Function of concentration

Example 13 The following data were recorded for the potential E of an electrode, measured against the saturated calomel electrode, as a function of concentration C (moles liter ). 

Peak currents in anodic stripping voltammetry are a linear function of concentration... 

Fixed-time integral methods are advantageous for systems in which the signal is a linear function of concentration. In this case it is not necessary to determine the concentration of the analyte or product at times ti or f2, because the relevant concentration terms can be replaced by the appropriate signal. For example, when a pseudo-first-order reaction is followed spectrophotometrically, when Beer s law... 

Although Eq. (10.50) is still plagued by remnants of the Taylor series expansion about the equilibrium point in the form of the factor (dn/dc2)o, we are now in a position to evaluate the latter quantity explicitly. Equation (8.87) gives an expression for the equilibrium osmotic pressure as a function of concentration n = RT(c2/M + Bc2 + ) Therefore... 

Concentration and Molecular Weight Effects. The viscosity of aqueous solutions of poly(ethylene oxide) depends on the concentration of the polymer solute, the molecular weight, the solution temperature, concentration of dissolved inorganic salts, and the shear rate. Viscosity increases with concentration and this dependence becomes more pronounced with increasing molecular weight. This combined effect is shown in Figure 3, in which solution viscosity is presented as a function of concentration for various molecular weight polymers. 

In Germany and France the Baumii scale is calculated using 144.3 as the constant. The Baumii scale only includes the sulfuric acid concentration range of 0—93.19% H2SO. Higher concentrations are not included in the Baumh scale because density is not a unique function of concentration between 93% and 100% acid. The density of sulfuric acid versus temperature and concentration is shown in Figure 4 (50). 

C), (cmVohm geqmv) K = Ci/R = specific conductance, (ohm cm) h C = solution concentration, (gequiv/ ) Ot = conductance cell constant (measured), (cm ) R = solution electrical resistance, which is measured (ohm) and/(C) = a complicated function of concentration. The resulting equation of the electrolyte diffusivity is... 

Antioxidant activity is not a linear function of concentration. As the antioxidant level increases, less and less improvement in oxidative stability is noted. Therefore, only enough antioxidant should be added to rubber adhesives, typically 1 to 2 phr. 

The differential reactor is used to evaluate the reaction rate as a function of concentration for a heterogeneous system. It consists of a tube that contains a small amount of catalyst as shown schematically in Figure 4-17. The conversion of the reactants in the bed is extremely small due to the small amount of catalyst used, as is the change in reactant concentration through the bed. The result is that the reactant concentration through the reactor is constant and nearly equal to the... 

The differential rate equations of a complex reaetion, expressing rates as functions of concentrations, are usually simpler in form than are the corresponding integrated equations, whieh express concentrations as funetions of time moreover, it is always possible to write down the differential rate equations for a postulated kinetie seheme, whereas it may be difficult or impossible to integrate them. Of course, we usually measure concentration as a funetion of time. If, however, we can measure rates, we may use the differential equations directly. 

The free energy of mixing Umix for the fee Cu-Zn alloys is shown as a function of concentration in Fig. 1. It is obtained from the usual formula... 

Although the viscosity B-coefficients for the fluorides are not known, we see. that the value for the ionic entropy of F" listed in Table 45 is — 2.3 + 2, very different from the value +13.5 for Cl". The value for F- is, in fact, very near the value —2.49 for (OH)-. We have then the very interesting question, whether the activities of the fluorides will fall in line with the other halides. In structure the ion F" certainly resembles Cl" and the other halide ions but according to the tentative scheme proposed above, we should perhaps focus attention on the solvent in the co-sphere of each ion. In this case we should expect to obtain for the fluorides a family of curves similar to that of the hydroxides, in contrast to that of the chlorides. The activities are known as a function of concentration for NaF and KF only. It is found that the curve for NaF lies below that of KF—that is to say, the order is the same as that of NaOH and KOII, in contrast to that of NaCl and KC1. 

Schild analysis, like all pharmacological tools, necessarily is predicated on the idea that the drugs involved have one and only one pharmacological activity. This often may not be the case and selectivity is only a function of concentration. If the concentrations used in the assay are below those that have secondary effects, then the tool will furnish the parameter of interest with no obfuscation. However, if a secondary effects are operative in the concentration range required to measure antagonism then the resulting parameter may be tainted by this secondary activity. 

In the general case the dispersion viscosity (i.e. a filled system) as a function of concentration r (cp) can be presented as a power series ... 

The activity of a volatile solvent in a solution that contains a nonvolatile solute can be obtained from an experimental technique known as the isopiestic method .19 An apparatus is constructed similar to that shown in Figure 6.17. The mixture in container A is a solution of a nonvolatile solute in a solvent in which A], the activity of the solvent, has been accurately determined in other experiments as a function of concentration. Containers B and C hold solutions of other nonvolatile solutes in the same solvent. These are the solutions for which the activity of the solvent is to be determined. 

E7.12 The following table gives the osmotic pressures as a function of concentration for the polymer polyisobutylene dissolved in benzene at 298.15 K. 

Finally, they measured the enthalpy of solution of C HsO in water as a function of concentration and extrapolated to infinite dilution to get a value of -5.84 kJ-mol-1 for the reaction... 

As the cell is discharged, Zn2+ ions are produced at the anode while Cu2+ ions are used up at the cathode. To maintain electrical neutrality, SO4- ions must migrate through the porous membrane,dd which serves to keep the two solutions from mixing. The result of this migration is a potential difference across the membrane. This junction potential works in opposition to the cell voltage E and affects the value obtained. Junction potentials are usually small, and in some cases, corrections can be made to E if the transference numbers of the ions are known as a function of concentration.ee It is difficult to accurately make these corrections, and, if possible, cells with transference should be avoided when using cell measurements to obtain thermodynamic data. 

The rate of a chemical reaction is always taken as a positive quantity, and the rate constant k is always positive as well. A negative rate constant is thus without meaning. An equation such as Eq. (1-4), which gives the reaction rate as a function of concentration, usually at constant temperature, is referred to as a rate law. The determination of the form in which the different concentrations enter into the rate law is one of the initial goals of a kinetic study, since it allows one to infer certain features of the mechanism. 

FIGURE 13.41 A plot of the rate of an enzyme-catalyzed reaction (relative to its maximum value, k2[E]0, when S is in very high concentration) as a function of concentration of substrate for various values of (CM. At low substrate concentrations, the rate of reaction is directly proportional to the substrate concentration (as indicated by the black line for KM = 10). At high substrate concentrations, the rate becomes constant at k2[E]0 once the enzyme molecules are "saturated" with substrate. The units of S are the same as those of KM. 

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