Crafts et al. — 36 — Water in Plants 



from Morse's data that give an idea of the corrections required to fit 

 formula (7) to observed values. Table 10 presents these values. 



Table 10. — Calculated hydration numbers for sucrose solutions at various tempera- 

 tures and concentrations: — 



Assuming again that hydration is a factor in determining the value of 

 b, hydration numbers have been calculated by Findlay (1919, Table 26) 

 for a set of determinations carried out by Berkeley and Hartley at 0° C. 



Since all of these hydration numbers were calculated in order to make 

 equation (P) fit the observed values, they simply indicate the correction 

 in volume required to account for the departure from ideal behavior of 

 these sucrose solutions. Since the attractive forces between adjacent 

 molecules have not been considered in these calculations, the whole devia- 

 tion has been thrown into the hydration number. 



The degree of hydration has not been established experimentally; the 

 above calculations are highly empirical. 



Equation (4) can be expressed in the form 



P„ = x(l + ^^x + ^x2 . . .) (Findlay, p. 61) (10) 



o 



If the concentration of the solution is expressed in terms of c gram- 

 molecules of solute in 1000 grams of water, x can be put equal to ^^ ^"^ ^ 

 where 55.5 represents the number of gram molecules in 1000 grams of 



1001.8 

 55.5 



water. Since the molecular volume of water at 20° C. is ., , , equation 



(10) may be written 



(81.6) (293) (55.5) 

 P 



1001.8 55.5 + c 



1 + 



\ 55.5 + c / 



(11) 



It has been assumed for years that water is associated. In order to 

 correct for association the term . in equation (11) has been altered to 



^°°^'^ where a is the association factor. Using van Laar's value 1.65 



55.5 -f-a 



at 20° C. for a, Vo = ^°°^'^ and if the osmotic pressure of weight normal 



sucrose is calculated by equation (11) the value of 23.50 is found for Po 

 in place of 23.64 (see Table 9). Since the observed value was 26.64, this 

 correction is of doubtful use. Evidently association is not important at 

 this concentration and at higher concentrations it should be lower accord- 

 ing to common opinion as to the effect of solutes on association at 20° C. 

 Correcting further by including a factor /3 for degree of hydration, the 

 term for the mol fraction takes the form .,,,"', ^ , > where c' is the 



55.5 -|- c — p c 



