Equilibrium constant mixed

It is sometimes advantageous to use a mixture of activities and concentrations and a mixed equilibrium constant, K, is defined as... 

The formation of Hg(SeCN)4 is well established by the potentiometric work of Toropova [56TOR], while her experimental data pertaining to the formation and the formation constant of Hg(SeCN)3 only comprise a few points. In their polarographic work Murayama and Takayanagi [72MUR/TAK] studied the anodic mercury wave in the presence of 0.001 to 0.003 M SeCN . The electrode process was assumed to comprise the charge transfer Hg(l) Hg + 2e combined with the formation of Hg(SeCN)2(aq) and Hg(SeCN)3. No primary data are provided and the evaluation procedure is rather involved, which makes the assessment difficult. The results are mixed equilibrium constants, since an activity coefficient correction was applied to the Hg ion. The following complexes are thus proposed to prevail in the Hg -SeCN system ... 

The significance of AH and AF in cases where a mixed equilibrium constant is in use will be clear in each particular case. Consider, for example, the formation of urea in aqueous solution by the... 

Equation 12.9.2 is an example of a mixed equilibrium constant—one using more than one kind of standard state. From the definition of the mean ionic activity coefficient (Eq. 10.3.7), we can replace the product y+Y- by y . where y is the mean ionic activity coefficient of aqueous Ca(HC03)2 ... 

Each of the entries in the expression is divided by the appropriate reference value, making the result dimensionless. Note that this equilibrium constant is neither a Kc nor a Kp. It is referred to simply as or as K p where the subscripted eq denotes equilibrium. We will encounter the use of "mixed equilibrium constants such as this in Chapters 19 and 20. 

The equilibrium binding constant for this 1 1 association is Xu = ki/lLi. The Xu values were measured spectrophotometrically, and the rate constants were determined by the T-jump method (independently of the X,j values), except for substrate No. 6, which could be studied by a conventional mixing technique. Perhaps the most striking feature of these data is the great variability of the rate constants with structure compared with the relative insensitivity of the equilibrium constants. This can be accounted for if the substrate must undergo desolvation before it enters the ligand cavity and then is largely resolvated in the final inclusion complex. ... 

Write an equationforthe reaction of chloroacetic acid (Ka = 1.5 X 103) with trimethylamine (Kj, = 5.9 X 10 5). Calculate die equilibrium constant for die reaction. If 0.10 M solutions of these two species are mixed, what will be their concentrations at equilibrium ... 

Reactants A and B are mixed, each at a concentration of 0.80 mole/liter. They react slowly, producing C and D A + B C + D. When equilibrium is reached, the concentration of C is measured and found to be 0.60 mole/liter. Calculate the value of the equilibrium constant. 

Experimentally, fCsp = 1.6 X 10 10 at 25°C, and the molar solubility of AgCl in water is 1.3 X 10 5 mol-IT. If we add sodium chloride to the solution, the concentration of Cl ions increases. For the equilibrium constant to remain constant, the concentration of Agf ions must decrease. Because there is now less Ag+ in solution, the solubility of AgCl is lower in a solution of NaCl than it is in pure water. A similar effect occurs whenever two salts having a common ion are mixed (Fig. 11.16). 

Sometimes it is important to know under what conditions a precipitate will form. For example, if we are analyzing a mixture of ions, we may want to precipitate only one type of ion to separate it from the mixture. In Section 9.5, we saw how to predict the direction in which a reaction will take place by comparing the values of J, the reaction quotient, and K, the equilibrium constant. Exactly the same techniques can be used to decide whether a precipitate is likely to form when two electrolyte solutions are mixed. In this case, the equilibrium constant is the solubility product, Ksp, and the reaction quotient is denoted Qsp. Precipitation occurs when Qsp is greater than Ksp (Fig. 11.17). 

As the LiF example illustrates, the most direct way to determine the value of an equilibrium constant is to mix substances that can undergo a chemical reaction, wait until the system reaches equilibrium, and measure the concentrations of the species present once equilibrium is established. Although the calculation of an equilibrium constant requires knowledge of the equilibrium concentrations of all species whose concentrations appear in the equilibrium constant expression, stoichiometric analysis often can be used to deduce the concentration of one... 

In its simplest form a partitioning model evaluates the distribution of a chemical between environmental compartments based on the thermodynamics of the system. The chemical will interact with its environment and tend to reach an equilibrium state among compartments. Hamaker(l) first used such an approach in attempting to calculate the percent of a chemical in the soil air in an air, water, solids soil system. The relationships between compartments were chemical equilibrium constants between the water and soil (soil partition coefficient) and between the water and air (Henry s Law constant). This model, as is true with all models of this type, assumes that all compartments are well mixed, at equilibrium, and are homogeneous. At this level the rates of movement between compartments and degradation rates within compartments are not considered. 

The products of oxidation (alcohol, ketone, acid) lower the concentration of active complexes and, in addition, form complexes with a mixed ligand sphere with lower catalytic activity (kdi >kd2). The values of equilibrium constants Ain (Lmol-1) measured spectrophotometri-cally in a decane solution for cupric stearate + product are given below [70],... 

Rate and equilibrium constant data, including substituent and isotope effects, for the reaction of [Pt(bpy)2]2+ with hydroxide, are all consistent with, and interpreted in terms of, reversible addition of the hydroxide to the coordinated 2,2 -bipyridyl (397). Equilibrium constants for addition of hydroxide to a series of platinum(II)-diimine cations [Pt(diimine)2]2+, the diimines being 2,2 -bipyridyl, 2,2 -bipyrazine, 3,3 -bipyridazine, and 2,2 -bipyrimidine, suggest that hydroxide adds at the 6 position of the coordinated ligand (398). Support for this covalent hydration mechanism for hydroxide attack at coordinated diimines comes from crystal structure determinations of binuclear mixed valence copper(I)/copper(II) complexes of 2-hydroxylated 1,10-phenanthroline and 2,2 -bipyridyl (399). 

Equilibrium constants have been reported for the stepwise conversion of MeRe(NAr)2(PR3)2 to the mixed-phosphine and then the (PR3)2 derivative. Both steric and electronic factors come into play, typical of phosphines. The stability ordering is PMe3 > dmpe>PMe2Ph > P(OMe)2Ph > PEt3 > P(OEt)3 > PMePh2 > P(OEt)Ph2 > PPh3 (58). 

A reversible reaction, At= B, takes place in a well-mixed tank reactor. This can be operated either batch-wise or continuously. It has a cooling jacket, which allows operation either isothermally or with a constant cooling water flowrate. Also without cooling it performs as an adiabatic reactor. In the simulation program the equilibrium constant can be set at a high value to give a first-order irreversible reaction. 

Equilibrium constants for the various mixed polyions in 0.6 M NaCl at 25° have been calculated from combined potentiometic and 61V NMR measurements over wide concentration ranges and 1.4 < pH < 7 (165). 

The relative magnitude of the two concentrations evidently depends on the magnitude of the equilibrium constants and of the concentrations of M and X. Two further points need to be made, (i) It is likely that the formation of 3 from 2 will be favoured, i.e., the equilibrium constant will be enhanced, by a statistical factor akin to an entropy of mixing, (ii) For the species 2 there is no front and back , the MP+BM is symmetrical, and therefore the probability of the propagation, i.e., the, is twice as great as it would be for XP+BM, even if the free energy of complexing is the same for X and M. 

The value of an equilibrium constant is calculated by measuring (or calculating) the equilibrium concentrations of the reactants and products. A calibration curve is constructed by measuring the absorbance of a colored solution versus its concentration. Known quantities of the reactants are mixed, and the calibration curve is used to determine the concentration of the colored substance in the resultant solution. (See the Equilibrium chapter.)... 

Standard Quantities in Chemical Thermodynamics. Fugacities, Activities, and Equilibrium Constants for Pure and Mixed Phases. IUPAC Recommendations 1994 Pure Appl. Chem. 1994, 66, 533-552. 

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