Specific rotation calculation

In this table C is number of grams of solute per 100 cc. of solution, M is the number of mols of solute in 1000 cc. of solution and (a)D is the specific rotation calculated from the equation... 

From the mean specific rotations, calculations have been made, for each sugar, of the other data relating to polarimetric readings in circular degrees see Table XVI). For those sugars with which the rotatory power varies appreciably with concentration and temperature, these data are, of course, exact only at 20° and for the usual concentrations. 

Table 5 Timings (in hours) for four-wavelength CCSD specific rotation calculations ...

The observed rotation a of an optically pure substance depends on how many mol ecules the light beam encounters A filled polarimeter tube twice the length of another produces twice the observed rotation as does a solution twice as concentrated To account for the effects of path length and concentration chemists have defined the term specific rotation, given the symbol [a] Specific rotation is calculated from the observed rotation according to the expression... 

Cholesterol, when isolated from natural sources, is obtained as a single enantiomer. The observed rotation a of a 0.3-g sample of cholesterol in 15 ml of chloroform solution contained in a 10-cm polarimeter tube is -0.78°. Calculate the specific rotation of cholesterol. 

When the solution is just cold the crystals, previously le-moved, are sown evenly over the bottom of the dish at distances of I—2 cms. apart and left for two days. The crystals will have now grown to a size which will enable the facets to be readily recognised. Each crystal is dried and carefully examined with a pocket lens in order to determine the position of the hemi-hedral facets, and placed in separate heaps. These facets lie to the right or left hand of the central prism face, as shown in Fig. 74. The crystals should be weighed, dissolved, and the solution diluted and examined in the polarimeter. The specific rotation may then be calculated. See Appe7idix., p. 264. 

For solid substances the substance is dissolved in a neutral solvent and the specific rotation is calculated from the formula—... 

A comparison of the thus calculated with the measured specific rotations of the 0th- to 4th-generation dendrimers of this kind gave a close resemblance, with a curve, approaching asymptotically a limiting value (Fig. 26). It was also shown that the shape of this curve was independent of solvent, concentration and temperature. This was not the case when CD spectra of these dendrimers were compared (Fig. 27) in solvents such as CH2C12 and f-butyl methyl ether a constant rise of the Cotton effect was observed, which correlates with the increasing amount of benzene chromophores in the dendrimers. However, in the... 

Neomycins B and C have been shown to differ in their specific rotation values, neomycin B having a specific rotation of + 80° and neomycin C a specific rotation of + 120° 1 7. Brooks et al -2 made this fact the basis for a number of methods to determine the B C content of commercial neomycin. The specific rotation of the test solution is determined at 25°C and total neomycin determined either titrimetrically or spectro-photometrically. By substitution of these values in a suitable equation the concentration of neomycins B and C are calculated. In a second method the same authors determined the specific rotation of the test-solution at temperatures of 25° and 75°C. The change in the value of specific rotation on increasing the temperature from 25°to 75°C can then be used to calculate the amounts of neomycin B and C in the sample. 

In the simplest case, where (+)-AH and (-)AD are isotopically pure, a = [a]H[AH]0 and a2 = [a]D[AD]0 where a is the specific rotation of the AH and AD isotopomers, respectively, and [AH]0 and [AD]0 are the concentrations of the substrates in g ml-1 at time t = 0. When the substrate is neither isotopically nor enantiomerically pure, corrections must be made in calculating fli and a2 (Bergson et al., 1977). It is important to note that the pre-exponential factors, a and a2, which contain the information about the starting conditions, can be determined with high accuracy. The extreme, ae (the maximum or minimum value of the optical rotation in the optical rotation versus time plot) and the corresponding reaction time, te, are functions of the rate constant ratio (5 = kHlkD) (65) and the difference between the rate constants (66), respectively. 

An interesting method for the estimation of optical purity of sulfoxides, which consists of the combination of chemical methods with NMR spectroscopy, was elaborated by Mislow and Raban (241). The optical purity is usually determined by the conversion of a mixture of enantiomers into a mixture of diastereomers, the ratio of which may be easily determined by NMR spectroscopy. In contrast to this, Mislow and Raban used as starting material for the synthesis of enantiomeric sulfoxides a diastereomeric mixture of pinacolyl p-toluenesulfinates 210. The ratio of the starting sulfinates 210 was 60.5 39.5, as evidenced by the H NMR spectrum. Since the Grignard reaction occurs with full stereospecificity, the ratio of enantiomers of the sulfoxide formed is expected to be almost identical to that of 210. This corresponds to a calculated optical purity of the sulfoxide of 20%. In this way the specific rotations of other alkyl or aryl p-tolyl sulfoxides can conveniently be determined. 

At the startup of the line, the extruder was operated at 91 rpm to produce the required rate of 148 kg/h for a specific rate of 1.63 kg/(h-rpm). The temperature of the extrudate was measured through the transfer line wall at 232 °C. Due to process safety constraints the extrudate temperature could not be measured using a handheld temperature sensor. The extrusion rate was required in order to maintain the downstream take-away equipment at its maximum rate. At first the extruder appeared to be operating well except that the specific rate was lower than predicted. That is, the screw was rotated at an rpm that was higher than expected to produce the 148 kg/h. At 91 rpm, the rotational flow rate was calculated at 228 kg/h the specific rotational flow rate was calculated at 2.51 kg/(h-rpm). Thus, the line was operating at only 65% of the rotational flow rate. A barrier design... 

The iead iength was 124 mm for the main flight of the barrier section and 88.9 mm for all other sections of the screw. The main flight width and clearance were 9 and 0.09 mm, respectively, in all sections of the screw. The first 2.5 diameters of the screw were inside a water-cooled feed casing. The compression ratio was 2.7 and the compression rate was 0.0050. The specific rotational rate was calculated at 2.51 kg/(h-rpm). ... 

The injection-molding press was producing a part and runner system that had a mass of 2.15 kg. The mass was plasticated using a 120 mm diameter, 8L/D screw. The screw used for the process had a barrier melting section that extended to the end of the screw, as shown by the specifications in Table 11.9. That is, the screw did not have a metering channel. Instead, the last sections of the barrier section were required to produce the pressure that was needed to flow the resin through the nonreturn valve and into the front of the screw. The specific rotational flow rate for the screw for the IRPS resin was calculated at 9.3 kg/(h-rpm) based on the depth of the channel at the end of the transition section. The screw was built with an extremely low compression ratio and compression rate of 1.5 and 0.0013, respectively. For IRPS resins and other PS resins, screws with low compression ratios and compression rates tend to operate partially filled. The compression ratio and compression rate for the screw are preferred to be around 3.0 and 0.0035, respectively. The flight radii on the screw were extremely small at about 0.2 times the channel depth. For IRPS resin, the ratio of the radii to the channel depth should be about 1. 

Several mechanisms could cause the specific rate of the screw to be considerably less than the calculated specific rotational flow rate for the screw. These mechanisms include (1) normal operation for a screw with a very short metering section and a low-viscosity resin, (2) the screw is rate-limited by solids conveying, causing the downstream sections of the screw to operate partially filled, and (3) the entry to the barrier section is restricting flow (see Section 11.10.1) to the downstream sections of the screw and causing the downstream sections to operate partially filled. The goal was to determine which of the above mechanisms was responsible for the low specific rates for the plasticator. 

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