Metal cations linear regression

Figure 19. Variation in dimension of the X-fold cation site in alkali-feldspar for 2+ cations (), obtained by fitting the experimental data of Icenhower and London (1996) for Dca, >sr and Dsa at 0.2 GPa and 650-750°C. In performing the fits was set at 91 GPa for all runs. Error bars are 1 s.d. The positive slope is consistent with measured changes in metal-oxygen bond length from albite to orthoclase (cf Fig. 6). The solid line shows the best-fit linear regression given in Equation (35).

The solid curves in Fig. 3 were calculated by simultaneous non-linear least-squares regression of reaction-rate data at all alkali-metal cation concentrations (20 kobs values using three different cations) to the complex rate constant in eq 15. The calculation was performed subject to the stipulation that aU three curves converge to a single k value. (Convergence to a single kobs value, k, at infinite dilution is implicit to derivation ofeq 15.) Simultaneous analysis of the three curves (one for each of the cations, Li, Na and K ) provides unique values for rate and equilibrium constants, kMi and Kmi, i.e., for kui, knai, kxi, Kbii, KnbI and Kki. 

The rate constant in eq 15 is formally a function of activities of all species present. However, 1 and BPHi possess small initial concentrations, and these concentrations are identical at the outset of each experiment. As a result, variation in the activities of these components are much less significant than changes in the activities of the alkali-metal cations themselves (the experimental variable). The cation concentrations vary from 5 to over 200 mM (based on grams of MCI salt added per liter of solution). Therefore, to obtain meaningful ki, kMi and Kmi values by non-linear regression of the kinetic data, the number of adjustable parameters was restricted to the most significant activity coefficient,... 

Table 9 Multiple Linear Regression Coefficients for Standard Molar Gibbs Energies of Transfer for Alkali Metal Cations Based on Solvent Properties t, DN, 1/e, and...

FIGURE 2,25 Linear regression fit of (a) capacitances against the pH of H2SO4 electrolyte and (b) capacitances against the pK of KCl electrolyte solutions for RuOj electrode. (Reprinted from Electrochimica Acta, 50, Wen, S. et al.. The role of cations of the electrolyte for the pseudocapacitive behavior of metal oxide electrodes, MnOj and RuOj, 849-855,... 

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