M 0 calculations

From a strictly quantum-mechanical point of view, the question of valence-shell expansion and d-orbital participation has two different aspects. One may either look for d-character in Lowdin s natural spin-orbitals of the complete, but unknown, total wave-function or one may ask the question whether the agreement with experimental results is ameliorated significantly when d-orbitals are included in the basis functions of approximate M. 0. calculations. It is a well known tendency for approximate calculations always to ameliorate in certain aspects when the basis is expanded, but also that the extent of this amelioration does not always bear a direct relation to the final results of far more sophisticated calculations. 

Dithiazoles. - Stable 1,3,2-dithiazolyl (404) and 1,3,2-dithiazolidinyl radicals (405), potentially useful spin probes and labels, result from reaction of SJ N2 with acetylenes435 436 and strained alkenes, respectively. Isotopic double labelling with 15N and 33S demonstrated the equivalence of the ring sulphur atoms. E.S.R. spectra have been analysed and M.0. calculations performed. 

Assuming that no other transfer reactions occur, calculate the values missing from the table. Criticize or defend the following proposition The v values obtained from the limit [SX]/[M] 0 show that the AIBN initiates polymerization identically in all solvents. 

Under 0 conditions occurring near room temperature, [r ] = 0.83 dl g for a polystyrene sample of molecular weight 10. f Use this information to evaluate tg and for polystyrene under these conditions. For polystyrene in ethylcyclohexane, 0 = 70°C and the corresponding calculation shows that (tQ /M) = 0.071 nm. Based on these two calculated results, criticize or defend the following proposition The discrepancy in calculated (rQ /M) values must arise from the uncertainty in T>, since this ratio should be a constant for polystyrene, independent of the nature of the solvent. 

The annual interest rate equivalent to a compound-interest rate of 5 percent per month (i.e., i /m = 0.05) is calculated from Eq. (9-38) to be... 

The heat effect per unit length by radiation and convection from a water-heated panel can be calculated theoretically. For example, consider panels of width 0.6 m, 0.9 m, and 1.2 m. Room temperature is 3 °C and surface temperature 30 °C, 50 °C, and 70 C of the panel. Let us compare the results with calculations for room temperature 15 °C and surface temperature 40 C, 60 "C, and 80 °C of the panel. 

At 25°C and 1.00 atm pressure, one liter of ammonia is bubbled into 725 mL of water. Assume that all the ammonia dissolves and the volume of the solution is the volume of the water. A 50.0-mL portion of the prepared solution is titrated with 0.2193 M HN03. Calculate the pH of the solution... 

The arcsine distribution is a good example of a situation where the notions of center and spread of the distribution must be taken with a grain of salt. The mean of this distribution is obviously located at its center of symmetry, m = 0. Its variance can now be calculated as follows ... 

E8.12 The melting point of 1,4-dichlorobenzene is 326.4 K and that of naphthalene is 353.4 K. The eutectic point occurs at a temperature of 303.4 K and a mole fraction of naphthalene in the liquid phase of 0.394. Assume ideal liquid solutions, no solid solubility, and ArusCp.m = 0 and calculate AfusHm for 1,4-dichlorobenzene. 

We have problems when we attempt to repeat this calculation in 0.010/77 KC1 and 0.010m KNO, since 7- is a function of the total concentration of ions, and, as we saw in Chapter 7, at m = 0.010 mol-kg-1, 7 differs significantly from one. Debye-Hiickel theory provides a method for calculating 7 for dilute solutions. 

Once a value of E° is obtained by extrapolation, the 7 corresponding to each molality can be obtained from equation (9.104). Figure 9.6 is a graph of ln7 calculated from Linhart s results plotted against m1/2. The Debye-Hiickel limiting law value is shown as the dashed line. The agreement is excellent below m1 2 = 0.10 (m = 0.03), which attests to the reliability of Linhart s work and the validity of the Debye-Hiickel limiting law. 

To compare the present results with those of DeCarvalho and Choppin, our results in 1 M acid must be corrected for the heat and entropy of HSOiJ ionization. Zebroski et al. (12) determined Ka = 0.084, while Zielen (9) gives the heat of ionization as AHa = +23.2 kj/m. The calculated entropy is ASa - +98 j/m-°K. 

Water flows at a velocity of 1 m/s over a plane surface 0.6 m wide and 1 m long. Calculate the total drag force acting on the surface if the transition from streamline to turbulent flow in the boundary layer occurs when the Reynolds group ReXc = 105. 

As charge-dipole interaction between the electron and the atom is small, the perturbation theory expansion may be used to estimate f. The odd terms of this expansion disappear after averaging over impact parameters due to isotropy of collisions. In the second order approximation only those elements of P that are bilinear in V are non-zero. Straightforward calculation showed [176] that all components of the Stark structure are broadened but only those for which m = 0 interfere with each other ... 

Spectral data from a (111) face of a crystal of magnesium stannide are given in Table I. Using the value of 3.591 for the density,2 these data place nz/m = 0.248 for the first reflection. No reflections were found on the Laue photographs with values of n less than 0.26 A. U., calculated for the unit containing four Mg2Sn, with n — 1, and di0o = 6.78 0.02 A. U. 

Results The raw data consisted of peak height ratios of signal internal standard, see data files VALIDl.dat (primary validation m - 0 repeats at every concentration), VALID2.dat (between-day variability), and VALID3. dat (combination of a single-day calibration with several repeats at 35 and 350 [ng/mlj in preparation of placing QC-sample concentration near these values). Fig. 4.29 shows the results of the back-calculation for all three files, for both the lin/lin and the log/log evaluations. Fig. 4.30 shows the pooled data from file VALID2.dat. 

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