Equation constants, determining

Enthalpies of activation are comparable but entropies differ. The maximum number of ligands is two, and the formation constants determined (equation 10) were /Jj = 1013 and / 2 = 10. 136... 

A proportional determinate error, in which the error s magnitude depends on the amount of sample, is more difficult to detect since the result of an analysis is independent of the amount of sample. Table 4.6 outlines an example showing the effect of a positive proportional error of 1.0% on the analysis of a sample that is 50.0% w/w in analyte. In terms of equations 4.4 and 4.5, the reagent blank, Sreag, is an example of a constant determinate error, and the sensitivity, k, may be affected by proportional errors. 

Equation 11.16 can be solved for the metal ion s concentration if its activity coefficient is known. This presents a serious complication since the activity coefficient may be difficult to determine. If, however, the standards and samples have an identical matrix, then yM + remains constant, and equation 11.16 simplifies to... 

The speed at which a sphere roUs down a cylindrical tube filled with a fluid or down an angled plate covered with a film of the fluid also gives a measure of viscosity. For the cylindrical tube geometry, equation 35, a generalized form of the Stokes equation is used for any given instmment, where p is the translational velocity of the rolling sphere and k is the instmment constant determined by caUbration with standard fluids. 

The actual form of an available chlorine bleach in solution must be determined from equations 1—4. The equiUbrium constants for equations 2 and 3 are 3.94 x 10 (9) and 2.88 x 10 M (10) at 25°C, respectively. Thus, above pH 9.5 more than 99% of the available chlorine is present as... 

Tj = expander inlet temperature I p = expander expansion ratio Cp, k = gas constants determined by the gas equations... 

A sizing constant of 1.2 can be used to make a reasonable approximation of many commercial sizes. The constant, c, varied from 1.11 to 1.27 for a number of the frames investigated. With the displaced size approximated, the delivered volume can be calculated. Use Equation 4.10 and an assumed volumetric efficiency of. 90. This is arbitrary, as the actual volumetric efficiency varies from. 95 to. 75 or lower for the higher differential pressure applications. Once a slip speed has been determined. Equation 4.9 can be used to complete the calculation. The tip speed should stay near 125 fps. 

Equation constants determined from isotherm curve fitting... 

The range of concentrations that could be used was somewhat restricted due to the immiscibility of certain solvent mixtures. The data given in Table 1 was fitted to equation (16) and the various constants determined. Employing the constants derived from the curve fitting process, the theoretical values for the retention volumes, at the... 

A reading of Section 2.2 shows that all of the methods for determining reaction order can lead also to estimates of the rate constant, and very commonly the order and rate constant are determined concurrently. However, the integrated rate equations are the most widely used means for rate constant determination. These equations can be solved analytically, graphically, or by least-squares regression analysis. 

In this equation, a is a constant determining the size (radial extent) of the function. The exponential function is multiplied by powers (possibly 0) of x, y, and z, and a constant for normalization so that the integral of over all space is 1 (note that therefore c must also be a funrtion of a). 

Attempts to determine the equilibrium constant for Equation (60), applying the method proposed by Fialkov [313] for an AB2 = A+2B type interaction, provided values that defy physical logic. This means that the equilibrium in Equation (60) shifts almost completely to the left, and that it is also disturbed by A + B = AB type interactions [313], which, in this case, correspond to the interaction F" + TaFs = TaF6". Due to the improbability of the presence of TaF5 in the melts, it makes more sense to attribute the TaFg ions to the equilibrium described in Equation (61), which provides an analogical effect on the additive values of the property. 

This determines the distance of closest approach in terms of the initial relative velocity, the impact parameter, and the dynamical quantities (masses and force law constants). The equation for the orbit of the relative motion is found from the first of Eqs. (1-8) and (1-9), using the identity (fj6) = (drjdd), as follows ... 

As mentioned earlier, radicals that do not react can go on a random walk and may meet later at time complex constant determined... 

Equation links time and concentration through the rate constant, and Equation links the rate constant to the half-life. Knowing a half-life, we can calculate the rate constant using Equation. Then the value of the rate constant and Equation can be used to determine the time required to reach a certain concentration. 

It is expected from the equilibrium ratios for equation (1-90) that the Ag/Au ratios of native gold and electrum are controlled by temperature and EAg/EAu in ore fluids, although the equilibrium constant for equation (1-90) has not experimentally been determined. 

Comproportionation equilibrium constants for Equation 9.3 between dications and neutral molecules of carotenoids were determined from the SEEPR measurements. It was confirmed that the oxidation of the carotenoids produced n-radical cations (Equations 9.1 and 9.3), dications (Equation 9.2), cations (Equation 9.4), and neutral ir-radicals (Equations 9.5 and 9.6) upon reduction of the cations. It was found that carotenoids with strong electron acceptor substituents like canthaxanthin exhibit large values of Kcom, on the order of 103, while carotenoids with electron donor substituents like (J-carotene exhibit Kcom, on the order of 1. Thus, upon oxidation 96% radical cations are formed for canthaxanthin, while 99.7% dications are formed for P-carotene. This is the reason that strong EPR signals in solution are observed during the electrochemical oxidation of canthaxanthin. 

A value of kjkp = 17 000 has been determined for partitioning of the acetophenone oxocarbenium ion [12+] in water.15,16 It is not possible to estimate an equilibrium constant for the addition of water to [12+], because of the instability of the hemiketal product of this reaction. However, kinetic and thermodynamic parameters have been determined for the reaction of [12+] with methanol to form protonated acetophenone dimethyl ketal [12]-OMeH+ and for loss of a proton to form a-methoxystyrene [13] in water (Scheme 10).15,16 Substitution of these rate and equilibrium constants into equation (3) gives values of AMeoH = 6.5 kcal mol-1 and Ap = 13.8 kcal mol-1 for the intrinsic... 

Compare a log-log plot of /xa against N with a log-log plot of ixa against y experimentally determined using a viscometer. Plot y against N on ordinary Cartesian coordinates for corresponding values of g,a. The plot is a straight line of slope k which is the dimensionless proportionality constant in equation 5.1. 

The rate constants and interlayer distances determined from X-ray diffraction patterns for the intercalation studies described above are given in Table V. In those systems where intercalation causes large changes in the interfacial potential (ZrP and TiS2), Equations 32 and 33 were modified using intrinsic rate constants. In cases where steady state reactive intermediates were postulated, the rate constants in Equations 32 and 33 were modified as shown in Table V. 

Oxygen + water. Battino s recommended four constant equation from an earlier work (5 ) was used to represent the low temperature (273-348 K) mole fraction oxygen solubility values. The data determined at the Battelle Memorial Institute laboratories in the early 1950 s (10,12) were used to estimate the one atmosphere oxygen pressure solubilities at higher temperatures. The data sets were combined in a linear regression to obtain the parameters of the three constant tentative equation for the solubility between 350 and 600 K (Table V, Figure 9). 

It has been recently reported that, contrary to previous assumptions, primary steric effects due to a branching in the amine do not produce a large decrease in the reaction rate when the first step is rate-determining82. In Sat Ar reactions of amines with fluoronitroben-zene, it is generally accepted that the second step of the mechanism depicted in Scheme 1 is rate-determining base catalysis is frequently found and the observed rate constants obey equation 2. Nevertheless, the reaction of o-fluoronitrobenzene with n- and iso-propylamine in toluene and in DMSO are only slightly sensitive to the nucleophile concentration. The... 

Equation (65) can have many roots. For each of these values of (x/m) there exists a value of (z/x) and a value of (y/x), as determined by Eqs. (66) and (67). But since Eqs. (68)-(70) contain only positive constants, these equations provide criteria that the roots must satisfy in order that they apply to the model. Thus, according to Eq. (68), (x/u) > 1 according to Eqs. (69) and (70), both (z/x) and (y/x) must be positive. Since (x/u), (z/x), and (y/x) are linked, rejection of one root means that the two associated roots must also be rejected. In the 1-butene case we were thus able to remove the multiple-root problem from Eq. (65), although we have not proved that such removal can always be accomplished by using these two criteria. 

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