Weighted average charge calculations

The first step in the calculation of a weighted average charge is to identify and quantify each of the metal species in solution. Equations to represent the total concentration—free ion and all complexed forms— are written for each metal in the sample solution  

The concentration of each metal complex is then rewritten using equations similar in form to eqns. 5-7  

The mole fraction of each metal species is then calculated and used to quantify the species in solution. The mole fraction of a mononuclear metal complex is represented by  

Equation 23 readily simplifies to show that the mole fraction of any mononuclear complex MLj is independent of the concentration of metal ion in solution  

Although there are no literature reported a-HIBA equilibria for aluminum, indium, or scandium, experimental evidence showed the elution 

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CALCULATED WEIGHTED AVERAGE CHARGE FOR LANTHANIDE IONS IN A SOLUTION CONTAINING 3.0 mM a-HIBA AT pH 4.5... 

CALCULATED WEIGHTED AVERAGE CHARGE FOR SOME METAL CATIONS IN A SOLUTION CONTAINING 58.2 mM a-HIBA AND 8.8 mM TARTARIC ACID, pH 4.1... 

Self-diffusion coefficients of distinct mobile species measured using PFG-NMR are based on spectral selectivity. In the context of IL selfdiffusion, PFG-NMR measures the time-averaged (miUisecond timescale) diffusion coefficients. Since ion-pair (cation-anion) interactions take place on a timescale faster than that, the measured diffusion coefficients are a weighted average over charged and neutral species. This is the reason for the variation between conductivity calculated from diffiasion coefficients determined by the Nemst-Einstein equation [15] (Eq. 1) and conductivity measured using impedance analysis ... 

The C stack calculation involved the positions (more precisely, the weighted averages of the probability distributions of the atomic nuclei) of five water clusters around a cytidine molecule (and five clusters in the planes above and below) computed by dementi s group with the aid of the Metropolis-Monte Carlo method. The five water clusters together contain 37 water molecules (see Figure 7.1). If three of their planes are selected, one has to construct the resultant effective potential of 111 water molecules. This was carried out with the help of the first (point-charge) version of the MCF method (see Section 6.2.1). 

Figures. Electrospray ionization/Fourier transform mass spectrum of poly(propylene glycol) 720. Only the single charge state oligomeric species are observed. The weight average molecular weight calculated from the mass spectrum is 687.

The functions Pcu(c,q) for the fee alloys can be averaged over the concentration c to obtain a probability Pcu(Q) that a Cu atom in any fee alloy will have a charge between q and q+dq. Recall that all of our calculations for fee were carried out with the same lattice constant. We approximate this function by averaging over the five concentrations that we considered, giving equal weight to all of them. It can be seen from the plot of this function in Fig. 5 that the probability is not uniform in q, but has thirteen prominent peeks. Since there are twelve atoms on the nearest-neighbor (nn) shell in a fee lattice, it is reasonable to write Pcu(q) as the sum of conditional probabilities Pcu(ci.q) where ci is the concentration of Cu atoms on the nn-shell. Five of the possible thirteen conditional probabilities are also plotted in... 

Fig. 2.2. Average electrostatic potential mc at the position of the methane-like Lennard-Jones particle Me as a function of its charge q. mc contains corrections for the finite system size. Results are shown from Monte Carlo simulations using Ewald summation with N = 256 (plus) and N = 128 (cross) as well as GRF calculations with N = 256 water molecules (square). Statistical errors are smaller than the size of the symbols. Also included are linear tits to the data with q < 0 and q > 0 (solid lines). The fit to the tanh-weighted model of two Gaussian distributions is shown with a dashed line. Reproduced with permission of the American Chemical Society...

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