726
H. B. JON.\SSEN AND A. W. MEIBOIIM
INORGANIC COMPLEX COMPOUNDS CONTAINING POLYDENTATE GROUPS. V
FORMATION CONSTANTS OF THE TRIETHYLENETETR.I.MINE-C~)PPEH(II) \ND NICKEL(II)COMPLEXIONS H A W B. JONASSEN
AND
ALVIN W . MEIBOHM
Richardson Cheitiical Laboratories, Tulane University, N e w Orleans, Louisiuna Received J u l y 7 , 1960
The complex ions of cations of the transition and near-transition elements have been studied to determine the nature of the complex ions or to establish the equilibrium constant for the reaction:
+
M NASMAN (1) Bjerrum (2) has indicated the importance of investigating the intermediate steps which compose the overall reaction: M+A*MA MA+A@MAz MA,-l+
A Ft MA,
MAN-,
+ A S MAN
In these equations M represents the central ion, A the coordinating agent, and MAN the fully coordinated complex ion. Concentration equilibrium constants may be written for each step (formation constants), as well as for the overall action (complexity constant). [A~ANI K N =(3) [MIFIN This paper reports the formation curves of triethylenetetramine (abbreviated as “trien”) complex ions with copper(I1) and nickel(I1) ions. The equations of Bjerrum apply in this case if the four nitrogen atoms of trien coordinate to the metal ion. CALCULATION O F THE CONSTANTS
Several symbols are required for the equations which are used in the calculation of the constants. CANol = total concentration of nitric acid, CMe = total concentration of metal ion, Ctrien = total concentration of trien, and [Hf] = concentration of hydrogen ion. Since trien is able to take up four hydrogen ions, the following expressions must be introduced:
Cirie,, = total concentration of trien not bound in a complex ion Cl,,,,, = [trien] [trienH+] [trienH:+] [trienH?] [trienH:+*]
+
+
+
+
(4)
727
COMPLEX IONS OF TRIETHYLENETETRAMINE
Ctrisn= concentration of trien bound in complex ion Ctrisn
=
Ctrien
- C'trien
(5)
C, = total concentration of hydrogen ions bound to trien C. = CHNOI - [H+] [OH-] = [trienH+] 2 [ t r i e n w ] 3[trienH:*]
+ +
+
atlie,,=
?it,i.,
=
+4 [ t r i e n p ]
(6)
fraction of trien in acid-base system present as free trien
average number of hydrogen ions bound to trien
Equations 7 and 8 are derived by substitution of values for the concentration of [trienH+], [trienH:+], etc. obtained from the corresponding dissociation constants of the base. The k values in the equations are the four dissociation constants of triethylenetetramine. In order to determine the formation constants of the complex ions of a specific metal ion and triethylenetetramine the average number of triethylenetetramine molecules bound per metal ion ( f z ) and the negative logarithm of the concentration of free triethylenetetramine (~[trien])must be determined. The formation function, 17, can be obt,ained from the equation: Ct,,,, = [trien]
+ [trienH+]+ [trienH:+] + [trienH?] + [trienH:+*] +
fiClde
(9)
Solution of equation 9 for li and substitution from equations 4 and 8 gives: ctrlr,>
ri=
C.
-fztrien
(10)
Cw P
Combination of equations 7 and 8 gives for the concehtration of free trien [trien] = C, at,i,, ntrir,"
and conversion to negative logarithms: p[trien] = -1ogitrien1
=
log
atrren
- log C.
(12)
From expressions 10 and 12 it may be seen that calculation of fi and p[trien] depends on knowledge of fit,,,, and fztrlen/atrlen. These in turn may readily be calculated from the pH of the solution and the previously determined acid-base constants of triethylenetetramine ( 5 ) . The values for the constants of trien were determined a t the same ionic strength as that of the copper and nickel solutions reported in this paper.
728
H. B . JONASSEN AND A. W. MEIBOHM
The value of the formation constant when n = 1 may be calculated by (3) : log kl = p[trien]
ii - log 1-?T
The value of log kl may also be obtained from the formation curve at the point where fi = 0.5, assuming that approximately equal amounts of MA,-1 and MA,, are present (2). With expansion of the coordination sphere the value for the formation constant of the complex ion MaAa may be obtained from the formation curve a t fi. = 1.25 or approximated by log liw = p[trien]
fi-1 - log 1.5 - li
pK1.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pK2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pKs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . pK, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
j
1
30'C.
10.C.
3.89 7.01 9.36 9.99
3.76 6.79 9.14 9.76
TABLE 1 Formation curve: c o p p e r ( I I ) and triethyleneletrainine Temperature = 30°C.; C M= ~ 0.1070 M ; C H N O ~= 0.0991 M ; ( C,
Cum.
0.0539
0.0898 0.0943 0.0988 0.1033 0.1078 0.1258
2.69 2.67 2.71 2.74 2.78 2.81 2.82 2.87 2.89 2.93 2.99 3.04 3.08 3.72
CUW
PH
0.0584
0.0629 0.0674 0.0718 0.0763 0.0808 0.0853
0.1437 O.li96 0.2002 0.2202 0.2603 0.3003
'7
6.89 9.23 9.56 9.70 9.92 10.07
3.06 2.55 3.67 4.82 6.92 9.07 9.93 15.6 18.7 26.8 45.8 71.7 102.3 25i00 LI
x
10'
1.176 0.069 0.187 0.262 0.103 0.504
:
3.94 3.94 3.94 3.94 3.93 3.92 3.92 3.91 3.91 3.90 3.89 3.88 3.87 3.60
0.0971 0.0970 0.0971 0.0973 0.0974 0.0975 0.0976 0.0978 0.0978 0.0979 0.0981 0.0982 0.0983 0.0989
-
n
pltrienl
21.12 21.20 21.04 20.92 20.ii 20.65 20.61 20.40 20.33 20.17 19.94 19.74 19.5s 17.15
0.0337 0.0382 0.0426 0.0470 0.0515 0.0559
0.273 0.316 0.357 0.398 0.440 0.481 0.523
0.0603
0.564
0.0648 0.0692 0.0736 0.0779 0.0823 0.1037
0.605
0.0292
0.647 0.687 0.728 0.770 0.969
__.
C.
%e.
2.57 1.54 1.13 0.97 0.73 0.58
0.0991 0.0991 0.1104* 0.1104' 0.1104' 0.1105*
p:trienl
7.34 2.35 1.74 1.53 1.21 1.02
A
n
0.1051 0.1151 0.1023 0.1063 0.1082 0.1087
11 FIG.1 FIG.1 . Formation curve for copper(I1) and triethylenetetramine FIG.2. Formation curve for nickel(I1) and triethylenetetramioe 729
R
0.982 1.075 0.956 0.993 1.011 1.016
730
H. B . JONASSEN AND A . W. MEIBOHM
TABLE 2 Complezity constant: copper(II)-triethyleneletranli?le 40'C.
3O'C.
p[trienl
p(trien1
21.20 21.04 20.92 20.77
20.65 20.61 20.40
m.33 m.17 19.94
0.316 0.357 0.398 0.440 0.481 0.523 0.564
0.605 0.647 0.687
1
Average.
14.82 14.55 14.40 14.33 14.M 14.07 13.91 13.91 13.76
20.87 20.79 20.75 20.66 m.61 m.65 20.51 20.52 20.44 20.37
lor K N
-
0.316 0.357 0.399 0.440 0.481 0.522
20.32 20.28 20.24 20.19 20.15 20.06 19.17 20.01 19.89 19.81
0.563
0.605 0.646 0.687
20.6 f 0.2
0.325 0.427 0.455
14.50 14.42 14.32 14.33 11.31 14.23 14.15 14.15 14.07
0.500 0.544
0.588 0.M1 0.631 0.675
Average.
20.65 20.53 20.41 20.30 20.19 20.02 19.86 19.82 19.63 19.47
n
l
14.3 f 0.2
14.52 11.29 11.16 14.06 13.90 13.77 13.68 13.68 13.55
I
0.324 0.112 0.155 0.499 0.543 0.587 0.631 0.631 0.675
,1
1
'1 1
Average
14.20 12.13 14.05 11.06 13.98 13.93 13.91 13.91 13.87 14.0 f 0.2
B. loa ka:r I
JOT.
5.99 5.78 5.64 5.32 5.08 Average.
1.19 1.22 1.26 1.30 1.33
5.76 5.68 5.68 5.49 5.38
1
5.6 f 0.2
40T.
5.80 5.62 5.46 5.17 4.85
1
Average.
1.18 1.22 1.26 1.29 1.32
1
5.54 5.50 5.48 5.32 5.11
I
5.4 f 0.2
i
solution and column two the measured pH values. The last six columns are calculated from equations 6, 7, 8, 10, and 12. Each horizontal row is a separate
COMPLEX IOhX OF TRIETHTLESETETRlMINE
731
solution in a 50.0-ml. volumetric flask. The data in the last two columns are plotted in figure 1 and are used to calculate the complexity constants from equation 13. Table 2 lists the values for the complexity constants of the copper(I1)-trien ion at 30" and 40°C. Table 3 contains the values for the formation constants of the nickel(I1)-trien ions at 30" and 40°C. The formation curves are shown in figure 2. DISCUSSION
The data indicate that copper(I1) and nickel(I1) ions form complex ions with one mole of triethylenetetramine. KOindication of a higher complex ion is shown for copper at the concentration used in this investigation.
FIG.3
FIG.4
FIG.3. Adsorption spect ra : copper( 11)-t riet hyleiiete tramine FIG.4. Continuous variation curves: copper(I1i-triethylenetetramine
Absorption data on a solution of copper(I1) ions and triethylenetetramine indicate one peak of maximum absorption a t 580 mM. Application of the-method of continuous variation a t 540, 580, and 680 mp indicated that only a 1 :1 complex ion is formed. The optical density measurements are shown in figure 3 and the continuous variation curves are in figure 4. The formation curve for the nickel(I1) ion indicates that a complex ion of three trien molecules to two nickel(I1) ions is formed. This ion had previously been isolated as the chloride and nitrate, and continuous variation studies also indicated the existence of both the 1:l and the 3:2 complex ion in solution (4). The formation curve extends beyond ri = 1.5,but the assumption that all amino groups are coordinated to nietal ions is no longer true and the method of calculation is no longer valid. I t will be noticed that the values of log k for nickel, to some degree, and for copper to a much greater extent, show a drift over the range 7t = 0.3-0.7. The
732
E. B . JONASSEN AND A . W. MEIBOHM
average values given in tables 2 and 3 correspond t o the graphically obtained values at fi = 0.5, the midpoint of the formation curve. No explanation for the drift, which is essentially temperature independent, is offered, but it may well be due to slight differences in the coordinating power of the primary and secondary amino groups. Steric effects may also be important in the drift of the constants. The nickel ion forms tetrahedral complexes with a coordination number of four and the triethylenetetramine molecule can readily enter this configuration with a minimum of strain. The copper ion, on the other hand, forms square-coplanar complex ions, which would introduce a slight strain in the triethylenetetramine molecule. TABLE 4 Thermodynamic quantities -F1
1
-Fxt
-FN
-B,
B1:r
IIN
---- I
Ni(I1) at 30°C.. ......... Ni(I1) at 40°C.. . . . . . . . . . .
kcal.
kcol.
kcal.
kcol.
kc&!.
hcrl.
19.S 20.1
7.8 7.8
27.6 27.9
13.0
8.7
21.7
Cu(I1) at 30°C... . . . . . . . . Cu(I1) at 40’C.. . . . . . . . . .
21.7
Comparison of the reported values with the stability of complex ions of nickel and copper ions with fl ,b’ ,b”-triaminotriethylamineas reported by Ackerman, Prue, and Schwarteenbach (1) supports the stereochemical discussion above. Their values for nickel and copper at 20°C. and an ionic strength of 0.1 are: nickel, 14.6; copper, 18.8. The @ ,/3’,/3”-triaminotriethylamine must be tetrahedral, so it is accommodated by nickel with greater stability than is triethylenetetramine. On the other hand, the copper complex ion is less stable, as the triaminoethylamine cannot enter the square-coplanar configuration as readily as can triethylenetetrmine. The free energy of formation of the complex ions was calculated from the relation AF = -RT In K . Approximate heats of formation for the complex ions were calculated from the values of the formation and complexity constants at two temperatures from the equation:
---
d l n k - AH dt RP A summary of the thermodynamic quantities is contained in table 4. SWMARY
1. The formation curves for the reactions of nickel(I1) and copper(I1) ions with triethylenetetramine have been determined.
MEASUREMENT OF LOW VAPOR PRESSURES
733
2. The formation constants and the complexity constants have been calculated from the formation curves. 3. Copper forms only a 1:1 complex ion with triethylenetetramine. 4. Nickel forms a 1:1 and a 3 :2 complex ion with triethylenetetramine. 5. Approximate values of the heats of formation of the complex ions have been calculated. 6. The free energies of formation of the complex ions have been calculated. 7. The data available indicate that certain steric factors may play a significant role in the coiirdination tendency of triethylenetetramine. Acknowledgment is extended to Dr. Theodore H. Dexter, who made the absorption and continuous variation measurements reported in this paper. REFERENCES (1) ACKERMANN, It., P R U E , J . E.,
G.: Nature 189, 723-5 (1949). (2) BJERRUM, J . : Metal Anaininc Forniation i n Aqueous Solution. Theory of the Reversible Step Reaction. P. Hsase and Son, Copenhagen (1041). (3) RJERRUY,J., AND ANDERSEN, P.: Kgl. Dsnske Vidcnskab. Selskab., Mat.-fya. Medd. 22, No. 7 , 21 (1946). (4) JONABSEN, H. B., AND DOUGLAS, 13. E . : J . Am. Chem. 8 o c . 71, 4094 (1949). (5) JONASSEN, H. B . , LEBLANC, R . 13.. ~ I E I B O H A.M R,. , A N D ROC:.4N, R . h f . : J . .4m. Climi. SOC. 73, 2430 (1050). AXD SCHW.4RTZENBACH,
THE MEASUREMENT OF LOW VAPOR PRESSURES BY MEANS OF A MASS SPECTROMETER' A. W. TICKNER'
AND
F . P. LOSSING
Division of Chemistry, National Research Laboratories, Ottawa, Canada Received J u l y 8 , 1950 INTRODUCTION
In the study of the kinetics of hydrocarbon reactions, low-temperature fractionation is an important aid in the separation and identification of products. Fractionations are often most efficient a t pressures below 0.01 mm. of mercury, so that it is important to know the vapor pressure of the hydrocarbons down to 0.01 mm. or leas. The vapor pressures of many heavy hydrocarbons have been determined down to very low pressures by the effusion method of Knudsen (5) or by the use of the Rodebush manometer (7, 8). For the more volatile hydrocarbons, direct pressure measurements on the vapor are more convenient. However, direct measurements of vapor pressure are subject to errors due to the presence of volatile impurities. At temperatures where the vapor pressure is small, Contribution No. 2406 from the Kational Research Council, Ottawa. Research Laboratories Post-Doctorate Fellowship.
* Holder of a National
