Theoretical ratio

Caustic Soda to Chlorine Balance. In 1988, the ratio of U.S. caustic soda to chlorine consumption was 0.96 1 (see Fig. 39). Since 1968 this ratio has ranged from alow of 0.88 1 (1978 and 1981) to a high of 0.98 1 (1969). No single factor can explain these variations, since caustic soda and chlorine, with few exceptions, have different markets and are therefore not driven by the same economic forces. This ratio is expected to trend upward over the next five years, however, since caustic soda consumption in the United States is forecasted to grow somewhat faster than chlorine consumption. It is expected that this ratio will remain within the range experienced in 1970—1990. Because caustic soda is co-produced with chlorine at a theoretical ratio of 1.1 1, a U.S. consumption ratio below that level results in excess avaHabihty of caustic soda. This material is typically shipped offshore to fill a significant export demand, and in 1988, for example, net U.S. exports of caustic soda amounted to 7.1% of production. 

Fig. 5.10. Illustration of the signal-to-noise ratio. The first isotopic peak of toluene molecular ion, m/z 93, (70 eV El, R = 4000) shows about S/N = 250, whereas the second isotopic peak at m/z 94 has S/N = 10. The theoretical ratio of intensities of m/z 92 93 94 = 100 7.7 0.3, i.e., the ratio of intensities also reflects the S/N ratio.

Experimental and theoretical ratios for paired reflections in Cr are listed in Table 11.1. The ratios are listed such that the reflection with the smallest value of h4 + k4 + l4 is in the numerator. It is evident that the reflections with smaller values of h4 + k4 + l4 are more intense by 1-2.5%, indicating a preferential occupancy of the t2g orbitals, which in the bcc structure are directed towards the nearest neighbors. 

Okada (Ref 15) states that the oxygen to carbon ratio for LOX of maximum brisance is 2.6. This is essentially the theoretical ratio to convert all the carbon to C02. This writer believes that Okada really meant maximum strength rather than maximum brisance, as the latter depends not only on compn but also on pack-... 

This value falls below the theoretical ratio for these isotopes but is based on the same efficiency and half-life data which were used to derive the atoms/Mg relationships. Therefore, we will find fa and fa so that the ratio of the total 137Cs to the total 155Eu equals 8.14. It is a property of the lognormal form of distribution function that if particle mass distribution is described by x and a, then the surface/volume distribution is given by (4) ... 

Meares and his collaborators are especially interested in transport processes across biological membranes. They wish to distinguish experimentally between the active and the passive transport of a solute. For that purpose they determined the fluxes of the sodium ions in each direction through the membrane, using the technique of radio-tracers. The ratio of these experimental fluxes was compared with the theoretical ratios. The same is done with regard to the chlorine ions. 

Potassium iodide prepared as described has been used in a very careful study of the absolute accuracy of the poten-tiometric iodide-silver titration,2 by comparing it directly against pure silver. The ratio KI Ag found in this way agreed to within 0.02 per cent with the theoretical ratio. This small deviation is to be attributed to a slight absorption of iodide ions by the silver iodide at the potentiometric end point and not to an impurity in the potassium iodide. 

The theoretical ratio of chlorine to phenol required for complete oxidation is about 6 1. For m-cresol the ratio is 3.84 1 (1). However, because of the presence of other chlorineconsuming compounds, such as oils from the preservatives employed and carbohydrates leached from the wood, much higher ratios are... 

Fig. 4. Change of the gas phase composition during conditioning of y-alumina using CHCFF at 532 K. (a) concentration of haloalkanes in the gas phase (b) concentration of HC1 released (c) dismutation ratio (dm = 1 represents the theoretical ratio) (reproduced with permission from J. Prakt. Chem., 334 (1992) 591 [53]).

Compare your experimental ratios with those calculated theoretically, and make any deductions you can about the rotational and vibrational contributions, taking due account of the uncertainties in the experimental values. For CO2, how would the theoretical ratio be affected if the molecule were nonlinear (such as SO2) instead of linear Could you decide between these two structures from the Cp j Cy ratio alone ... 

From the average value of the spacing X/2 between adjacent nodes and the known frequency f, calculate the speed of sound cin each gas. Use Eq. (24) to calculate y, and compare these experimental values with the theoretical values predicted by the equipartition theorem. In the case of N2 and CO2, calculate the theoretical ratio both with and without a vibrational contribution to C of R per vibrational degree of freedom. 

Optional At 273 K, 7 23 (for He-Ar) is 0.653 cm s . From Du, Di, and D23 at room temperature, calculate c/12, c/13, and c/23. (To correct diffusion constants from one temperature to another, assume a dependence if the temperature change is small. This is only approximate, since the ds may vaiy in some degree with the temperature.) Then obtain d-[, di, and c/3 and use these to calculate D, Di, and D, from Eq. (V-35). Determine the ratios of the self-diffusion constants to their respective viscosities. How do these compare with the theoretical ratios discussed in the introductory section of Chapter V ... 

For both the enol and the keto forms, compare experimental and theoretical ratios of the integrated intensities for different types of protons (e.g., methyl to methylene protons in the keto form). 

The matrix element is always quite small and, as indicated in the Solid State Table, we take — 0, and drop the final term in Eq. (20-4). This step was taken to reduce the number of free parameters before theoretical ratios between them had been established. In a subsequent analysis it would probably be better to retain all the free parameters. F"or the particular case of Eq. (20-4), the interatomic matrix element is the same for all nearest neighbors, and is + 2/9Vjj . 

More importantly the fifth ligand apparently has greatly reduced the memory effect on the mass spectrometer. The results of a repeat of our earlier experiment where we inject natural zinc enriched zinc and natural zinc are shown in Figure 5. The solid lines shown with each set represent the theoretical ratios. Firsts it is clear that we have essentially eliminated the memory and approached the theoretical ratios from either natural or enriched solution. This in Itself represents a substantial step forward. Second, it is Important to note that we have not completely eliminated the memory effect. A loading dose of 5 to 10 times the injected amounts is necessary to eliminate the final vestiges of earlier injections. Again, work is currently in progress to help understand the causes of this effect and to eliminate them. 

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