Conditional concentration quotient

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)... 

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)... 

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. 

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-... 

The symbol E ° is used to denote the so-called formal potential [74PAR]. The formal (or conditional ) potential can be regarded as a standard potential for a particular medium in which the activity coefficients are independent (or approximately so) of the reactant concentrations [85BAR/PAR] (the definition of E° parallels that of concentration quotients for equilibria). Therefore, from... 

Strategy The standard emf (E°) can be calculated using the standard reduction potentials in Table 19.1 of the text. Because the reactions are not run under standard-state conditions (concentrations are not 1M), we need Nemst s equation [Equation (19.8) of the text] to calculate the emf ( ) of a hypothetical galvanic cell. Remember that solids do not appear in the reaction quotient (Q) term in the Nemst equation. We can calculate AG from E using Equation (19.2) of the text AG = -nFEcsW. 

The term "conditional" (or alternatively, apparent or effective) constant is sometimes used in analytical chemistry and frequently used in biological chemistry. A conditional constant is a concentration quotient that applies only when the concentration of one or more reactants or products is fixed at a particular constant value. For example, when the equilibrium M + H L ML + nH is studied at fixed pH, an effective constant can be defined by Eq. 5 ... 

The first term, AG°, is the change in Gibb s free energy under standard-state conditions defined as a temperature of 298 K, all gases with partial pressures of 1 atm, all solids and liquids pure, and all solutes present with 1 M concentrations. The second term, which includes the reaction quotient, Q, accounts for nonstandard-state pressures or concentrations. Eor reaction 6.1 the reaction quotient is... 

In most laboratories, electrochemistiy is practiced under nonstandard conditions. That is, concentrations of dissolved solutes often are not 1 M, and gases are not necessarily at 1 bar. Recall from Chapter 14 that ZlG changes with concentration and pressure. The equation that links A G ° with free energy changes under nonstandard conditions is Equation AG = AG° + i 7 lng Here, Q is the reaction quotient. 

The quotient of rate constants obtained in steady-state treatments of enzyme behavior to define a substrate s interaction with an enzyme. While the Michaelis constant (with overall units of molarity) is a rate parameter, it is not itself a rate constant. Likewise, the Michaelis constant often is only a rough gauge of an enzyme s affinity for a substrate. 2. Historically, the term Michaelis constant referred to the true dissociation constant for the enzyme-substrate binary complex, and this parameter was obtained in the Michaelis-Menten rapid-equilibrium treatment of a one-substrate enzyme-catalyzed reaction. In this case, the Michaelis constant is usually symbolized by Ks. 3. The value equal to the concentration of substrate at which the initial rate, v, is one-half the maximum velocity (Lmax) of the enzyme-catalyzed reaction under steady state conditions. 

Tetranectin (TN). Tetranectin is a plasma protein of about 80 kDa. A reduction in the serum TN level has been described in malignant disease and in other conditions with tissue remodeling, whereas it does not seem to exhibit acute-phase reactant behavior. Using a polyclonal ELISA to determine the TN concentrations in pair of CSF/serum quotient in pair of CSE and serum, it was found that the CSE/serum quotient compared to the QAib was compatible with intrathecal TN synthesis. In clinically definite multiple sclerosis a reduced CSF/serum quotient was found, suggesting that the hypothesis of a reduced TN level as a marker of tissue remodeling may be extended to the CNS (C5). 

NACs in a laboratory column system containing aquifer material from the banks of a river-groundwater infiltration site (Fig. 14.11). The columns were run under ferrogenic conditions. Note that zero-order kinetics suggests that the reactive sites were always saturated such as encountered in enzyme kinetics at saturation (Box 12.2). In this system, all model compounds as well as other NACs including again TNT, ADNTs, and DANTs (data not shown, see Hofstetter et al., 1999) reacted at virtually the same rate. However, when present in mixtures, the compounds showed competition for the reactive sites. A competition quotient, Qc (competition with the reference compound 4-C1-NB present at about equal concentrations) was determined for all model compounds ... 

The individual rates vq and v i are affected by temperature, pressure, and the concentrations of the species in Eq. (5.36). At equilibrium, the left side of Eq. (5.37) will disappear and v]eq/v ]eq where eq is the equilibrium condition will be a function of temperature, pressure, and the equilibrium composition of the exchanger and aqueous solution phase. Because the activities of the species in Eq. (5.36) have an identical dependence, vleq/v leq depends on temperature, pressure, and the species activities (Denbigh, 1981). But this same relationship applies to the quotient of the right and left sides of Eq. (5.38) for the determination of the exchange equilibrium constant (Ksx) for the reaction in Eq. (5.36), which can be expressed as,... 

Equation (16-7) is a remarkable statement. It implies that Qeq, the value of the reaction quotient under equilibrium conditions, depends only on thermodynamic quantities that are constant in the reaction (the temperature, and the standard free-energy change for the reaction at that temperature), and is independent of the actual starting concentrations of reactants or products. For this reason, Qeq is usually denoted the equilibrium constant, K, and (16-7) is rewritten as... 

That is, the particular function of the three concentrations defined by Q (reaction quotient) is always the same at equilibrium. This is true even though any individual concentration may vary by as much as a magnitude of 10. This unifying principle allows the calculation of conditions at equilibrium under virtually any set of conditions. 

It should also be noted however that, under certain conditions no division by c° is necessary, for example because the equilibrium constant quotient contains as many concentration terms in its numerator as in its denominator. In such cases we could say that ... 

The key components for process monitoring were selected according to these data and some additional information. The in situ monitoring of the DO as well as the oxygen and carbon dioxide concentrations in the off gas allowed the evaluation of the oxygen transfer rate (OTR), the C02 production rate (CPR) and the respiratory quotient (RQ). The control of the pH-value and the DO was the prerequisite for the maintenance of the optimal growth and product formation conditions. 

The Partition Coefficient itself is a constant. It is defined as the ratio of concentration of compound in aqueous phase to the concentration in an immiscible solvent, as the neutral molecule. The partition coefficient (P) therefore is the quotient of two concentrations and is usually given in the form of its logarithm to base 10 (log P). The Log P will vary according to the conditions under which it is measured and the choice of partitioning solvent. 

Figure 2. Variation of the apparent acidity quotient (pQai) of a-FeOOH as a function of surface charge and concentration of supporting electrolyte, NaCl. Lines are contours for constant electrolyte or constant surface charge. The condition a = C = 0 yields a—FeOOH/NaCl. Balistrieri and Murray (1978).

The reaction quotient has the same form as the equilibrium constant, but it involves specific values that are not necessarily equilibrium concentrations. If they are equilibrium concentrations, then Q = K. The concept of the reaction quotient is very useful. We can compare the magnitude of Q with that of for a reaction under given conditions to decide whether... 

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