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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

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