluble forms of Ag+. 

Substituting the equilibrium constant expressions for reactions 8.3-8.S into equation 8.6 defines the solubility of AgCl in terms of the equilibrium concentration of Ch. 

Clearly the equilibrium concentration of chloride is an important parameter if the concentration of silver is to be determined gravimetrically by precipitating AgCl. In particular, a large excess of chloride must be avoided. 

Equation 8.7 shows how the solubility of AgCl varies as a function of the equilibrium concentration of Ch. Derive a similar equation to describe the solubility of AgCl as a function of the equilibrium concentration of Ag+. Graph the resulting solubility function and compare it with that shown in Figure 8.1. 

To determine the equilibrium constant s value, we prepare a solution in which the reaction exists in a state of equilibrium and determine the equilibrium concentration of H3O+, HIn, and Im. The concentration of H3O+ is easily determined by measuring... 

Protonic acids dissociate to some extent in the nonaqueous reaction mixtures to produce an equilibrium concentration of protons ... 

At equilibrium, these concentration and pressure effects must be equal and opposite for Eq. (8.75) to apply. Equation (8.13) describes the concentration dependence of jui, and Eq. (8.12) describes the pressure effect. Assembling these results, we write... 

Fig. 15. Correlation of effective average slope m of nonisothermal equilibrium line (concentrated part of absorber) equilibrium line concave downward. The...

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