Bases solution equilibrium calculations

The following example shows how this can be modeled in PHREEQC. First of all, a master- ami a solution species tritium T or T1 have to be defined. Since the input of data for log k und -gamma within the key word SOLUTION SPECIES is required, but unknown, any value can be entered here as a free parameter ( dummy , e g. 0.0). This value is not used for kinetic calculations and thus, does not cause any problems. However, all results based on equilibrium calculations (e.g. the calculation of the saturation index) are nonsense for this species . The tritium values have to be entered in tritium units. However, in order not to have to define or convert them in an extra step, they are entered fictitiously with the unit umol/kgw instead of TU in PHREEQC. As no interactions of tritium with any other species are defined, the unit is eventually irrelevant. After modeling, remember that the result is displayed in mol/kgw as always in PHREEQC and has to be recalculated to the fictitious tritium unit umol/kgw. Entering mol/kgw in the input file, the solution algorithm quits due to problems with too high total ionic strengths. 

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

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... 

Examples through illustrate the two main types of equilibrium calculations as they apply to solutions of acids and bases. Notice that the techniques are the same as those introduced in Chapter 16 and applied to weak acids in Examples and. We can calculate values of equilibrium constants from a knowledge of concentrations at equilibrium (Examples and), and we can calculate equilibrium concentrations from a knowledge of equilibrium constants and initial concentrations (Examples, and ). 

However, as already noted, the barite content in Kuroko ore inversely correlates to the quartz content and the occurrences of barite and quartz in the submarine hydrothermal ore deposits are different. The discrepancy between the results of thermochemical equilibrium calculations based on the mixing model and the mode of occurrences of barite and quartz in the submarine hydrothermal ore deposits clearly indicate that barite and quartz precipitated from supersaturated solutions under non-equilibrium conditions. Thus, it is considered that the flow rate and precipitation kinetics affect the precipitations of barite and quartz. 

New NH3/NH4+ buffer When 0.142 mol per liter of HC1 is added to the original buffer presented in (a), it reacts with the base component of the buffer, NH3, to form more of the acid component, NH4+ (the conjugate acid of NH3). Since HC1 is in the gaseous phase, there is no total volume change. A new buffer solution is created with a slightly more acidic pH. In this type of problem, always perform the acid-base limiting reactant problem first, then the equilibrium calculation. 

An important advance in the understanding of the chemical behaviour of glasses in aqueous solution was made in 1977, when Paul (1977) published a theoretical model for the various processes based on the calculation of the standard free energy (AG ) and equilibrium constants for the reactions of the components with water. This model successfully predicted many of the empirically derived phenomena described above, such as the increased durability resulting from the addition of small amounts of CaO to the glass, and forms the basis for our current understanding of the kinetic and thermodynamic behaviour of glass in aqueous media. 

The common-ion effect is an application of Le Chatelicr s principle to equilibrium systems of slightly soluble salts. A buffer is a solution that resists a change in pH if we add an acid or base. We can calculate the pH of a buffer using the Henderson-Hasselbalch equation. We use titrations to determine the concentration of an acid or base solution. We can represent solubility equilibria by the solubility product constant expression, Ksp. We can use the concepts associated with weak acids and bases to calculate the pH at any point during a titration. 

Schiff s base formation occurs by condensation of the free amine base with aldehyde A in EtOAc/MeOff. The free amine base solution of glycine methyl ester in methanol is generated from the corresponding hydrochloride and triethylamine. Table 4 shows the reaction concentration profiles at 20-25°C. The Schiffs base formation is second order with respect to both the aldehyde and glycine ester. The equilibrium constant (ratio k(forward)/ k(reverse)) is calculated to be 67. 

In textbooks of computational chemistry you will invariably find examples calculating the pH = - lg [H+]/(mol/l)> in weak acid - strong base or strong acid - weak base solutions. Indeed, these examples are important in the study of acids, bases and of complex formation, as well as for calculating titration curves. Following (ref. 24) we consider here the aquous solution that contains a weak tribasic acid H A and its sodium salts NaH, Na HA and Na A in known initial concentrations. The dissociation reactions and equilibrium relations are given as follows. 

To address these limitations to the commercial evaluation and implementation of C02 as a substitute solvent, we (1) present a methodology to measure and model high-pressure phase behavior of C02-based reaction systems using minimal experimental data and (2) present a new computational technique for high-pressure phase equilibrium calculations that provides a guarantee of the correct solution to the flash problem. 

Acid solutions are often analyzed by titration with a solution of a strong base of known concentration similarly, solutions of bases are analyzed by titration with a strong acid. In either case, the measured pH is plotted as a function of the titrant volume. Calculation of a pH titration curve is a particularly good introduction to acid-base equilibrium calculations since a variety of calculations are involved. 

A basic premise of solubility considerations is that a solution in contact with a solid can be in an equilibrium state with that solid so that no change occurs in the composition of solid or solution with time. It is possible from thermodynamics to predict what an equilibrium ion activity product should be for a given mineral for a set of specified conditions. As will be shown later in this chapter, however, it is not always possible to obtain a solution of the proper composition to produce the equilibrium conditions if other minerals of greater stability can form from the solution. It shall also be shown that while it is possible to calculate what mineral should form from a solution based on equilibrium thermodynamics, carbonate minerals usually behave in a manner inconsistent with such predictions. 

The goal of this research was to improve activity coefficient prediction, and hence, equilibrium calculations in flue gas desulfurization (FGD) processes of both low and high ionic strength. A data base and methods were developed to use the local composition model by Chen et al. (MIT/Aspen Technology). The model was used to predict solubilities in various multicomponent systems for gypsum, magnesium sulfite, calcium sulfite, calcium carbonate, and magnesium carbonate SCU vapor pressure over sulfite/ bisulfite solutions and, C02 vapor pressure over car-bonate/bicarbonate solutions. 

Because K, depends on concentrations and the product KyKx is concentration independent, Kx must also depend on concentration. This shows that the simple equilibrium calculations usually carried out in first courses in chemistry are approximations. Actually such calculations are often rather poor approximations when applied to solutions of ionic species, where deviations from ideality are quite large. We shall see that calculations using Eq. (47) can present some computational difficulties. Concentrations are needed in order to obtain activity coefficients, but activity coefficients are needed before an equilibrium constant for calculating concentrations can be obtained. Such problems are usually handled by the method of successive approximations, whereby concentrations are initially calculated assuming ideal behavior and these concentrations are used for a first estimate of activity coefficients, which are then used for a better estimate of concentrations, and so forth. A G is calculated with the standard state used to define the activity. If molality-based activity coefficients are used, the relevant equation is... 

From Eqn. (14) it follows that with an exothermic reaction - and this is the case for most reactions in reactive absorption processes - decreases with increasing temperature. The electrolyte solution chemistry involves a variety of chemical reactions in the liquid phase, for example, complete dissociation of strong electrolytes, partial dissociation of weak electrolytes, reactions among ionic species, and complex ion formation. These reactions occur very rapidly, and hence, chemical equilibrium conditions are often assumed. Therefore, for electrolyte systems, chemical equilibrium calculations are of special importance. Concentration or activity-based reaction equilibrium constants as functions of temperature can be found in the literature [50]. 

Many commercially available and investigational drugs are anionic or cationic salt forms of weak acids or weak bases (undissociated). Their properties (solubility, partition coefficient, bioavailability, etc.) are strongly dependent upon the degree of ionization, the pH of the solution, and other constituents in the solutions of the drugs. In this chapter, ionic equilibrium calculations will be demonstrated in order to facilitate study of their properties. 

This same basic approach (equilibrium, material balance, and electroneutrality equations) applies to the calculation of the concentration of OH in a solution of a weak base at equilibrium. The resulting equation is ... 

This shows that the ionic equilibrium calculation for the salt formed between the weak base and the strong acid is identical for the undissociated acid. Therefore, one may use Equation (2.15), Equation (2.17), and Equation (2.19) for the calculation of H+ in the solution of a salt between a weak base and a strong acid. Equation (2.21a), Equation (2.21b), and Equation (2.21c) may be used for the calculation of OH- in the solution of the salt between a weak acid and a strong base along with Equation (2.20). 

Make sure you aren t getting mixed up about the changing concentrations of the buffer constituents and the signs in the A column. The change in concentration that occurs because of the addition of strong acid or base takes place in a separate reaction to the one in the equilibrium calculation table. The effects of these changes are reflected in the different amounts in the start row of the table. The other events shown in the table only describe the equilibrium of the acetic acid solution, which will always increase the concentration of acetate ion. 

C) pH = 4.0. This is a buffer solution containing a weak acid and its conjugate base. In this problem, you set up the equilibrium calculation table with amounts for HCH02 and CH02 in the start column ... 

Lewin and coworkers [255-260] developed an accessibility system based on equilibrium sorption of bromine, from its water solution at pH below 2 and at room temperature, on the glycosidic oxygens of the cellulose. The size of the bromine molecule, its simple structure, hydrophobicity, nonswelling, and very slow reactivity with cellulose in acidic solutions, contribute to the accuracy and reproducibility of the data obtained. The cellulose (10 g/1) is suspended in aqueous bromine solutions of 0.01-0.02 mol/1 for 1-3 h, depending on the nature of the cellulose, to reach sorption equilibrium. The diffusion coefficients of bromine in cotton and rayon are 4.6 and 0.37 x 10 cm /min, respectively. The sorption was found to strictly obey the Langmuir isotherm, which enables the calculation of the accessibility of the cellulose as follows ... 

An acidic buffer solution has an excess of all the reactants and products, except for H30. Thus, when we try to change the concentration of H30 by adding strong acid or base, the equilibrium shifts, in accordance with LeChatelier s principle, to resist that change. The pH changes very little. (We will do calculations to show quantitatively how little the pH changes in such systems later in this section.)... 

If strong acid or strong base is added to a buffer solution, a net reaction takes place. To calculate the pH of such solutions, we first assume that the strong acid or base reacts as completely as possible, given that some reactant is present in limiting quantity, as discussed in Section 10.4. Only then do we concentrate on the equilibrium calculation. 

The sodium acetate solution is an example of an important general case. For any salt whose cation has neutral properties (such as Na+ or K+) and whose anion is the conjugate base of a weak acid, the aqueous solution will be basic. The Kb value for the anion can be obtained from the relationship Kb = Kw/Ka. Equilibrium calculations of this type are illustrated in Example 7.11. 

In treating buffered solutions in this chapter, we will start by considering the equilibrium calculations. We will then use these results to show how buffering works. That is, we will answer the question How does a buffered solution resist changes in pH when an acid or base is added ... 

When a strong acid or base is added to a buffered solution, it is best to deal with the stoichiometry of the resulting reaction first. After the stoichiometric calculations are completed, then consider the equilibrium calculations. This procedure can be represented as follows ... 

Their calculation of the equilibrium constant was based on spectroscopic measurements of the Br2 concentration. They were able to observe a time variation of the Br2 concentration after mixing but report no rates. In ether and formaldehyde solutions equilibrium was achieved so rapidly that the variation with time of [Br2] could not be detected. 

We conclude this discussion with one final reminder. The vapor-liquid equilibrium calculations we have shown in Section 6.4c are based on the ideal-solution assumption and the corresponding use of Raoult s law. Many commercially important systems involve nonideal solutions, or systems of immiscible or partially miscible liquids, for which Raoult s law is inapplicable and the Txy diagram looks nothing like the one shown for benzene and toluene. 

A frequent complication is that several simultaneous equilibria must be considered (Section 3-1). Our objective is to simplify mathematical operations by suitable approximations, without loss of chemical precision. An experienced chemist with sound chemical instinct usually can handle several solution equilibria correctly. Frequently, the greatest uncertainty in equilibrium calculations is imposed not so much by the necessity to approximate as by the existence of equilibria that are unsuspected or for which quantitative data for equilibrium constants are not available. Many calculations can be based on concentrations rather than activities, a procedure justifiable on the practical grounds that values of equilibrium constants are obtained by determining equilibrium concentrations at finite ionic strengths and that extrapolated values at zero ionic strength are unavailable. Often the thermodynamic values based on activities may be less useful than the practical values determined under conditions comparable to those under which the values are used. Similarly, thermodynamically significant standard electrode potentials may be of less immediate value than formal potentials measured under actual conditions. 

Equilibrium calculations based on mineral saturation indices also show how the concentration of solutes that are present in trace amounts are influenced by mineral dissolution/ precipitation reactions. Eor example, the concentration of barium in groundwater appears to be buffered by the saturation index of barite (BaS04) (Eigure 2). 

Hydrolysis equilibria can be interpreted in a meaningful way if the solutions are not oversaturated with respect to the solid hydroxide or oxide. Occasionally, it is desirable to extend equilibrium calculations into the region of oversaturation but quantitative interpretations for the species distribution must not be made unless metastable supersaturation can be demonstrated to exist. Most hydrolysis equilibrium constants have been determined in the presence of a swamping inert electrolyte of constant ionic strength (/ = 0.1, 1, or 3 M). As we have seen before, the formation of hydroxo species can be formulated in terms of acid-base equilibria. The formulation of equilibria of hydrolysis reactions is in agreement with that generally used for complex formation equilibria (see Table 6.2). 

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