Ion calculations

Given Ksp and the equilibrium concentration of one ion, calculate the equilibrium concentration of the other ion. 

Monoisotopic mass The mass of an ion calculated using the exact mass of the most abundant isotope of each element in the formula (e.g., C = 12.0000, O = 15.9949). 

Prediction of the energy level structure for Pu2+ (5f ) is of particular interest since no spectra for this valence state of Pu have been reported. On the basis of what is known of the spectra of Am2+ (26), Cf2" (27), and Es2+ (28), there appears to be evidence for a very small crystal-field splitting of the free-ion levels. Such evidence encourages use of a free-ion calculation in this particular case. The parameter values selected are indicated in Table V. Based on the systematics given by Brewer (19), the first f- d transition should occur near 11000 cm-, so the f- -f transitions at higher energies would be expected to be at least partially obscured. A... 

The initial kinetic energy of 0 ions produced by dissociative attachment in 02 at an electron energy of 6.9 e.v. may be determined from Equation 4 to be 1.64 e.v. using values of 1.465 e.v. (1) for A(0) and 5.09 e.v. (7) for D(O—O). The residence time for 0 ions calculated from Equation 1 is 6.0 X 10 7 sec. at 10 volts repeller potential. Rate constants for Reaction 6 determined from data at varying Vr are shown in Table I and are seen to increase sharply with increasing repeller potential, as expected for an endothermic process. 

In Table IV are given values of the mole refraction of gaseous ions calculated from equations (24) and (29) with the use of the values found above for SE and ASe. Values for hydrogen-like atoms and ions are also included these are, of course, accurate, since no screening constant is needed. Table IV is... 

Finally, beyond the second stoichiometric point the pH is determined by the amount of excess hydroxide ion. Calculate the amount of hydroxide ion in 1.00 mL of the NaOH solution ... 

The surface potential of a solution can be calculated, according to Eq. (10.18), from the dilference between the experimental real energy of solvation of one of the ions and the chemical energy of solvation of the same ion calculated from the theory of ion-dipole interaction. Such calculations lead to a value of -1-0.13 V for the surface potential of water. The positive sign indicates that in the surface layer, the water molecules are oriented with their negative ends away from the bulk. 

The total amounts of hydroxide ions, calculated by summing moles of 0H added (as NaOH, Pr NOH, sodium aluminate or sodium silicate) and by substracting moles of acid added (as H2SO4 or aluminium sulfate), are 16.45, 19.3 and 8.8 for mixtures A, B and B respectively. Their final ingredient molar ratios are compared in Table I. 

Negative of the Energies (Atomic Units) of Some Negative Ions Calculated with the Potential Wx Equation 7.34... 

Table 9.1 presents excitation energies for a few atoms and ions. Calculations were performed with the generalized KLI approximation [69,74], For comparison, experimental data and the results obtained with the local-spin-density (LSD) exchange-correlation potential [75] are shown. The KLI method contains only the exchange. 

Figure 7. Potentials for lower and upper surfaces in Creutz-Taube ion calculated by method of Piepho, Krausz, and Schatz, as function of dimensionless coordinate, y, with J = 0.4 eV,

I have predicted that the very unusual low-frequency IR behavior for the Creutz-Taube ion calculated by Piepho, Schatz and Krausz [Piepho, S. B. Krausz, E. R. Schatz, P. N. J. Am. Chem. Soc. 1978, 100, 2996] on the assumption of only antisymmetric mode involvement in electron-vibrational interaction would not be found, and that it was an artifact of the method. The failure of experiments designed to locate such IR bands has subsequently been reported by Krausz, et al. 

Fig. 1. This figure shows the electron energies of the H2 ion calculated using the Shibuya-Wulfman technique, with 15 orbitals on each center. The nearly-exact values of Koga and Matsuhashi are indicated by dots for the ground state. Excited states with m = 0 are also shown.

Table 1 po for the first few isoelectronic series of atoms and ions, calculated in the crudest approximation. E = -pI/2. 

Table 1. Energy-level diagram for the free C -3+ ion. (Calculated values include L—S coupling to first order) A was chosen to be 90 cm J...

Table IV gives the relative catalytic reactivities of the various ions calculated on the basis that the undissociated ion given is the catalytic species.

Tab. 7.3 Solvation numbers of ions calculated from the effective ionic radii...

The conductivity curve for the hydrogen sulphate ion calculated by means of this equation is shown in Fig. 2. It may be seen that it predicts a much smaller decrease in the equivalent conductivity than... 

Figure 3. Surface density N of adsorbed sulfide ions calculated from the change in flatband potential V/6 reported in Ref. 26 (27J.

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