Indicator conditional constant

According to (11-23) and (11-24) the indicator color change is affected by the hydrogen ion concentration. From a practical viewpoint a conditional indicator constant which depends on the pH of the buffered solution, may be conveniently defined by... 

Using the values given in Section 11-5 for conditional indicator constants for calmagite and the titration error curves calculated in Figure 11-7, estimate the titration errors with calmagite for a 0.01 M magnesium titration at pH values of 8 and 9. 

Equation (3.40) is the DFT equivalent of the Schrbdinger equation. The subscript Vext indicates that this is under conditions of constant external potential (i.e. fixed nuclear po.-,ilions). It is interesting to note that the Lagrange multiplier, p, can be identified with (lu chemical potential of an electron cloud for its nuclei, which in turn is related to the... 

With reference to Fig. 18-81 (both graphs), EF represents the locus of overflow compositions for the case in which the overflow stream contains no inert sohds. E F represents the overflow streams containing some inert sohds, either by entrainment or by partial solubihty in the overflow solution. Lines GF, GL, and GM represent the loci of underflow compositions for the three different conditions indicated on the diagram. In Fig. 18-81 7, the constant underflow line GM is par-aUel to EF, the hypotenuse of the triangle, whereas GF passes through... 

The results clearly indicated that the ventilation noise was perceived as most acceptable when the tone was situated in the low er part of the frequency range. The experience of disturbance and the associated effects occur at exposure levels above the auditory perception threshold. Above this level, the risk of these effects increases as the perceived loudness increases, provided that the other conditions remain constant. Since the loudness can be predicted relatively accurately by means of technical measurements, any differences in the degree of disturbance can also be predicted by reference to these measurements, provided that they are dependent on differences in the loudness. 

Dividing by dT while indicating the condition of constant p gives... 

Equation (5.52) is the first of our criteria. The subscripts indicate that equation (5.52) applies to the condition of constant entropy, volume, and total moles, with the equality applying to the equilibrium process and the inequality to the spontaneous process. 

The bed depth has no influence on the size of the bubble produced. This indicates that the bubbles are foxmed under either constant flow or constant pressure conditions. In the intermediate region, Padmavathy, Kumar, and Kuloor (PI) have shown that the bubble volume in an air-water system is highly sensitive to the variation in the depth of the liquid column above the bubble forming nozzle. As the bed has no surface tension, no variation of flow is expected during bubble formation, and the conditions of constant flow are approximated. This explanation is due to present authors. 

Some experiments conducted under constant pressure conditions indicate that the above equivalence does not hold for this situation. 

We are interested in the value of the derivative dP/dT at a specified temperature and pressure such as is indicated by point a in Figure 8.1. For an isothermal, reversible (that is, equilibrium) condition at constant pressure, from Equation (7.26),... 

Equations (6) and (7) express these relationships. are the elastic compliance constants OC are the linear thermal expansion coefficients 4 and d jj,are the direct and converse piezoelectric strain coefficients, respectively Pk are the pyroelectric coefficients and X are the dielectric susceptibility constants. The superscript a on Pk, Pk, and %ki indicates that these quantities are defined under the conditions of constant stress. If is taken to be the independent variable, then O and are the dependent quantities ... 

Here, Q are the elastic stiffness constants, are the thermal stress coefficients, and gkj and are the direct and converse piezoelectic stress coefficients, respectively. The superscript , on Pk, p k, and Xki indicates that these quantities are now defined under the conditions of constant strain. 

An examination of Figures 1-6 indicates that Equation 1 is valid under conditions of constant x for potassium, ammonium, and tetramethylammonium bromides in ethanol-water mixtures. All three salts show an ability to salt out ethanol from these mixtures (i.e., increase its concentration in the equilibrium vapor) which is verified by their k values shown in Table XVIII. Also, the results for tetra-n-propylammonium bromide and tetra-n-butylammonium bromide in ethanol-water mixtures reveal that Equation 1 can be used to predict the salt effects of these systems however, these two salts demonstrate a propensity to salt in ethanol (i.e., decrease its vapor concentration) in ethanol-water mixtures. On the other hand, Figures 7-9 and the data in Table XVIII reveal that Equation 1 cannot be used to correlate the salt effects of tetraethylammonium bromide in ethanol-water. For this system, a linear dependence of log aja vs. z is observed initially however, a gradual levelling off occurs at higher concentrations. 

In a direct titration, analyte is titrated with standard EDTA. The analyte is buffered to a pH at which the conditional formation constant for the metal-EDTA complex is large and the color of the free indicator is distinctly different from that of the metal-indicator complex. 

The comparison of dependencies o(oc) obtained under conditions of constant force and constant strain velocity indicates that the strain velocities are approximately similar at the points of their crossing. 

The two become equal upon cessation of flow when the mold is full. The difference I — P2 indicates the pressure drop over the sprue and runner system. The pressure drop across the gate is given approximated by P2 — Pj,. We note that just downstream of the gate, the pressure P3 increases with time throughout the filling process (from about 0.4 s to 1.3 s). As Example 13.1 pointed out, such a pressure trace approaches conditions of constant filling rate. This is supported by ram position measurements, which were also retrieved at 0.02-s intervals. We further note that, upon mold filling, when P5 sharply increases, there is also a steep increase in all the pressures except the nozzle pressure, which is then reduced to 5500 psi. 

The electronic nature of silylsilver intermediate was interrogated through inter-molecular competition experiments between substituted styrenes and the silylsilver intermediate (77).83 The product ratios from these experiments correlated well with the Hammett equation to provide a p value of —0.62 using op constants (Scheme 7.19). Woerpel and coworkers interpreted this p value to suggest that this silylsilver species is electrophilic. Smaller p values were obtained when the temperature of the intermolecular competition reactions was reduced [p = — 0.71 (8°C) and —0.79 (—8°C)]. From these experiments, the isokinetic temperature was estimated to be 129°C, which meant that the product-determining step of silver-catalyzed silylene transfer was under enthalpic control. In contrast, related intermolecular competition reactions under metal-free thermal conditions indicated the product-determining step of free silylene transfer to be under entropic control. The combination of the observed catalytically active silylsilver intermediate and the Hammett correlation data led Woerpel and colleagues to conclude that the silver functions to both decompose the sacrificial cyclohexene silacyclopropane as well as transfer the di-terf-butylsilylene to the olefin substrate. 

This indicates that any irreversible process, if occurring at constant entropy S and pressure p, is accompanied by a decrease in the enthalpy from the initial high level Hjnijal toward the final low level Hfiml of the system. From the foregoing we see that the internal energy and enthalpy may play the role of thermodynamic potentials for an irreversible process if occurring under the condition of constant entropy S. This condition of constant entropy, however, is unrealistic because entropy S contains both created entropy Sirr and transferred entropy Sm. 

This equation indicates that the affinity corresponds to the thermodynamic potentials of U and H under the conditions of constant entropy S and to the thermodynamic potentials of F and G under the conditions of constant temperature T. 

---