H Calculations

We will In the following section look at methods for calculating pH values in a number of different solutions. 

---

STM and AFM profiles distort the shape of a particle because the side of the tip rides up on the particle. This effect can be corrected for. Consider, say, a spherical gold particle on a smooth surface. The sphere may be truncated, that is, the center may be a distance q above the surface, where q < r, the radius of the sphere. Assume the tip to be a cone of cone angle a. The observed profile in the vertical plane containing the center of the sphere will be a rounded hump of base width 2d and height h. Calculate q and r for the case where a - 32° and d and h are 275 nm and 300 nm, respectively. Note Chapter XVI, Ref. 133a. Can you show how to obtain the relevent equation ... 

Gilson, M. K., Sharp, K. A., Honig, B. H. Calculating the electrostatic potential of molecules in solution Method and error assessment. J. Comp. Chem. 9 (1988) 327-335. 

Because the datay are random, the statistics based on y, S(y), are also random. For all possible data y (usually simulated) that can be predicted from H, calculate p(S(ysim) H), the probability distribution of the statistic S on simulated data y ii given the truth of the hypothesis H. If H is the statement that 6 = 0, then y i might be generated by averaging samples of size N (a characteristic of the actual data) with variance G- = G- (yacmai) (yet another characteristic of the data). 

The value of this coefficient depends on the relative height of the flow along the floor h /H (calculated in the free conditions), where... 

Groie, S. H., Calculating Pressure Release Times. Chem. Eng., July 17, 1967, p. 203. 

Figure 5-5. Valence band spectra of r/wu-polyacetyienc, recorded using synchrotron radiation at 27 eV and 50 eV photon energy, and the corresponding DOVS derived from Vl-H calculations. The VEH band structure is shown in the lower part of the figure (from Ref. 1281).

H+], calculation of, 192, see also Hydrogen ion Haber, Fritz, 151 Haber process, 140, 150 Hafnium, oxidation number, 414 Haldane, J. B. S., 436 Half-cell potentials effect of concentration, 213 measuring, 210 standard, 210 table of, 211, 452 Half-cell reactions, 201 Half-life, 416 Half-reaction, 201 balancing, 218 potentials, 452 Halides... 

John, P. and Sachs, H. Calculating the Numbers of Perfect Matchings and of Spanning Tress, Pauling s Bond Orders, the Characteristic Polynomial, and the Eigenvectors of a Benzenoid System. 153, 145-180 (1990). 

A.25 The maximum ground speed of a chicken is 14 km-h". Calculate the kinetic energy of a chicken of mass 4.2 kg crossing a road at its maximum speed. 

The following plot shows how the partial pressures of reactant and products vary with time for the decomposition of compound A into compounds B and C. All three compounds are gases. Use this plot to do the following (a) Write a balanced chemical equation for the reaction, (h) Calculate the equilibrium constant for the reaction, (c) Calculate the value of Kc for the reaction at 25°C. 

To compute each of the n(ct ), one can generalize the methods used to compute ihG- Hence, the most elegant method would be to use basis functions that satisfy the boundary conditions of Eq. (43), if this were practical to implement. A more general method would be to extend the Mead-Truhlar vector-potential approach [6]. This approach would involve carrying out h calculations, each including a... 

Kim, K. H. Calculation of hydrophobic parameters directly from three-dimensional structures using comparative molecular field analysis. J. Comput.-Aided Mol. Des. 1995, 9,... 

The feed stream to a reactor contains ethylene 16 per cent, oxygen 9 per cent, nitrogen 31 per cent, and hydrogen chloride. If the ethylene flow is 5000 kg/h, calculate the individual component flows and the total stream flow. All percentages are by weight. 

If the maximum flow-rate required is 20,000 kg/h, calculate the pump motor rating (power) needed. Take the pump efficiency as 70 per cent and allow for a pressure drop of 0.5 bar across the control valve and a loss of 10 velocity heads across the orifice. 

Cagiao, J. Gomez, B. Domenech, J.L. Gutierrez Mainar, S. Gutierrez Lanza, H. Calculation of the corporate carbon footprint of the cement industry by the application... 

Calculate the percent composition of C2H4. (h) Calculate the percent composition of C4HK. (c) Compare the results and explain the reason for these results. 

Wang, C. X. Liu, H. Y. Shi, Y. Y. Huang, F. H., Calculations of relative free energy surfaces in configuration space using an integration method, Chem. Phys. Lett. 1991, 179, 475 178... 

Warwicker, J. Watson, H., Calculation of the electrostatic potential in the active site cleft due to a helix dipoles, J. Mol. Biol. 1982,157, 671-679... 

Energy changes are for the isodesmic reaction shown in Scheme 13.33 h Calculated from the ab initio energies of R-[16]-OH and R-[17].33... 

Surface Water t,A = 5.79 h, calculated half-life based on evaporative loss at 25°C and 1 m depth of water (Mackay Leinonen 1975). 

Surface Water t,/2 = 16 h (calculated for river water 1 m deep, water velocity 0.5 m/s, wind velocity 1 m/s from air-water partition coefficients (Southworth 1979 Hallett Brecher 1984)... 

Figure 11 Ladder H-calculated HOMO energy for oligosilanes with uniform dihedral angle, cj.228 Adapted with permission from Schepers, T. Michl, J. J. Phys. Org. Chem. 2002, 15, 490-498, 2002 John Wiley and Sons Ltd.

The different solvation energetics of R and R- will also lead to errors in the bond dissociation enthalpies calculated with equation 16.33. For instance, in the case of phenol, whose interactions with proton-acceptor solvents (like DMSO) are obviously stronger than those for the phenoxy radical, a negative correction should be applied to the value of Z)//°(PhO-H) calculated from equation 16.33 (see also equation 16.32). It is probably unwise to ascribe the 7 kJ mol-1 difference between the electrochemical and the recommended DH° (PhO—R) value to the differential solvation effects. Although this discrepancy is in the correct direction, it lies within the suggested uncertainty of the method. 

UQCISD/6-31G(d) geometries. h Calculated using experimental BDEs from Table 6.9. 

---