INSTITUTE OF SCIENCE       www.instituteofscience.com DIRECT CALCULATION OF HYDRATION NUMBERS FOR LIGHTER IONS (Nature SXA011*) Hydration numbers calculated from conductance ----- three steps: (a) total ionic weight is derived as inverse-square of conductance; (b) weight of anhydrous solute is subtracted from total ionic weight to derive weight of water of hydration; (c) weight of water of hydration is divided by weight per water unit (18) to derive number of water units (hydration number). ----- illustrating and validating Lewis Herrick Flint's description of hydrational potentiality (which may in the future be referred to as Flint's Laws Of Hydration): H (hydration number) = 23n - Z+C; when Z = atomic number; C = valence; and n=1 for (Z+C)=0-23, n=2 for (Z+C)=23-46, n=3 for (Z+C)=46-69, and n=4 for (Z+C)=69-92. Equation used in calculations: Hcalc = (k/(conductance2) - AW)/18; k=517336 AN INVERSE LINEAR RELATION BETWEEN: ATOMIC-NUMBER-PLUS-VALENCE; AND HYDRATION NUMBERS DERIVED FROM IONIC WEIGHTS CALCULATED AS INVERSE-SQUARE-OF-CONDUCTANCE/MOBILITY PER LAW OF KINETIC ENERGY by Stuart Hale Shakman, P.O. Box 382, Santa Monica, CA90406; ae735@lafn.org 26 September 1996 For cations with Z = 3-191 -- Li+, Na+, Mg++, Al+++ and K+ -- an approximate inverse linear relation between calculated hydration numbers (H) and sums of atomic number (Z) plus valence (C) is exhibited when solute ionic weight is calculated as the inverse-square-of-conductance and adjusted to a base weight value of 85.4768 for Rb+. The subtraction of atomic weights (A.W.) from solute ionic weights yields calculated values for the weights of water of hydration, against zero2 for Rb+; weights of water of hydration, divided by the weight of a single water unit, 18, yield calculated hydration numbers. (See Table 1). Figure 1 plots calculated hydration numbers against respective sums of atomic number and valence. The inverse linear result shown in Figure 1 illustrates the essential foundation of a methodology first discussed by L. H. Flint in 19323, wherein, for the hydrated lighter ions, Z + C + H was proposed to equal 23. As shown in Table 1 and Figure 1, calculations for H+, OH-, and the base ion, Rb+, also yield an approximate linear result at H = 0. The suggestion that relatively large conductivities of H+ and OH- indicate they are not hydrated was first made by Abegg and Bodlander4, first calculated by Flint3, and explained by Flint as evidencing dehydration due to the electrical stress imposed in measuring conductance5. 1. Noggle, J.H., Physical Chemistry, 1996, p. 411. 2. Gluekauf, E., Faraday Soc., Transactions 51 1241 (1955). 3. Flint, L. H., J. Wash. Acad. of Sci. 22, 97-119, 211-217 & 233-237 (1932). 4. Abegg and Bodlander, Zeit. f. Anorg. Chem. 454-499 (1899). 5. Flint, L.H., Dissenting Ape, Dahlia Street, New York, 1973.2 Table 1: Inverse square of limiting ionic conductance (l) adjusted to base weight of 85.47 for Rb+; minus respective atomic weights (A.W.), equals weight of water of hydration, divided by 18 equals calculated hydration number (H). ``` ION C Z A.W. Cond. 517336/ -A.W. /18 Hcalc+Z+C (Cond.2) =IONIC =WATER =Hcalc WEIGHT WEIGHT Rb +1 37 85.4678 77.8 85.47(BASE) .00 .00 Li +1 3 6.941 38.69 345.59 338.65 18.81 22.81 Na +1 11 22.989768 50.11 206.02 183.03 10.17 22.17 Mg +2 12 24.3050 53.06 183.75 159.45 8.86 22.86 Al +3 13 26.981539 63 130.34 103.36 5.74 21.74 K +1 19 39.0983 73.50 95.76 56.66 3.15 23.15 H +1 1 1.0078 349.8 4.23 3.22 .18 OH -1 9 17.00734 197.6 13.25 -3.76 -.21 Figure I. Correlation of calculated hydration numbers (H) with sums of atomic numbers and valences (Z+C) Z+C: 38- * 0 (Rb+ = BASE) 37- | 36- 35- | 34- 33- | 32- 31- | 30- 29- | 28- 27- | 26- 25- | 24- 23- | 22- 21- | 20- * 3.15 (K+) 19- | 18- 17- | 16- * (Al+++ = 5.74) 15- | 14- * (Mg++ = 8.86) 13- | 12- * (Na+ = 10.17) 11- | 10- 09- | 08- * (OH- = -.21) 07- | 06- 05- | 04- * 18.81 (Li+) 03- | 02- * (H+ = .18) 01- | 00-------------------------------------------------------------------------------------------------- | | | | | | | | | | | | | | | | | | | | | | | | H: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 ``` *The above article was submitted to Nature, 26 Sept. 1996 as proposed scientific correspondence; registered by Nature as SXA011; and subsequently rejected without further explanation: Associated Correspondence IOS BOOKS Copyright 1996, 1998 S H Shakman. All rights reserved.   Email: mail@instituteofscience.com