The Solubility of Sodium Sulfamate in Water

Abstract

Vol. 69The author' recently showed that for carboncarbon ban& the points of plot of E, the bondenergy in kcal., against the bondorder N lie on the parabola (1 -N/4)' -1 -E/133The fact that the number four appears as a constant associated with N may be of si@icance since this is the theoretical maximum bondorder for carbon-carbon bonds as well as being the number of carbon valence electrons.By eliminating N from (1) and (3) we obtain the equationwhere y = 4 -4 dl -E/133, relating E and D for carbon-carbon bonds. The numerical values' of a, b and n are 1.015, 0.875 and 2, respectively.Inspection of the points of plot of E against D for C -C , C=C, and c-=C bonds (58.6,100,123 kca). and 1.54, 1.33, and 1.204 A,, rtqectively)'J shows that the relation is very nearly linear.Cherton' has given a simple linear expression relating these variables. If we assume that this relationship is actually linear, then by setting(5) in (3) we derive a relation between N and D for carbon-carbon bonds of quite a Merent type from (1) which relates these Same variables. USing the known values of D for C -C , C=C and c--C bonds we find from (3) and (5) that' (1 -N/4)' = 1.488(D -1.162) (6) and E = 197.9(1.834 -D) (7)The curves represented by (1) (for carboncarbon bonds) and (6) correspoad very closely in the range under consideration and for N = 1, 2, 3 the correspondence is exact. Two points are required to determine the two constants for both of these relatioas and in each case the curve determined by any two points passes through the third.Parabolic equations of the type (6) fit the nitrogen-nitrogen (q,s = 1.330, 1.047) bond values' to within 0.14% and when used with the carbon-nitiogen (q,s = 1.582, 1.114) and phosphorus-pbsphorus (4,s = 1.428, 1.816) single and triple bond values' lead to almost exactly the Same predictions for the double bond values as do (I)' and Pauling's' covalent radii development. Thus, (1) and (8) fit the known experhental data equally well.(1 -N/4)' = q(D -S) By a treatment based upon the molecular orbital method, Couloon' has calculated the bondorders of benzene and graphite to be 1.667 and (8) (8) J. L. Knvonnu. J . C k n . Phyr., 16, 77 (1847). (4) R Chaton, Bull. roc. chin. &It.. 61, 26 (1918). (5) ne d c h t i o n d to 4 digits i. rw mmpuative pur-POKI. U n i v d t y R@n, Itbro. New Y a k , 1840. (6) L. h d i o g , "The Nature of the Chemical Bond," Cornel (7) C. & Codeon, Proc. Roy. SOS. (Lodor), I6@& 413 (1838). 1.53, respectively. Equation (6) leads to the values 1.670 and 1.522, whi& (1) yields the values 1.668 a d 1.50s (D--1.39 A., Docrp~u = 1.42 A,).] ~hese values agree clo~ely with those derived by C o b and evidently N of (1) and (6) may be interpreted 88 the bond-order as defined by Coulson's molecular orbital treatment. Using the valencebond rcswanc(t method, Penney' has calculated the values 1.623 and 1.45 for tlpese same quantities. Taking the energy of the benzene bond to be l/, (&(Benzene)) -6Ec-a') = 85.9 k d . in (3) yielde N-e = 1.62.However, since the interatomic distance appear to b...