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The resolution of complex spectra
J. inorg,nucl. Chem., 1968, Vol. 30, pp. 3095 to 3098. PergamonPress. Printedin Great Britain
NOTES
The resolution
of complex
spectra
(Received 15 December 1967) ISOSnESTiC points are u s e d in solution c h e m i s t r y to provide evidence about the n u m b e r o f chemical species present in the solutions studied[l]. If a series o f spectra s h o w several isosbestic p o i n t s it c a n usually be concluded that there are only two absorbing species, or for instance three species o f which two h a v e idemical spectra. T h i s test, though simple, is open to the objection that it u s e s only a small part o f the available information, viz. that referring to the wavelengths at t h e isosbestic points. It c a n also h a p p e n that there are no intersections in the s p e c t r a concerned, or that the intersections are at a w k w a r d angles w h i c h leave possible isosbestic points ill-defined. T h e purpose o f this note is to indicate a more powerful test, using the whole of the spectrum, which is still very simple to apply. C o n s i d e r a mixture o f two species o f molar concentrations cl and c~ and molar extinction coefficients • 1 a n d ~2. T h e n the extinction coefficient of the mixture is given by
: C1~1+ ca~z. F o r a s e c o n d mixture, indicated by a prime, we have
,~' = c'~, + c ; ~ . Subtracting we obtain
• - ~ ' = ( c , - c',)~,+ ( c ~ - c~)~,. If we n o w impose the condition that ct + c2 is a constant, this b e c o m e s
~ - ~ ' = ( c , - c'~)(el- E2).
(1)
F o r three c o m p o n e n t s , on t h e o t h e r h a n d , the equation does not simplify f u r t h e r t h a n E - ~' = (cl - c'~) (~1 - ~ ) + (c~ - c~) (~2 - ~a),
(2)
w h e n the only condition i m p o s e d is the c o n s t a n c y of c~ + c~+ ca, t h o u g h it does reduce to (1) if both (ct + ca) a n d ca are constant. Equation (I) s h o w s that, with two species, at wavelengths w h e r e e~ = ~2 we shall have ~ = ~' for all mixtures, i.e. we shall h a v e isosbestic points. In a t e r n a r y mixture in which the proportions of all three species can vary, h o w e v e r , Equation (2) s h o w s that we should need to h a v e ~ = ~2 = ea to get an isosbestic point. T h i s might h a p p e n by a coincidence at a particular wavelength, but it is an unlikely event; it is still less likely that is would h a p p e n twice or more in a given s y s t e m . T h i s is the basis of the isosbestic test. Equation (1) also s h o w s that for a n y pair of binary mixtures ~ - ~' is proportional to ~ - E~. T h a t is to say, we shall g e t the s a m e difference s p e c t r u m f r o m a n y pair, apart f r o m a proportionality factor. E q u a t i o n (2) s h o w s that this is not true for a ternary s y s t e m except w h e n two species have identical spectra, e.g. w h e n ~t = ~ at all wavelengths, or w h e n one species is present in a c o n s t a n t proportion. T h i s is the basis of the proposed n e w test.
1. See for e x a m p l e C. K. JOrgensen, Absorption Spectra and Chemical Bonding in Complexes, p. 90. P e r g a m o n Press, O x f o r d (! 962). 3095
ABSORPTION 0
0
,~
DENSITY (Icm. c¢11) 0
0
,~
,~
0 ,
=;
,
o
~p m
~
a~
0
0
!1
I TI
TT I
I
"g .O '~ te
saloN
960£
u
0-2
0-4
0.6
0"8
l'O
~d
~
6so 600
550
(m.~)
500
P Q R S
Solution 0.02 0.02 0.02 0.02
U(IV)
2.00 2.00 2.00 2.00
H
0.04 0.01 0.00 0.00
(M)
Cs
2.02 1.22 0.72 0.12
0.10 0-87 1.36 1-96
NOa CIO4
Fig. 1. Spectra of uranium(IV) solutions.
DIFFERENCE S P E C T R A
WAVELENGTH
450
4uO
...........
__,--=--,--
.
S-P
P-S
R-P Q-p
~D -,-4
o
Z
3098
Notes
Difference spectra are readily obtained experimentally. All that is necessary is to treat one of the solutions concerned as the unknown and the other as the reference standard in the usual type of spectrophotometer. The positions of the solutions can be reversed to cover spectral regions where e~ -- E2 changes sign. We have applied the test, by way of illustration, to mixed solutions of cobalt and nickel of known composition and fixed total metal concentration. Care was taken to maintain a constant anionic composition, so that the metals were complexed to essentially the same extent throughout. As expected, the difference spectra were all of very nearly the same shape apart from scaling factors. As a second illustration difference spectra were obtained for a system already studied in this laboratory, viz. uranium(IV) in a mixed HNO3-HCIO4 medium[2]. Figure 1 shows both the difference spectra and the separate spectra. The isosbestic points in a similar series were used earlier as evidence that the spectra can be resolved into two components; one of these was ascribed to uncomplexed U 4+ and the other to the complexes UNO33+, U(NO3)22+ . . . etc., all of which were postulated as giving essentially the same spectra. This example clearly demonstrates the advantages of using the difference spectra. In the first place it was possible to double the length of the cells used in obtaining the difference spectra as compared with the separate spectra, so that the critical features were enlarged. Secondly, there are several wavelengths where all the differences vanish, but not all of these can be recognised clearly as isosbestic points. Thirdly, detailed examination shows that the difference spectra are not all perfectly of the same shape, but it is much harder to discern this from the separate spectra. The slight divergences may be due to experimental error or may possibly be due to small differences between, say, the UNO3 a+ and U(NO3)~2+ spectra.
Atomic Energy Research Establishment Harwell, Didcot Berkshire
H.A.C.
McKAY
D. SCARG ILL
2. H. A. C. McKay andJ. L. Woodhead,J. chem. Soc. 717 (1964).
J. inorg, nucl. Chem., 1968, Vol. 30, pp. 3098 to 3100.
Pergamon Press.
Printed in Great Britain
Kinetics of thermal decomposition of some basic salts of beryllium IN OUR previous communications we reported our results on the kinetics of thermal decomposition of beryllium hydroxide [ 1] and beryllium sulphate tetrahydrate [2] using the thermogravimetric technique. In this communication we briefly report our results on the kinetics of thermal decomposition of the basic sulphate, basic succinate, and basic phthalate of beryllium obtained by the homogeneous precipitation technique. The methods of Freeman and Carroll [3] and Coats and Redfern[4] are used for calculating the kinetic parameters. EXPERIMENTAL The precipitates of beryllium basic sulphate[5], basic succinate[6] and basic phthalate[7] were obtained by the methods described earlier. All the precipitates were dried in vacuum over silica gel for several hours before being subjected to thermogravimetric analysis. A Stanton model TR-1 thermobalance was used for the purpose. I. 2. 3. 4. 5. 6. 7.
T. P. Prasad and M. N. Sastri,J. inorg, nucl. Chem. 29,246 (1967). M. N. Sastri and T. P. Prasad, J. inorg, nucl. Chem. 30, 1639 (1968). E. S. Freeman and B. Carroll, J. phys. Chem. 62, 394 (1958). A. W. Coats and J. P. Redfern, Nature, Lond, 201, 68 (1964). T. P. Prasad and M. N. Sastri, Talanta 13, 1517 (1966). T. P. Prasad and M. N. Sastri, Talanta 15, 141 (1968). T. P. Prasad and M. N. Sastri, Cur. Sci. (India), 35, 617 (1966).
NOTES
The resolution
of complex
spectra
(Received 15 December 1967) ISOSnESTiC points are u s e d in solution c h e m i s t r y to provide evidence about the n u m b e r o f chemical species present in the solutions studied[l]. If a series o f spectra s h o w several isosbestic p o i n t s it c a n usually be concluded that there are only two absorbing species, or for instance three species o f which two h a v e idemical spectra. T h i s test, though simple, is open to the objection that it u s e s only a small part o f the available information, viz. that referring to the wavelengths at t h e isosbestic points. It c a n also h a p p e n that there are no intersections in the s p e c t r a concerned, or that the intersections are at a w k w a r d angles w h i c h leave possible isosbestic points ill-defined. T h e purpose o f this note is to indicate a more powerful test, using the whole of the spectrum, which is still very simple to apply. C o n s i d e r a mixture o f two species o f molar concentrations cl and c~ and molar extinction coefficients • 1 a n d ~2. T h e n the extinction coefficient of the mixture is given by
: C1~1+ ca~z. F o r a s e c o n d mixture, indicated by a prime, we have
,~' = c'~, + c ; ~ . Subtracting we obtain
• - ~ ' = ( c , - c',)~,+ ( c ~ - c~)~,. If we n o w impose the condition that ct + c2 is a constant, this b e c o m e s
~ - ~ ' = ( c , - c'~)(el- E2).
(1)
F o r three c o m p o n e n t s , on t h e o t h e r h a n d , the equation does not simplify f u r t h e r t h a n E - ~' = (cl - c'~) (~1 - ~ ) + (c~ - c~) (~2 - ~a),
(2)
w h e n the only condition i m p o s e d is the c o n s t a n c y of c~ + c~+ ca, t h o u g h it does reduce to (1) if both (ct + ca) a n d ca are constant. Equation (I) s h o w s that, with two species, at wavelengths w h e r e e~ = ~2 we shall have ~ = ~' for all mixtures, i.e. we shall h a v e isosbestic points. In a t e r n a r y mixture in which the proportions of all three species can vary, h o w e v e r , Equation (2) s h o w s that we should need to h a v e ~ = ~2 = ea to get an isosbestic point. T h i s might h a p p e n by a coincidence at a particular wavelength, but it is an unlikely event; it is still less likely that is would h a p p e n twice or more in a given s y s t e m . T h i s is the basis of the isosbestic test. Equation (1) also s h o w s that for a n y pair of binary mixtures ~ - ~' is proportional to ~ - E~. T h a t is to say, we shall g e t the s a m e difference s p e c t r u m f r o m a n y pair, apart f r o m a proportionality factor. E q u a t i o n (2) s h o w s that this is not true for a ternary s y s t e m except w h e n two species have identical spectra, e.g. w h e n ~t = ~ at all wavelengths, or w h e n one species is present in a c o n s t a n t proportion. T h i s is the basis of the proposed n e w test.
1. See for e x a m p l e C. K. JOrgensen, Absorption Spectra and Chemical Bonding in Complexes, p. 90. P e r g a m o n Press, O x f o r d (! 962). 3095
ABSORPTION 0
0
,~
DENSITY (Icm. c¢11) 0
0
,~
,~
0 ,
=;
,
o
~p m
~
a~
0
0
!1
I TI
TT I
I
"g .O '~ te
saloN
960£
u
0-2
0-4
0.6
0"8
l'O
~d
~
6so 600
550
(m.~)
500
P Q R S
Solution 0.02 0.02 0.02 0.02
U(IV)
2.00 2.00 2.00 2.00
H
0.04 0.01 0.00 0.00
(M)
Cs
2.02 1.22 0.72 0.12
0.10 0-87 1.36 1-96
NOa CIO4
Fig. 1. Spectra of uranium(IV) solutions.
DIFFERENCE S P E C T R A
WAVELENGTH
450
4uO
...........
__,--=--,--
.
S-P
P-S
R-P Q-p
~D -,-4
o
Z
3098
Notes
Difference spectra are readily obtained experimentally. All that is necessary is to treat one of the solutions concerned as the unknown and the other as the reference standard in the usual type of spectrophotometer. The positions of the solutions can be reversed to cover spectral regions where e~ -- E2 changes sign. We have applied the test, by way of illustration, to mixed solutions of cobalt and nickel of known composition and fixed total metal concentration. Care was taken to maintain a constant anionic composition, so that the metals were complexed to essentially the same extent throughout. As expected, the difference spectra were all of very nearly the same shape apart from scaling factors. As a second illustration difference spectra were obtained for a system already studied in this laboratory, viz. uranium(IV) in a mixed HNO3-HCIO4 medium[2]. Figure 1 shows both the difference spectra and the separate spectra. The isosbestic points in a similar series were used earlier as evidence that the spectra can be resolved into two components; one of these was ascribed to uncomplexed U 4+ and the other to the complexes UNO33+, U(NO3)22+ . . . etc., all of which were postulated as giving essentially the same spectra. This example clearly demonstrates the advantages of using the difference spectra. In the first place it was possible to double the length of the cells used in obtaining the difference spectra as compared with the separate spectra, so that the critical features were enlarged. Secondly, there are several wavelengths where all the differences vanish, but not all of these can be recognised clearly as isosbestic points. Thirdly, detailed examination shows that the difference spectra are not all perfectly of the same shape, but it is much harder to discern this from the separate spectra. The slight divergences may be due to experimental error or may possibly be due to small differences between, say, the UNO3 a+ and U(NO3)~2+ spectra.
Atomic Energy Research Establishment Harwell, Didcot Berkshire
H.A.C.
McKAY
D. SCARG ILL
2. H. A. C. McKay andJ. L. Woodhead,J. chem. Soc. 717 (1964).
J. inorg, nucl. Chem., 1968, Vol. 30, pp. 3098 to 3100.
Pergamon Press.
Printed in Great Britain
Kinetics of thermal decomposition of some basic salts of beryllium IN OUR previous communications we reported our results on the kinetics of thermal decomposition of beryllium hydroxide [ 1] and beryllium sulphate tetrahydrate [2] using the thermogravimetric technique. In this communication we briefly report our results on the kinetics of thermal decomposition of the basic sulphate, basic succinate, and basic phthalate of beryllium obtained by the homogeneous precipitation technique. The methods of Freeman and Carroll [3] and Coats and Redfern[4] are used for calculating the kinetic parameters. EXPERIMENTAL The precipitates of beryllium basic sulphate[5], basic succinate[6] and basic phthalate[7] were obtained by the methods described earlier. All the precipitates were dried in vacuum over silica gel for several hours before being subjected to thermogravimetric analysis. A Stanton model TR-1 thermobalance was used for the purpose. I. 2. 3. 4. 5. 6. 7.
T. P. Prasad and M. N. Sastri,J. inorg, nucl. Chem. 29,246 (1967). M. N. Sastri and T. P. Prasad, J. inorg, nucl. Chem. 30, 1639 (1968). E. S. Freeman and B. Carroll, J. phys. Chem. 62, 394 (1958). A. W. Coats and J. P. Redfern, Nature, Lond, 201, 68 (1964). T. P. Prasad and M. N. Sastri, Talanta 13, 1517 (1966). T. P. Prasad and M. N. Sastri, Talanta 15, 141 (1968). T. P. Prasad and M. N. Sastri, Cur. Sci. (India), 35, 617 (1966).