Equilibrium quotient

The basic relationships between solubility and pH can be derived for any given equilibrium model. The model refers to a set of equilibrium equations and the associated equilibrium quotients. In a saturated solution, three additional equations need to be considered, along with the ionization Eqs. (2a)-(2d), which describe the equilibria between the dissolved acid, base or ampholyte in solutions containing a suspension of the (usually crystaUine) solid form of the compounds ... 

Listed after the reactions are the corresponding equilibrium quotients. The law of mass action sets the concentration relations of the reactants and products in a reversible chemical reaction. The negative log (logarithm, base 10) of the quotients in Eqs. (3.1)—(3.4) yields the familiar Henderson-Hasselbalch equations, where p represents the operator -log ... 

In this expression, the square brackets refer to the activity of the component although it is more convenient to use its concentration. This approximation is generally satisfactory, except at very high concentrations, and is particularly suitable for analytical use. Where it is necessary to distinguish between the constant obtained using concentrations and the true thermodynamic equilibrium constant Ka the former may be termed the equilibrium quotient and assigned the symbol Q. The exact relation between Ke and Q has been the subject of much investigation and speculation. In this... 

In these reactions, K is the equilibrium quotient for the formation of the precursor complex, k is the rate for electron... 

Ha et al. [18] have measured the equilibrium quotients for the formation of a complex between the lac repressor protein and a symmetric operator sequence of DNA as a function of temperature. Their results are given below. (The standard state is 1 mol dm. )... 

Since the equilibrium quotient K is small, a nonnueleophilic base is added to the reaction mixture to react with liberated protons and drive the reaction to completion (left to right). Using an excess of ROH then ensures simple unidirectional pseudo first-order (rate constant Atj) kinetics ... 

A more common form of Eq. (2) is given by the equilibrium quotient... 

To examine the possibility that the different kinetic behaviors for series al, a3, and a5 may be due to differences in ionic strength, the solutions of series al and a3 were replaced by solutions of slighdy different compositions in which small amounts of sodium perchlorate were included. Extreme assumptions about the way that the sodium perchlorate would affect the equilibrium quotients for the bisulfate dissociation were used to calculate the detailed compositions of the new solutions in order to maintain constant ionic strength at 1.50, constant sulfate ion concentration at 0.276Af, and hydrogen ion concentrations close to those of solutions al and a3. No matter which of the assumptions was made in computing the compositions, the kinetic behaviors observed for the new solution series were very similar to those reported herein for series al and a3. 

Cation Exchange Capacity. Various techniques have been used to measure the cation exchange capacity of the clay samples. Unless otherwise noted, in computation of equilibrium quotients, we shall use a value of 0.78 equivalents/kg clay, determined by a column method (14) on the calcium form of Wyoming montmoril-lonite at pH 5. 

Figure 5. Effect of loading on equilibrium quotients [mcaFaq/(Ca )ciayD cJ of Wyoming montmorillonite predominately in the calcium form (pH 5, equilibration for 77 hr) C), 0.5M CaCl, + O.OIM Ca(OAc)2 O, 0.05M CaCl, + O.OIM Ca(OAc)i.

Figure 8-1 Student data showing that the equilibrium quotient of concentrations for the reaction Fe3 + SCN Fe(SCN)21 decreases as potassium nitrate is added to the solution. Color Plate 3 shows the fading of the red color of Fe(SCN)2 after KN03 has been added. Problem 13-11 gives more information on this chemical system. [From R. J. Stolzberg, "Discovering a Change in Equilibrium Constant with Change in Ionic Strength," J. Chem. Ed. 1999, 76.640.]...

To use activity coefficients, first solve the equilibrium problem with all activity coefficients equal to unity. From the resulting concentrations, compute the ionic strength and use the Davies equation to find activity coefficients. With activity coefficients, calculate the effective equilibrium constant K for each chemical reaction. K is the equilibrium quotient of concentrations at a particular ionic strength. Solve the problem again with K values and find a new ionic strength. Repeat the cycle until the concentrations reach constant values. 

The intrinsic solubility, ), of the salt is simply the equilibrium quotient forthe Lrst step of this scheme ... 

Thesolubility productKsp, is deLned as the equilibrium expression that relates the concentrations of the Lnal dissociated ions to the solid substance. It is an overall equilibrium quotient that reveals nothing about the concentrations of the intermediate species. 

Significant amounts of SO4- will be removed by protonation giving HSO4, and this will also reduce the amount of H3O, and so the actual concentrations will be significantly less than the total concentrations of these species. The actual concentrations can be calculated from the equilibrium quotient... 

Rather than the equilibrium constants, the equilibrium quotients ... 

If the reaction mixture is very dilute in the reactants and the products, the activity coefficients can all be approximated by unity. Then the last term on the right hand side of Eq. (2.20) vanishes, and the left hand side can be written as AG° = -RT n ATsolution, the equilibrium quotient becoming the equilibrium constant. Under ordinary conditions, however, the activity coefficient term must be taken into account, since there are solvent effects on all the terms on the right hand side except -RTIn K". The fact that different numbers of solvent molecules may specifically associate with the reactants and the products and that solvent molecules may be released or consumed in the reaction should not be included explicitly, since this effect is already covered by the terms in AG s of solvation of the reactants and products according to our definition of this concept. 

They represent only average equilibrium quotients or overall site concentrations for a range of site types having widely different affinities. 

Complexation by humic substances. The average equilibrium quotients for fulvic and... 

Figure 8.13(a) Collection of published values for Cu" complexation equilibrium quotient (K) in various micro-organism systems (bacteria and algae) (adapted from Town and Filella, 1999). Symbols O, cells + exudates O, cells , exudates. 

Process (VIA) is the net reaction in excess arsenite ([H3As03]o/[IOJ]0 > 3) it is equivalent to (VIB) + 3 (VIC). Process (VIB), the Dushman reaction, is normally rate determining. Therefore, the net process (VIA) is autocatalytic in [I-], which causes a dramatic color change to arise at the stoichiometric point due to the sudden appearance of I2. Bognar and Sarosi exploited this fact to devise a chronometric technique for the determination of traces of iodide43. Process (VIC), the Roebuck reaction44, has played an important role in the development of chemical kinetics and teaching of physical chemistry, as it was the first multi-step reaction for which it was shown that the quotient of the independently determined forward and reverse rate laws equals the equilibrium quotient obtained from the law of mass action. 

Gal and Nikolic22) have shown that Job s method of continuous variations could be successfully used for finding out the composition of the species responsible for synergism and also for calculating the equilibrium quotients. In this method the distribution ratio data are obtained using a fixed composition of the aqueous phase and employing mix-... 

The Nernst Equation accurately predicts half-cell potentials only when the equilibrium quotient term Q is expressed in activities. Ionic activities depart increasingly from concentrations when the latter exceed 10-10-3 M, depending on the size and charge of the ion. 

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