True yield constant

Experimentally, while the determination of absorption cross sections is fairly straightforward, measuring primary quantum yields is not, due to interference from rapid secondary reactions. As a result, in cases where quantum yield data are not available, calculations of maximum rates of photolysis are often carried out in which it is assumed that (A) = 1.0. It should be emphasized in such cases that this represents only a maximum rate constant for photolysis the true rate constant may be much smaller, even zero, if photophysical fates of the excited molecule such as fluorescence or quenching predominate. 

Kinetic traces are now exponential and the first-order treatment yields /cv, which will exhibit a linear dependence on [B]. The true rate constant k can then be easily obtained from the relationship/c Ar, (/ B. A similar treatment is applicable to other reaction types as well. A third-order reaction, for example, can be run under pseudo-first- or pseudo-second-order conditions, depending on the precise rate law and the chemistry involved. 

We have shown that there is good agreement between dissociation constants obtained by kinetic studies, and by measurements of the substrate-induced enzyme inactivation (4) the latter may yield true equilibrium constants, as is the case for Kj determinations, free from kinetic variables that may be present in estimations of Km (6). However, the constants determined by inducing inactivations cannot be accepted without properly evaluating other factors (14). 

In equation (1) K y is referred to as the Stern-Volmer constant Equation (1) applies when a quencher inhibits either a photochemical reaction or a photophysical process by a single reaction. <1>° and M° are the quantum yield and emission intensity (radiant exitance), respectively, in the absence of the quencher Q, while <1> and M are the same quantities in the presence of the different concentrations of Q. In the case of dynamic quenching the constant K y is the product of the true quenching constant kq and the excited state lifetime, t°, in the absence of quencher, kq is the bimolecular reaction rate constant for the elementary reaction of the excited state with the particular quencher Q. Equation (1) can therefore be replaced by the expression (2)... 

Constant stress (creep) measurements A constant is stress is applied to the system and the strain y or compliance J (y/a) is followed as a function of time. By measuring creep curves at increasing stress values, it is possible to obtain the residual (zero-shear) viscosity ri 6) and the critical stress that is, the stress above which the structure starts to break down. <7 is sometimes referred to as the true yield value. 

Basically, a constant stress cr is applied on the system and the compliance J(Pa ) is plotted as a function of time (see Chapter 20). These experiments are repeated several times, increasing the stress in small increments from the smallest possible value that can be applied by the instrament). A set of creep curves is produced at various applied stresses, and from the slope of the linear portion of the creep curve (when the system has reached steady state) the viscosity at each applied stress, //, can be calculated. A plot of versus cr allows the limiting (or zero shear) viscosity /(o) and the critical stress cr (which may be identified with the true yield stress of the system) to be obtained (see also Chapter 4). The values of //(o) and <7 may be used to assess the flocculation of the dispersion on storage. 

Often, the two model parameters, Tq and /rg, are treated as curve fltting constants irrespective of whether or not the fluid possesses a true yield stress. 

Electrolysis efficiency is always lower than 100% and for this reason the true yield is higher than the theoretical yield. However, because the pattern is linear, the real value can be extrapolated correctly by multiplying Equation [16.23] for a constant value of 1.07. 

Rheological measurements are used to investigate the bulk properties of suspension concentrates (see Chapter 7 for details). Three types of measurements can be applied (1) Steady-state shear stress-shear rate measurements that allow one to obtain the viscosity of the suspensions and its yield value. (2) Constant stress or creep measurements, which allow one to determine the residual or zero shear viscosity (which can predict sedimentation) and the critical stress above which the structure starts to break-down (the true yield stress). (3) Dynamic or oscillatory measurements that allow one to obtain the complex modulus, the storage modulus (the elastic component) and the loss modulus (the viscous component) as a function of applied strain amplitude and frequency. From a knowledge of the storage modulus and the critical strain above which the structure starts to break-down , one can obtain the cohesive energy density of the structure. 

It is worth mentioning that a(a) cannot be simply replaced by any time-dependent function, such as f(t) = because in this case the meaning of basic kinetic equation would alter yielding a contentious form, a = k,(T) r f(a). This mode was once popular and serviced in metallurgy, where it was applied in the form of the so-called Austin-Rickett equation [525]. From the viewpoint of kinetic evaluation it, however, is inconsistent as this equation contains on its right-hand side two variables of the same nature (a and t) but in different connotation so that the kinetic constant k,(T) is not a true kinetic constant. As a result, the parallel use of these both variables, provides incompatible values of kinetic data, which can be prevented by simple manipulation and re-substitution. Practically, the Austin-Rickett equation can be straightforwardly transferred back to the standard kinetic form [3] to contain either variable or or t on its own by, e.g., a simplified assumption that a and a = f/p and a = = cl . 

At a given temperature, a true ionization constant is a thermodynamic quantity related to the standard free energy change in the reaction. Theoretically this value should be independent of the concentration taken initially for its determination. In practice, however, application of equation (9 7) to the determination of the ionization constant of acetic acid yields values of which vary with concentration as shown in Table 9.2. 

Range of constant width test conditions covered. Soiid bars show vaiues of true yield stress in regime... 

The component with the lowest equilibrium constant is called the key component in the stripping process, because it yields the largest value of Vnjm- This largest value is the true minimum air flowrate, whereas the actual air flowrate should be selected at 1.20 to 2.0 times the minimum. This becomes a balance between fewer theoretical stages at actual air flowrate, yet requires a larger diameter column to carry out the operation. 

Barium sulphate exhibits a marked tendency to carry down other salts (see co-precipitation, Section 11.5). Whether the results will be low or high will depend upon the nature of the co-precipitated salt. Thus barium chloride and barium nitrate are readily co-precipitated. These salts will be an addition to the true weight of the barium sulphate, hence the results will be high, since the chloride is unchanged upon ignition and the nitrate will yield barium oxide. The error due to the chloride will be considerably reduced by the very slow addition of hot dilute barium chloride solution to the hot sulphate solution, which is constantly stirred that due to the nitrate cannot be avoided, and hence nitrate ion must always be removed by evaporation with a large excess of hydrochloric acid before precipitation. Chlorate has a similar effect to nitrate, and is similarly removed. 

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