Ratio method

Both the method of continuous variations and the mole-ratio method rely on an extrapolation of absorbance data collected under conditions in which a linear relationship exists between absorbance and the relative amounts of metal and ligand. When a metal-ligand complex is very weak, a plot of absorbance versus Ay or n-J m may be curved, making it impossible to determine the stoichiometry by extrapolation. In this case the slope ratio may be used. 

In the slope-ratio method two sets of solutions are prepared. The first set consists of a constant amount of metal and a variable amount of ligand, chosen such that the total concentration of metal, Cm, is much greater than the total concentration of ligand. Cl- Under these conditions we may assume that essentially all the ligand is complexed. The concentration of a metal-ligand complex of the general... 

An important assumption in the slope-ratio method is that the complexation reaction continues to completion in the presence of a sufficiently large excess of metal or ligand. The slope-ratio method also is limited to systems that obey Beer s law and in which only a single complex is formed. 

This experiment describes the use of FIA for determining the stoichiometry of the Fe +-o-phenanthroline complex using the method of continuous variations and the mole-ratio method. Directions are also provided for determining the stoichiometry of the oxidation of ascorbic acid by dichromate and for determining the rate constant for the reaction at different pH levels and different concentration ratios of the reactants. 

A second order-of-magnitude approach is the ratio method, based on the assumption that capital investment can be correlated with plant capacity in a manner similar to that used for equipment. This gives... 

The ratio method is also particularly useful for quick estimates over a range of capacities after a calculated estimate for one size has been made (10). The calculated estimate can be separated into groups C, C2,. .., according to individual equipment exponents n, n2,. Then an overall plant capacity exponent n can be calculated from... 

It has been proved lately that the NAA method of Mo determination meets the requirements of primary ratio methods of measurements. 

An alternative approach to the quantitative analysis formalism is the ratio method. Here we consider the ratio of the intensities of any two edges A and B. Using Equation (3) we can show that... 

The accuracy achievable by the ratio method amounts to approximately 5-10 atom% when ionization edges of the same type are used, i. e. only K edges or only L edges, whereas the error in quantification increases to +15-20 atom% for the use of dissimilar edges. Improvement of the quantification accuracy up to approximately 1 atom% is possible if standards are used. 

An established design method for this type of system is not available. The practical design of the low-momentum supply with exterior hood system described in the previous part of this section used the flow ratio method. How-evec, the actual exhaust flow rate was adjusted visually to the appropriate value in order to exhaust only the contaminants transported by the supply airflow. 

The flow ratio method was first suggested for use in designing receptor hoods and then it was suggested for design of push-pull systems. The concept of the method is described as follows. 

Applying the flow ratio method to the low-momentum supply system, the required exhaust flow rate is often in excess of practical values. This is because the value of is given as the value at which all the supplied airflow should be exhausted by the exterior hood. In the low-momentum supply system, contaminant sources should usually be between the supply inlet and the exterior hood. The supply airflow is contaminated at the position of the sources and it flows to the exterior hood. Therefore, all of the airflow is not always contaminated. Unfortunately, a design method considering such cases (the diffusion of contaminants within the airflow) has not been established yet, and the appropriate exhaust flow rate has to be adjusted after the system is installed. 

The method of evaluation of the rate constants for this reaction scheme will depend upon the type of analytical information available. This depends in part upon the nature of the reaction, but it also depends upon the contemporary state of analytical chemistry. Up to the middle of the 20th century, titrimetry was a widely applied means of studying reaction kinetics. Titrimetric analysis is not highly sensitive, nor is it very selective, but it is accurate and has the considerable advantage of providing absolute concentrations. When used to study the A —> B — C system in which the same substance is either produced or consumed in each step (e.g., the hydrolysis of a diamide or a diester), titration results yield a quantity F = Cb + 2cc- Swain devised a technique, called the time-ratio method, to evaluate the rate... 

Pp = pressure pulsation magnitude, peak-to-peak, psi = pulsation attenuation by area-ratio method, or... 

Three different forms of EPR test can be employed, designated as the single loop, double loop and reactivation ratio methods in Figure 19.20. 

Entry Substrate ratio, (method)[b] Aziridine Scale (mmol) Yield1 1 (mp)... 

In both the standard oxygen analytical procedure and the Cu/O ratio method, the primer was counted for 20 sec following a 25 sec irradiation and a 4.5 sec transfer from completion of irradiation to start of count... 

This feasibility study shows that determination of pellet wt by fast neutron oxygen activation analysis can be used for quality assurance inspection of M34 primers. Either direct oxygen analysis, where a comparison standard (such as lucite) is used, or a ratio method, utilizing the Cu in the cup-anvil combination as an internal standard, can be applied. In general, the uniformity of production primers is quite satisfactory, as is usually the case where production procedures are standardized. It seems likely that the light pellet is one which has been improperly manufd and will probably be well below specifications in pellet wt. Production experience with such primers indicates that only one in 3x10s primers is expected to show low pellet wt therefore, one would not expect to find a reject in a small sampling. Nevertheless, detection and rejection of this one bad unit is critical for the prevention of weapon malfunctions and possible injuries to personnel... 

Modern instruments capable of obtaining excitation-emission matrices (EEMs) allow use of new data-analysis techniques to resolve overlapped spectra. Resolution techniques such as the ratio method (28) and others (29,30) may provide further differentiation of the components present in the phases separated by solvent extraction. 

White, J. W. (1992). Internal standard stable carbon isotope ratio method for determination of C-4 plant sugars in honey Collaborative trial study, and evaluation of improved protein preparation procedure. J. Assoc. Ojfic. Anal. Chem. 75,543-548. 

The absorbance ratio AnlAxi for the solute peak should be close to zero. If it is not, then this suggests that the peak is not what we think it is. For example, there may be another component that elutes at the same time, so the ratio method is a simple way of indicating the purity of the peaks. 

If we let and t2 represent the times corresponding to reaction progress variables and <5J, respectively, the time ratio t2/tl for fixed values of <5 and <5 will depend only on the ratio of rate constants k. One may readily prepare a table or graph of <5 versus k t for fixed k and then cross-plot or cross-tabulate the data to obtain the relation between k and ktt at a fixed value of <5. Table 5.1 is of this type. At specified values of <5 and S one may compute the difference log(fe1t)2 — log f) which is identical with log t2 — log tj. One then enters the table using experimental values of t2 and tx and reads off the value of k = k2/kv One application of this time-ratio method is given in Illustration 5.5. 

ILLUSTRATION 5.5 DETERMINATION OF RELATIVE RATE CONSTANTS USING THE TIME-RATIO METHOD... 

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