Water equilibrium calculations

The occurrence of arsenic in source waters (and particularly groundwater) can be rationalized by examining the mechanisms of arsenic release from the aquifer solids to the contacting water. Equilibrium calculations provide a constraint on arsenic concentrations that may be expected for water in contact with various solids but slow kinetics (e.g., of dissolution) may result in significant discrepancies between predicted and observed concentrations of dissolved arsenic. 

Conformational free energy simulations are being widely used in modeling of complex molecular systems [1]. Recent examples of applications include study of torsions in n-butane [2] and peptide sidechains [3, 4], as well as aggregation of methane [5] and a helix bundle protein in water [6]. Calculating free energy differences between molecular states is valuable because they are observable thermodynamic quantities, related to equilibrium constants and... 

Weak acid An acid that is only partially dissociated to H+ ions in water, 81 calculation of [H+] in, 363-366 calculation of [OH-] in, 369-370 equilibrium constants, 359-367, 378-379q, 638... 

The experimental value of Kb for ammonia in water at 25°C is 1.8 X I(T5. This small value tells us that normally only a small proportion of the NH molecules are present as NH4+. Equilibrium calculations show that only about 1 in 100 molecules are protonated in a typical solution (Fig. 10.16). In general, the basicity constant for a base B in water is... 

Even in relatively concentrated solutions, the mole fraction of water remains close to 1.00. At a solute concentration of 0.50 M, for example, H2 O = 0.99, only 1% different from 1.00. Equilibrium calculations are seldom accurate to better than 5%, so this small deviation from 1.00 can be neglected. Consequently, we treat solvent water just like a pure substance its concentration is essentially invariant, so it is omitted from the equilibrium constant expression. 

For any aqueous strong base, the hydroxide ion concentration can be calculated directly from the overall solution molarity. As is the case for aqueous strong acids, the hydronium and hydroxide ion concentrations are linked through the water equilibrium, as shown by Example. ... 

For this example, we summarize the first four steps of the method The problem asks for the concentration of ions. Sodium hydroxide is a strong base that dissolves in water to generate Na cations and OH- anions quantitatively. The concentration of hydroxide ion equals the concentration of the base. The water equilibrium links the concentrations of OH" and H3 O" ", so an equilibrium calculation is required to determine the concentration of hydronium ion. What remains is to organize the data, carry out the calculations, and check for reasonableness. 

To convert from pH to ion concentrations, first apply Equation to calculate [H3 O ]. pH = - log [H3 O J Then make use of the water equilibrium to calculate [OH ]. 

After completing our analysis of the effects of the dominant equilibrium, we may need to consider the effects of other equilibria. The calculation of [H3 O ] in a solution of weak base illustrates circumstances where this secondary consideration is necessary. Here, the dominant equilibrium does not include the species, H3 O, whose concentration we wish to know. In such cases, we must turn to an equilibrium expression that has the species of interest as a product. The reactants should be species that are involved in the dominant equilibrium, because the concentrations of these species are determined by the dominant equilibrium. We can use these concentrations as the initial concentrations for our calculations based on secondary equilibria. Look again at Example for another application of this idea. In that example, the dominant equilibrium is the reaction between hypochlorite anions and water molecules H2 0 l) + OCr(c2 q) HOCl((2 q) + OH ((2 q) Working with this equilibrium, we can determine the concentrations of OCl, HOCl, and OH. To find the concentration of hydronium ions, however, we must invoke a second equilibrium, the water equilibrium 2 H2 0(/) H3 O (a q) + OH (a q)... 

Vapor-liquid equilibrium data and calculated values for the dietlnia-mine-water system. Calculations were done using parameters from unconstrained LS estimation [reprinted from Computers < Chemical Engineering with permission from Elsevier Science /. 

Chen B, Xing JH, Siepmann JI (2000) Development of polarizable water force fields for phase equilibrium calculations. J Phys Chem B 104(10) 2391—2401... 

The amount of lead that remains in solution in surface waters depends upon the pH of the water and the dissolved salt content. Equilibrium calculations show that at pH >5.4, the total solubility of lead is approximately 30 pg/L in hard water and approximately 500 pg/L in soft water. Sulfate ions, if present... 

Since the components in the adsorbed polyelectrolyte layer are considered to be the same as the bulk phase with a three component system which consists of polyelectrolyte, simple salt, and water, we calculate the adsorbances of polyelectrolyte and salt by assuming the Donnan equilibrium between the bulk phase and the adsorbed polyelectrolyte layer, as described previously (5). 

As an example of an equilibrium calculation accounting for surface complexation, we consider the sorption of mercury, lead, and sulfate onto hydrous ferric oxide at pH 4 and 8. We use ferric hydroxide [Fe(OH)3] precipitate from the LLNL database to represent in the calculation hydrous ferric oxide (FeOOH /1H2O). Following Dzombak and Morel (1990), we assume a sorbing surface area of 600 m2 g-1 and site densities for the weakly and strongly binding sites, respectively, of 0.2 and 0.005 mol (mol FeOOH)-1. We choose a system containing 1 kg of solvent water (the default) in contact with 1 g of ferric hydroxide. 

Predictions of high explosive detonation based on the new approach yield excellent results. A similar theory for ionic species model43 compares very well with MD simulations. Nevertheless, high explosive chemical equilibrium calculations that include ionization are beyond the current abilities of the Cheetah code, because of the presence of multiple minima in the free energy surface. Such calculations will require additional algorithmic developments. In addition, the possibility of partial ionization, suggested by first principles simulations of water discussed below, also needs to be added to the Cheetah code framework. 

PAH PAN PBN PCT PES PHREEQC PIC PM PMATCHC PM-10 PM-2.5 PRB PUREX PW PWR PZC Polycyclic aromatic hydrocarbon Peroxyacetylnitrate Peroxybenzoylnitrate Product consistency test Plasma emission spectroscopy pH redox equilibrium calculations (computer program) Product of incomplete combustion Particulate matter Program to manage thermochemical data, written in C++ Particulate matter with an aerodynamic diameter <10 p,m Particulate matter with an aerodynamic diameter <2.5 p,m Powder River Basin Pu-U-recovery-extraction Purex waste Pressurized water reactor Point of zero charge... 

At intermediate concentrations of 10"6 to 10"8 M, the effects of water ionization and the added acid or base are comparable. Only in this region is a systematic equilibrium calculation necessary. 

Equilibrium calculations suggested that Hg complexation varies greatly among redox and pH levels typical of the regions of lakes sampled during this study. In an oxic lake, pore water, and groundwater, Hg complexation with organic matter most likely dominates. Under anoxic conditions in the hypolimnion and pore waters, Hg most likely forms soluble bisulfide and polysulfide complexes. 

Reduced forms of sulfur, such as sulfide and thiols, also react rapidly with Mn02 (26-28) as well as with FeOx. However, sulfur in fresh water is often present in substoichiometric amounts with respect to iron. Thus little or no free reduced S is present even under strongly anoxic conditions because of the formation of very insoluble FeS x species. Our equilibrium calculations (29) indicate that complexation with reduced sulfur species is not a quantitatively important aspect of Mn speciation in Lake Richard B. Russell (RBR). However, this result does not rule out the occurrence of such species as transient intermediates. 

Some limitations of the equilibrium model of sea water do exist. Sillen has pointed out that based on equilibrium calculations all the nitrogen in the ocean-atmosphere system should be present as N03 in sea water however, most of the nitrogen is present as Nj gas in the atmosphere. Also, the concentrations of the major alkaline earth elements. Mg, Ca, and Sr, in sea water may vary slightly with depth or geographic location. 

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