Hyd roIys is Constant of Quadrivalent Cerium from Spectrometric Measurements H. G. OFFNER' and
D. A. SKOOG
Chemistry Department, Stanford University, Stanford, Calif. The hydrolysis reaction of quadrivalent cerium in acid solutions was studied by an optical absorbance technique. Equations were derived relating the measured absorbance values to the hydrolysis constant, and the latter was then calculated from the experimental data. From the Beer's law behavior of solutions of varying ceric concentrations, it was concluded that polymerization reactions did not occur over the concentration range studied.
2.40
.
2.25
-
2.10
-
1.95
-
T
cerium ion, reacting like other polyvalent metal ions as a Lewis acid, hydrolyzes in both basic and acid solutions. Reported values for the magnitude of the hydrolysis constant in acid solutions range from 0.6 as derived from potentiometric data (4), to 5.2 from spectrophotometric measurements ( S ) , a t 25' C. A further study by absorption spectrometry of the hydrolysis reaction of ceric ion in acid solutions is described in this report. The experimental technique differs {ram the previous work of Robertson and Hartwig (3) principally in that measurements were made a t a wavelength where much greater differences in solution absorbance as a function of acidity could be observed, enabling a more accurate value of the constant to be calculated. I n the course of this investigation it was also experimentally determined, from the Beer's law behavior of solutions a t constant acidity and varying ceric concentrations, that polymerization reactions did not occur over the concentration range studied. HE QUADRIVALENT
THEORY
In the following theoretical treatment, an expression is derived relating experimental absorbance values to the unknown hydrolysis constant, so that the latter may be calculated from experimental data. The hydrolysis reaction is represented by the equation Ce+4 nHsO = Ce(OH),+(4-n) n H +
+
+
'Present address, Rocketdyne, a Division of North American Aviation, Inc., Canoga Park, Calif. 1520
ANALYTICAL CHEMISTRY
l"I/ 1.65 I
I
I
145
245
345 (c,,)
Figure 1.
54s
44s
645
2 (A,-A I x 104
Data plotted from Table
I using n = 2
The molar concentrations are denoted as follows: co = Cet4 co = Ce(OH),+('-n)
Also
Also, let iiObe the absorbance of the ceric solutions with no hydrolysis, A the observed absorbance, ctnd €0 and ea the corresponding molar absorptivities.
Substituting Equation 2 in 4:
A
-4 =
=
COCO
toct
-
+ coca
€&a
+
coco
H3O'
ch
=
ct
= ca
+ c.
Simplifying, and with M~ = A.
(total cerium concentration) The hydrolysis constant is expressed as
K h =: C&h" -co
(1)
or
From Equation 7, the plot of A VS.CA"(Ao A ) will be linear for a fixed value of c f , and the slope of the line will be ~/KA. The value of A . may be calculated from any three measured absorbance values as follows:
-
Let A , = absorbance at acid concentration A Z = absorbance at acid concentrac tion ch, A I = absorbance at acid concentration c h i Substituting these values in Equation 7 to obtain three simultaneous equations and solving for A. gives
the recalculated value for Ao was, in fact, 2.69. The reciprocal slope of this line, which represents the hydrolysis constant Ki, is0.21. On theassumption that n = 2, the relationship is nonlinear, as shown in Figure 1, indicating that n = 1 is the correct value. The effect of ionic strength on the hydrolysis constant was also investi~ gated Over the rrtnge of o , to~ 1.70, and no significant deviation was observed, as shown in Table 11, The standard heat of the hvdrolvsis reaction, AHf,,' was calculatlkd from the values of Kh obtained a t 25' and 5' C. The experimentally determined
+ Chi" A2(A3 - A i ) + chanAa(Ai- Az)
Ao = ChinA1(Az - -43) Chln(Az - - 4 3 )
+ CrS"(A3 - A i ) 4- Ch,"(Ai - Az)
This equation contains the unknown term n, and its value is defined as that giving a linear relationship between A and ch" (Ao- A ) as noted above, but is not a function of Ao. I t will be shown that the value of n is unity over the acid concentration range used in the experiments. EXPERIMENTAL
Apparatus. All absorbance measurements were made with a Beckman DU Spectrophotometer equipped with a photomultiplier detector and a constant temperature cell compartment using a 1-cm. path length quartz cell. Reagents. Ceric perchlorate, 0.5M in 6 M perchloric acid, was obtained from the G. F. Smith Chemical Co. The ceric and acid concentrations were determined as described in a previous study on ceric-alcohol reactions (1).
Procedure. Absorbance measurements were made a t 305 mp, a region of maximum absorbance changes as a function of acid concentration. A sodium chromate solution was used as a blank to set the instrument for 100% transmission to allow more accurate measurements at high absorbance values. This method of using optically dense solutions as reference standards to obtain high relative accuracies has been reviewed (8). A constant ionic strength for all solutions of varying acid concentrations was maintained by the addition of equivalent amounts of sodium perchlorate.
Table II.
Absorbance as Function of Acid Concentration'
HClOi concn. Sample M X 10
Absorb-
+
ance
CA ( A o A) 1.63 0.101 1.73 0.120 1.81 0.137 1.88 0.159 1.98 0,174 2.06 0.187 2.10 0.203 2.16 0,208 2.21 0.217 2.23 0.229 2.29 0.238 2.34 0.247 2.36 0.262 2.40 0.266 Cet4 concentration = 1.548 X lO-*M. Ionic strength = 0.91. Temperature = 25" C.
1 2 3 4 5 6 7 8 9 10 11 12 13 14
(8)
0.947 1.247 1.547 1.947 2.447 2.947 3.447 3.947 4.447 4.947 5.947 6.947 7.947 8.947
Hydrolysis Constant as Function of tonic Strength
(Temperature Ce+' concn., M x 103
Ionic strength
1,548 1.576 1.586 1.346
0.91 1.33 1.66 1.70
= 25'
C.) Hydrolysis constant, K A
HClO, concn., M 0 . 1 to 0 . 9
0.20 0.19 0.19 0.21
0 . 1 to 1 . 3 0 . 1 to 1 . 6 0 . 1 to 1 . 7
Table 111.
Ce+' concn.
M x
103
1.033 2.066 4.132 6.198 8.264 10.33
Absorptivities of Ceric Solutions (HClO4 concentration = 0.1935M) Molar absorptivities at mp
420
410
400
390
380
76.4 77.8 78.4 77.0 75.6 74.5
106 109 107 108 107 105
150 151 150 149 148 146
206 209 210 210 210 209
278 282 285 286 288 288
value of Kh at 5' C. was 0.11. Assuming AHf,,' independent of temperature in the 5' to 25' C.-range, the integrated van% Hoff equation may be used :
wavelengths and are summarized in Table 111. These data indicate no polymerization over the entire concentration range, and are especially significant in the region of 1 to 2 X lO-3M Cef4, where the hydrolysis experiments were run.
The calculated AHf.,' = 4.9 kcal./mole. The extent of any polymerization reactions, such as
LITERATURE CITED
RESULTS A N D DISCUSSION
Data from one experiment are shown in Table I. The value for A . was calculated from Equation 8, taking n as unity. For samples 1, 7, and 14, the calculated value for A . = 2.69. For samples 2, 6, and 13, A . becomes 2.66. Using the value 2.69, a preliminary curve was drawn from Equation 7 , and taking n = 1 , a straight line was obtained. Using one point on this curve,
Table 1.
2Ce(OH)+3 = Ce-O-Ce+6
+ HzO
would be observed as a Beer's law deviation for solutions of varying ceric ion and constant acid concentrations. Measurements were made at several
(1) Offner, H. G., Skoog, D. A., ANAL. CHEM.37, 1018 (1965). (2) Reilley, C. N., Crawford, C. M,, Ibzd., 27, 716 (1955). (3) Robertson, T. J., Hartwig, E., Can. J. Chem. 29, 818 (1951). (4) Sherill, M. S.,King, C. B., Spooner, R. C., J . A m . Chem. Soc. 65, 170 (1943). RECEIVEDfor review May 27, 1966. Accepted August 8, 1966. VOL 38, NO. 11, OCTOBER 1 9 6 6
1521
