Concentration exponent

Concentration of right moving steps at position x Concentration of left moving steps at position x Lauritzen number = L2i/4g Concentration of polymer in solution Concentration exponent... 

As already stressed, the actual physical situation is unlikely to be any of these limiting cases, and a variety of factors will influence the concentration exponent, including smaller effects not considered here. However, the conclusion of this section is that nucleation is not inconsistent with the experimental trends of concentration, although it would be difficult to make any a priori predictions. 

The net equation contains no kinetic information. One cannot infer that the reaction rates (v) are given as vi = [Fe2l-]2[T13+] or v2 = [ArCl][R2NH]2. Although the rates will almost certainly depend upon the concentrations of the reactants, or at least on one of them, these particular power dependences are not required. The actual form must be determined experimentally. Unlike the situation in thermodynamics, the concentration exponents in the expression for the rate of reaction are not predictable from the net chemical reaction. 

It was realized at the end of the nineteenth century that there was an exponential relationship between potency and concentration. Thus, if the log)o of a death time, that is the time to kill a standard inoculum, is plotted against the logio of the concentration, a straight line is usually obtained, the slope of which is the concentration exponent (77)... 

Table 11.1 Concentration exponents, 77, for some disinfectant substances...

Mercuric chloride has a concentration exponent of 1 thus, the activity will be reduced by the power of 1 on dilution, and a threefold dilution means the disinfectant activity will be reduced by the value 3 or 3, that is to a third. Put another way the disinfection time will be three times as long. In the case of phenol, however, with a concentration exponent of 6, a threefold dilution will mean a decrease in activity of 3 = 729, a figure 243 times the value for mercuric chloride. This explains why phenols may be rapidly inactivated by dilution and should sound a warning bell regarding claims for diluted phenol solutions based on data obtained at high concentrations. 

Change the concentration exponent value to 2.00 instead of 2.75 in the probit equation, and rerun your spreadsheet for a total release amount of 5 kg. How sensitive are the results to this exponent ... 

Parameter of order unity in the continuous form of the Rouse spectrum. Concentration exponent in Jt° and xm correlations. 

The equilibrium constant, K, is a pure number (no units) whose magnitude depends not only on the temperature, but also, generally, on the standard-state concentration to which all concentrations are referred. In this chapter, the standard state for dissolved substances will be taken as a 1M concentration, unless a statement is made to the contrary. The magnitude of K is independent of the choice of standard concentration in the special case where the sum of the concentration exponents in the numerator equals the sum of the exponents in the denominator. 

Table 2 Some examples of preservative concentration exponents...

Fig. 3 Comparisons of the activity and concentration exponents of four hypothetical preservatives. Agents A B and C D have similar concentration exponents but different activities, whereas A C and B D have similar activities yet different concentration exponents.

Knowledge of the pKa of a preservative allows the calculation of the fraction undissociated at any particular pH and hence (via the concentration exponent) the level of activity at that pH. 

Bronopol owes its usefulness as a preservative largely to its activity against Pseudomonas aeruginosa, and its affinity for polar solvents, which prevents the loss of preservative into the oil phase of emulsions that is seen with some other preservatives. Other advantages include a low incidence of microbial resistance low concentration exponent and good compatibility with most surfactants, other excipients, and preservatives, with which it can therefore be used in combination. 

Changes in the efficacy of preservatives vary exponentially with changes in concentration. The effect of changes in concentration (concentration exponent, t, Chapter 11) varies with the type of agent. For example, halving the concentration of phenol (r) = 6) gives a 64-fold (26) reduction in killing activity, while a similar dilution for chlorhexidine (r = 2)... 

Data for different molar masses of the same polymer species combine into a single plot in good solvent [Fig. 9.10(a)] if specific viscosity = ( 7 — r/sZ/ ls is plotted as a function of reduced concentration This simple data collapse works in a good solvent because the correlation length and the tube diameter are proportional to each other, with the same concentration exponents. The line in Fig. 9.10(a) has the slope of 3.9 expected by Eq. (9.46) for semidilute entangled solutions. 

Fits of two principal reaction mechanisms, both of which have the above general form, were made, after initial trials of rate expressions corresponding to mechanisms with other forms of rate expression had resulted in the rejection of these forms. In the above equation the Molecular Adsorption Model (MAM) predicts n=2, m=l while the Dissociative Adsorption Model (DAM) leads to n=2, m=l/2. The two mechanisms differ in that MAM assumes that adsorbed molecular oxygen reacts with adsorbed carbon monoxide molecules, both of which reside on identical sites. Alternatively, the DAM assumes that the adsorbed oxygen molecules dissociate into atoms before reaction with the adsorbed carbon monoxide molecules, once more both residing on identical sites. The two concentration exponents, referred to as orders of reaction, are temperature independent and integral. All the other constants are temperature dependent and follow the Arrhenius relationship. These comprise lq, a catalytic rate constant, and two adsorption equilibrium constants K all subject to the constraints described in Chapter 9. Notice that a mechanistic rate expression always presumes that the rate is measured at constant volume. 

The predicted concentration exponents for the viscosity-exponential dependence in a good solvent in the semidilute regime can be expressed as ... 

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