Equilibrium simultaneous

Simultaneous equilibria, 213 Single potential-differences, 474 Softening, 193... 

As shown in Section 1.5.5, application of the law of mass action to these simultaneous equilibria leads to the following expression for the proportion of the binding sites occupied by agonist ... 

When B and C are applied together, as in (3) above, and the agonist A is also present, we have four simultaneous equilibria (at least in principle) ... 

Solutions of alkali metals in liquid ammonia have been studied by many techniques. These include electrical conductivity, magnetic susceptibility, nuclear magnetic resonance (NMR), volume expansion, spectroscopy (visible and infrared), and other techniques. The data obtained indicate that the metals dissolve with ionization and that the metal ion and electron are solvated. Several simultaneous equilibria have been postulated to explain the unique properties of the solutions. These are generally represented as follows ... 

In the preceding section, we have described two methods that are frequently used to determine the composition of complexes in solution. We will now turn our attention to a consideration of the simultaneous equilibria that are involved in complex formation. The widely used approach described here is known as Bjerrum s method, and it was described by Jannik Bjerrum many years ago. 

An extension of the procedure for calculating the deton velocities to include those expls which.yield solid carbon as a reaction product has been accomplished by the same investigators (See Ref 32) on the assumption that the volumes of solid and gas are additive, that the gas obeys eq 23 and that the solid has zero coefficients of thermal expansion and basic compression. The composition of the reaction products was assumed to be that of chemical equilibrium at the temp and pressure immediately behind the deton wave, and a numerical procedure, involving successive approximations, was developed for the determination of the composition from a consideration of the simultaneous equilibria involved. This method of calculation was briefly discussed in Ref 39, pp 86-7... 

This optional chapter provides tools to compute the concentrations of species in systems with many simultaneous equilibria.3 The most important tool is the systematic treatment of equilibrium from Chapter 8. The other tool is a spreadsheet for numerical solution of the equilibrium equations. We will also see how to incorporate activity coefficients into equilibrium calculations. Later chapters in this book do not depend on this chapter. 

The theoretical yields of cyanogen obtained by the reaction of carbon and nitrogen can also be derived from thermodynamic data. At high temperatures cyanogen is partly dissociated into cyanogen radicals, and the following simultaneous equilibria must be considered ... 

The calculations for problems such as this must be based on the Ksv of the more soluble compound—in this case, the Mg(OH)2. Two simultaneous equilibria are involved the solubility of Mg(OH)2 (horizontal equation), and the dissociation of NH3 (vertical equation). The coefficient of 2 belongs only with the horizontal equation. The concentration of OH" is common to both equilibria. 

Two simultaneous equilibria are involved the solubility equilibrium (horizontal equation), and the dissociation of the complex ion (vertical equation). The Ag+ is shared in common with both equilibria. 

As long as one has to consider no more than a single chemical reaction, one need compute only a single equilibrium constant from which the equilibrium compns are readily obtained. When, however, chemical processes take place at extreme temps and pressures, a large number of simultaneous equilibria may exist. For example, to calculate the flame temp for the combustion of a hydrocarbon in air it may be necessary to consider as many as 20 chemical reactions. As the number of reactions increases, so does the mathematical difficulty because no... 

The thermal stability of the sulfate anion varies with the cation, as was described for the carbonates, i.e., stability decreases with increasing polarizing power of the cation. Thus small cationic size and high charge promote decomposition. The primary decomposition is to the oxide and S03, accompanied by decomposition of that gas to S02 and 02. Thus in a closed system there will also be two simultaneous equilibria ... 

Equilibrium constants and their applications, including their use for simultaneous equilibria... 

Electrode of the third kind — Electrodes of the third kind contain a metal and two salts with a common anion. For instance, Zn(s) ZnC2C>4(s), CaC204(s) Ca(NC>3)2(aq). In these electrodes simultaneous equilibria with respect to anions and cations exist. The electrode reaction is... 

The four initial equations are thus reduced into two independent equations, namely, Eqs. 4.11 and 4.12, for which we must find simultaneous equilibria. All components present in the original four equations are contained in Eqs. 4.11 and 4.12. 

The formation probability of products in a system of coupled reactions can be calculated from the simultaneous equilibria 3. 36]. For complex systems like the Fischer-Tropsch synthesis, however, a simplillcation has to be made by the assumption that the reactions selected are independent of each other. 

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. 

Aside from its welhkno vn function as an oxygen carrier, hemoglobin plays an important role as a blood buffer. In order to understand the interrelationship between oxygen uptake and release, and the buffering action of hemoglobin, we must consider the interaction of several simultaneous equilibria, A greatly simplified version of the equilibria is developed below. 

Two simultaneous equilibria are involved in the ionization of a diprotic acid such as H2C03 ... 

A quantitative calculation of metal sulfide solubility requires treating several simultaneous equilibria, as the following example illustrates. 

The discussion that follows deals with the use of equilibrium-constant expressions to gain information about analytical systems in which no more than one or two equilibria are present. Chapter 11 extends these methods to systems containing several simultaneous equilibria. Such complex systems are often encountered in analytical chemistry. 

Fractional Precipitation Simultaneous Equilibria Involving Slightly Soluble Compounds Dissolving Precipitates... 

Explain how simultaneous equilibria can be used to control solubility... 

QQ SIMULTANEOUS EQUILIBRIA INVOLVING SLIGHTLY SOLUBLE COMPOUNDS... 

The three Salem samples show increased leaching rates as a function of increased acidity, but not the rate values predicted by simple chemical stoichiometry. A pH decrease from 5.6 to 4.0 is a 39.8x increase in acidity, while a change from 4.0 to 3.0 is a 10x acidity increase. The observed changes were factors of 2.88x and 1.58x, respectively. These discrepancies can be attributed to the complex equilibrium interactions involved in the solubilities of the metal carbonates. These two solubility equilibria are further complicated by the two acid equilibria for the carbonic acid/bicarbon-ate/carbonate system in addition to the equilibrium solubility of congas in water. The solution of these simultaneous equilibria processes to determine the relationship between carbonate solubility and acid concentration is a non-trivial one (sixth degree in concentration). This solubility problem has been approached from several different viewpoints (31-35), the most convenient being a graphical solution of the solubility as a function of initial solution and final solution pH. From this method, it can be theoreti-... 

Three simultaneous equilibria are set up in a buffer solution, and all must be considered when formulating the expressions for [H30 ]actuai or [OH ]actuai- Carrying out actual calculations of the pH of a buffer solution is straightforward provided that approximate expressions for deriving the expressions for [H30 ]actuai or [OH ]actuai are used. However, the reasoning used in the derivations and approximations is more tricky, and demonstrates the absolute necessity to be aware of what approximations are being made, and their implications and limitations. 

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