Concentration quotient

Glycolysis is the source of energy in human red blood cells. In these cells, the concentration of glucose is 5.0 x 10 3Af, while that of lactic acid is 2.9 x 103 M. Calculate AG for glycolysis in human blood cells under these conditions. Use the equation AG = AG° + RT In Q, where Q is the concentration quotient analogous to K. 

Later experiments (4 ) were designed to determine a cell e.m.f. for the plutonium disproportionation system with a particular light source. Concentration quotients for the light and dark conditions, Qg and Qj, were determined, and an energy difference of 1.65 kcal (32 mV) was calculated by the relation -RTln C /Qd This reversible photochemical shift may be the only single-element system known at this time and certainly is the simplest such system. Even though the radioactive properties could prevent development and utilization of a plutonium photoconversion system, these studies certainly suggest that similar nonradioactive and more acceptable systems could be discovered and developed. 

First, verify that each concentration quotient has products in the numerator and reactants in the denominator. Then examine the concentration ratio and relate it to the general types of equilibrium constants. 

The logarithm of the concentration quotient can be separated by using the fact that logx y — logx + log ... 

Recall that the numerator of Q contains concentrations of products, and the denominator contains concentrations of reactants, all raised to powers equal to their stoichiometric coefficients. Solvents and pure solids and liquids do not appear in the concentration quotient. Thus, only solutes and gases appearing in the cell reaction affect its cell potential. Nevertheless, most cell reactions involve solutes, so a typical cell potential differs from E °. Example... 

Stability (or binding) constants Ks are often used instead of dissociation constants (Ks = 1/Kd). These equilibrium constants are concentration quotients as the corresponding activity coefficients are given the value 1. However, in many practical situations, other... 

Another method to detect locally synthesized IgG is based on CSF/serum concentration quotients ... 

Figure 8-1, Demonstration 8-1, and Color Plate 3 show that the concentration quotient in Equation 8-1 decreases if you add the inert salt KN03 to the solution. That is, the equilibrium constant is not really constant. This chapter explains why concentrations are replaced by activities in the equilibrium constant and how activities are used.

Equation 8-5 is the rear equilibrium constant. Equation 6-2. the concentration quotient, K,., did not include activity coefficients ... 

Equilibrium constants can be determined by measuring concentration quotients at several low-ionic strengths and extrapolating to 0 ionic strength. 

Experience shows that the activity coefficients on this scale stay near unity (usually within experimental error) as long as the concentrations of the reactants are kept low, say less than 10% of the concentrations of the medium ions. The activity ( concentration) of several ions, notably H+, can be determined conveniently and accurately by means of e.m.f. methods, either with or without a liquid junction. In the latter case the liquid junction potential is small (mainly a function of [H+] ) and easily corrected for (3). The equilibrium constant for any reaction, on the ionic medium scale, may then be defined as the limiting value for the concentration quotient ... 

We define equilibrium constants as concentration quotients, as in Equation (3) for A and /CK. Provided that the experiments are done at low and constant ionic strengths, /< 0.1 m, these can be converted to thermodynamic constants, Aa°, using known or estimated activity coefficients.16... 

Table 1 Kinetic and thermodynamic parameters determined for various tautomeric equilibria in aqueous solution at 25°C. The symbols for the rate constants k and the equilibrium constants K are explained in the text (first paragraph of section Examples ). Acidity constants are concentration quotients of ionization at ionic strength 7=0.1 m... 

The derivation of the law of mass action from the second law of thermodynamics defines equilibrium constants K° in terms of activities. For dilute solutions and low ionic strengths, the numerical values of the molar concentration quotients of the solutes, if necessary amended by activity coefficients, are acceptable approximations to K° [Equation (3)]. However, there exists no justification for using the numerical value of a solvent s molar concentration as an approximation for the pure solvent s activity, which is unity by definition.76,77... 

Remembering that a concentration quotient of this form can be expressed in terms of fractionation factors and n (cf. equation (32)) and assuming that the total number of water molecules per unit volume does not change (as is very nearly true), we can write... 

Figure 5 Comparison of measured and modelled plant/air concentration quotients for PCBs and PCDD/Fs as a function of the octanol/air partition coefficient (Modified from ref. 37)...

Plutonium chemists use reaction (1) as the net reaction for reactions (2), (3), and (4). This is clearly documented in the Plutonium Handbook edited by Wick, and in Cleveland s book. The Chemistry of Plutonium. Reaction (1) is an accurate representation of an equilibrium and the equilibrium concentration quotient is the product of the quotients for reactions (2), (3), and (4). Therefore, it is correct to discuss equilibrium concentrations of Pu(IV), Pu(VI), and Pu(III), without Pu(V). Circumstances where the net reaction has not been properly considered are those where concentrations of oxidation states in solutions with low acidity are calculated without consideration of Pu(IV) hydrolysis and polymerization. The distributions of Pu oxidation states (including Pu(V) and Pu(IV) polymer in nitric acid systems) were reported in JINC 609 (1973), and Silver has not included... 

In a constant ionic medium, the concentration quotient becomes the equilibrium constant... 

More exactly, on the ionic medium scale, the equilibrium constant may be defined as the limiting value (as the solution composition approaches that of the pure ionic medium) for the equilibrium concentration quotient L. In usual measurements at low reactant concentrations, the deviaticins of L from are usually smaller than the experimental errors hence it is preferable to set L = rather than to extrapolate. 

In a way similar to the expression of activity as a product of concentration and activity coefficient, an acidity constant can be expressed in terms of a product of an equilibrium concentration quotient L = ([H ][B])/[HB] and an activity coefficient factor. Correspondingly, we can interrelate the various constants defined above in the following way ... 

Apparent or stoichiometric equilibrium constants expressed as concentration quotients and valid for a medium of given ionic strength. 

Equilibrium constants in the form of concentration quotients are just as thermodynamically valid as the traditional thermodynamic constants, the main difference being the choice of activity scale and reference state. 

Activity Corrections The solubility equilibrium is influenced by the ionic strength of the solution. Often it is most convenient to use operational equilibrium constants, that is, constants expressed as concentration quotients and valid for a medium of given ionic strength. For freshwater conditions, the Debye-... 

Solubility products as concentration quotients, are preliminary unpubli ed observations by B. Alexander, E. C. Ko and A. J. Parker unless stated otherwise. Ferrocene is a polar molecule, not a salt, this value is log (solubility) in mole litre i. Ferrocene is denoted by F, Ferricinium cation by F+in the mathematical expressions. Seetext. < Luehis,Iwamoto and Kleinberg (1966). /Pavlopoulis and Strehlow (1964). v Comparable results are in reference e. Comparable results are in reference /. 

Fio. 8. Linear Free Energy Bielationship between solubility products of silver salts, AgY, expressed as concentration quotients, (logK g/K ), and relative rates of reaction of Y" with methyl iodide (logA /iP) in DMF and in methanol at 25°0. (Alexander and Parker, unpublished work). 

Table 2.5. The chemical composition of hydrothermal end-member water from the Hanging Garden hydrothermal vent at 21° N in the North Pacific Ocean and the (hydrothermal end member) (seawater) concentration quotients Data are from Von Damm etal. (1985) and are an example of the values determined for the hydrothermal end member solution. Note there are many more data and concentrations vary among data sets. ...

Curve C is a plot of K (XIO ), the concentration quotient for the equilibrium involving the dissociation of acetic acid, as a function of electrolyte concentration. Here again, the ordinate function approaches a limiting value A, which is the thermodynamic acid dissociation constant for acetic acid. 

When we look carefully at Equations 18-11 and 18-12, we see that the constant is the electrode potential whenever the concentration quotient (actually, the activity quotient) has a value of 1. This constant is by definition the standard electrode potential for the half-reaction. Note that the quotient is always equal to 1 when the activities of the reactants and products of a half-reaction are unity. 

The concentration quotient in Equation 19-11 is not the usual ratio of product concentrations and reactant concentrations that appear in equilibrium-constant expressions. 

Substitution of these equalities into Equation 19-11 results in the concentration quotient becoming unity and the logarithmic term becomin zero-... 

The maximum CC of HSs should, however, be regarded as a constant quantity that is characteristic of the HS sample rather than a variable parameter (MacCarthy and Perdue, 1991). According to these authors, the apparent variations of the CC of HSs would, in fact, result from the inability to saturate all the ligand sites under some experimental conditions, and this effect would arise from the variability in the conditional concentration quotient (see Section 4.3) and the influence of dilution on complex formation. 

Metal-ligand complexation reactions are usually investigated at constant pH and ionic strength using experimental techniques that are able to distinguish the metal-ligand complex from the uncomplexed metal (i.e., from all forms of the ligand tliat are not bound to the metal ion. Thus, a conditional stability constant, or more precisely, a conditional concentration quotient, K, can be written (MacCarthy and Perdue, 1991)... 

Assuming for simplicity a 1 1 stoichiometry for aU ML, complexes, the complexation reaction of a suigle metal ion M with a multiligand system such as HS containing a number of ligands L, can be described by an average stability constant, or, more appropriately, an average concentration quotient (MacCarthy and Perdue, 1991) ... 

An average conditional concentration quotient, also called a stability function, K, can be defined for the overall binding of a single metal ion to multiligand systems such as HSs (MacCarthy and Perdue, 1991) and calculated directly from experimental data as (Perdue, 1989)... 

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