Conventional pa, Values for Buffer Solutions of Piperazine Phosphate from 0" to 50" C Hannah B. Hetzer, R. A. Robinson, and Roger G . Bates National Bureau of Standards, Washington, D . C. 20234
PIPERAZINE PHOSPHATE, a salt of the composition PzH8P04where Pz = C4HloNz-has a pH value of 6.26 at 25" C in the 0.05m aqueous solution ( I ) . Its solutions, therefore, contain both the PzH2*+and PzH+ cations and both the primary and secondary phosphate anions H2P04- and HP042-. The salt is available commercially and is readily crystallizable from water. Its buffer capacity and stability are high, and the salt is a useful buffer substance. We have now made emf measurements of the pax values of 0.02m and 0.05m solutions of piperazine phosphate from 0" to 50" C. EXPERIMENTAL
Materials. Piperazine phosphate monohydrate was recrystallized twice from water, air-dried, and stored for several days over Drierite. The salt is not appreciably hygroscopic; instead, dehydration is reported to begin gradually at 70" C and to proceed rapidly from 145"-175" C (2). The phosphorus content was determined as quinolinium phosphomolybdate (calcd 15.32%, found 15.33x). The preparation of bromide-free potassium chloride and of the electrodes has been described previously (3). Apparatus. The usual instruments for the precise measurement of electromotive force were employed. Cells were provided with all-glass joints. The temperature of the water thermostat containing the cells was controlled to within 0.02" C and monitored by a platinum resistance thermometer. The cell employed was Pt; Hz(g, 1 atm), PzH3P04(0.02m or 0.05m), KCl (0.005m, 0.010m or 0.015m), AgCl; Ag. Values of the emf of this cell from 0" to 50" C are given in Table I. On the average, duplicate cells agreed to 0.06 mV (0.001 pH unit). RESULTS
The emf of the cell is related to the hydrogen ion activity
of the solution by means of the equation ( E - E")/k
+ log mcl-
=
- log ( a H + yc1-1
=
~ ( U H ~ C I )(1)
where E" is the standard potential of the silver-silver chloride electrode (4)and k = (RT In lO)/F. Values of p(aHyC1) for solutions containing 0,005, 0.010, and 0.015m potassium chloride, calculated from the emf data in Table I, are given in Tables I1 and 111. By linear extrapolation of the p(aaycl) values for these 3 solutions, values ofp(aHycl)" for the limiting case of zero potassium chloride concentration can be calculated. These limiting values are also given in the tables. (1) E. V. Grove-Rasmussen, Acta Chem. Scand., 7 , 231 (1953). (2) T. Noto, H. Sawada, Y.Sato, and N. Fukuda, Tanabe Seiyaku Kenkyu Nempo, 2, 53 (1957); Chem. Abstr., 52, 8463 (1958). (3) R. G. Bates, "Determination of pH," Wiley, New York, 1964, Chapter 9. (4) R. G. Bates and V. E. Bower, J. Res. Natf. Bur. Std., 53, 283 (1954). 634
ANALYTICAL CHEMISTRY
By introducing the Bates-Guggenheim convention (5),
- logyci-
+ 1.5 1"')
A PZ/(l
(2)
where A is the slope parameter of the Debye-Huckel equation (on the molal scale), conventional values of paH (= - log a=+) can be calculated. These are given in Tables I1 and I11 along with smoothed values calculated by means of the equation pa^ = a b(t - 25) c(t - 25)' (3)
+
+
where t designates the temperature in "C. The estimated uncertainty of these values, based on the precision of the experimental data and the extrapolations, is 0.003 unit in paH. The pa^ values were fitted to Equation 3 by the method of least squares with the aid of OMNITAB. The total ionic strength, I , appears in Equation 2. If piperazine phosphate existed in solution as (PzHZ2+)(HP0h2-), the total ionic strength of a 0.02m solution would be 0.08, whereas if the salt were in the form (PzH+) (HzPOd-) it would be 0.02. It will be shown in the appendix that the salt exists mainly in the latter form; at 25" C, I is 1.314 times the molality and - log ycl- has the values 0.067 and 0.095 at 0.02m and 0.05m, respectively. The proportion of (PzH+) (HzP04-) increases, and the total ionic strength therefore decreases, with increasing temperature. However, the value of A in Equation 2 also increases; the two effects nearly cancel and - log ycl- is almost independent of temperature. The ~ U value H of the 0.02m solution interpolated at 24" C is 6.294 and that for the 0.05m solution is 6.304. For the latter solution, Grove-Rasmussen ( I ) found pH = 6.27 at 24" C. He made measurements at temperatures from 14" to 26" C and, over this range of temperature, his pH values are about 0.035 lower than the pa^ values interpolated in Table 111. A cell with liquid junction containing a calomel electrode and a glass electrode was used for the measurements. It was supplemented, at 18" C, by a hydrogen electrode. Using a glass electrode standardized in the equimolal (0.025m) phosphate buffer solution, we have found pH = 6.26 for both the 0.02m piperazine phosphate solution at 24" C and the 0.05m solution at 24.5" C. For piperazine phosphate solutions, therefore, a distinction must be made between the conventional paH as determined by means of a cell without liquid junction, together with the Bates-Guggenheim convention for the activity coefficient of the chloride ion, and the operational pH derived from measurements of a cell with liquid junction. This difference has been studied previously for both aqueous and water-methanol solutions (6). For aqueous solutions, the respective values of ~ C Z H and pH were 2.620, 2.623 in a citric acid solution; 3.830, 3.833 for one succinate buffer and 5.533, 5.532 for another succinate buffer; 4.694, 4.699 for an acetate buffer; 7.011, ( 5 ) R. G. Bates and E. A. Guggenheim, Pure Appl. Chem., 1,
163 (1960). (6) R. G. Bates, M. Paabo, and R. A. Robinson, J. Phys. Chem., 67, 1833 (1963).
Electromotive Force of the Cell: Pt; HZ(g, 1atm), PzHsPOa (4,KCl (md, AgCl; Ag from 0" to 50" C (in V)
Table I. ml 0.015 0.010 0.005
0"
5 O
10"
0,69636 0,70572 0.72180
0,69861 0.70816 0.72452
0.70079 0.71048 0.72710
20" 25" 30" 0.02rn piperazine phosphate 0.70486 0.70673 0.70853 0.70287 0.71490 0.71694 0.71890 0.71274 0.72966 0.73211 0.73446 0.73672 15"
35"
40"
45 "
50"
0.71030 0.72079 0.73890
0.71190 0.72262 0.74100
0.71344 0.72433 0.74300
0.71492 0.72602 0.74496
0.71236 0.72296 0.74111
0.71399 0.72478 0.74322
0.71558 0.72654 0.74527
0.71711 0.72822 0.74718
0.05m piperazine phosphate
0.015 0.010 0.005
0,70267 0.71243 0.72914
0.70048 0.71004 0.72650
0.69819 0.70761 0.72374
0.70486 0.71484 0.73181
0.70687 0.71696 0.73427
7.015 for a phosphate buffer solution; 9.174, 9.171 for a s o h tion of borax, and 10.083, 10.087 for a carbonate-bicarbonate buffer solution. The greatest difference between ~ U Hand pH is only 0.005. Nevertheless, when the acid constituent of the buffer mixture is of the BH+ type, the difference is larger, the respective values of paH and pH being 9.185, 9.177 for the 4-aminopyridine buffer solution; 9.311, 9.297 for the ammonia-ammonium chloride system; and 8.141, 8.124 for the tris(hydroxymethy1)aminomethane buffer solution. The average difference is 0.013. It is now apparent that the disparity is even greater with piperazine phosphate, where the acid constituent is partly of the BH22+type, the pH values recorded by Grove-Rasmussen (I) between 14" and 26' C being 0.03 lower than the ~ U H values interpolated from Table 11. These effects, which are probably related to liquid-junction abnormalities, deserve further study.
0.70877 0.71904 0.73664
0.71061 0.72106 0.73891
Table 11.
~ U H Values
of the 0.02m Piperazine Phosphate Solution from 0" to 50" C p(aH?'Cl)' t("C) 0.015m 0.010m 0.005m Om ~ U H paH(ca1c) 6.649 6.582 6.580 0 6.660 6.657 6.650 6.581 6.514 6.515 5 6.593 6.589 6.585 6.518 6.451 6.453 10 6.531 6.527 6.522 6.469 6.464 6.461 6.394 6.394 15 6.472 6.404 6.337 6.338 20 6.416 6.413 6.408 6.352 6.285 6.284 25 6.365 6.361 6.356 6.302 6.235 6.234 30 6.314 6.310 6.306 6.253 6.186 6.185 35 6.266 6.262 6.257 6.208 6.141 6.140 40 6.221 6.217 6.212 45 6.178 6.174 6.169 6.165 6.098 6.097 6.134 6.128 6.123 6.056 6.058 50 6.137 a Values in these four columns are for the indicated molalities of potassium chloride. PUH (calc) = 6.2844 - 0.01044(t - 25) 0.000055(t - 25)2; standard deviation, 0.0016.
+
ACKNOWLEDGMENT
The authors acknowledge the assistance of John R. Baldwin, who analyzed the piperazine phosphate monohydrate for its phosphorus content. APPENDIX
Solutions of piperazine phosphate contain the ions BH+ and HA- in addition to BH22+and A2-; here B represents piperazine and A represents HP04. To calculate the ionic strength, one needs to know the proportions in which the four ions are present. It can be shown that the amounts of undissociated phosphoric acid molecules, piperazine molecules, and P043- ions present in a solution of piperazine phosphate are negligible. Let kl and kz be the concentration dissociation constants for the reactions BHzz+
H+
+ BH+
Table 111.
~ U H Values
of the 0.05m Piperazine Phosphate Solution from 0 " to 50' C P(aH?'Cl)"
r ( " C ) 0.015m
0.01Om 0.005m Om - PUH paH(calc)b 6.686 6.591 6.589 6.692 6.689 0 6.694 5 6.627 6.624 6.621 6.618 6.523 6.525 6.556 6.461 6.463 10 6.565 6.562 6.559 6.499 6.404 6.404 15 6.507 6.505 6.501 20 6.451 6.449 6.445 6.443 6.348 6.348 6.396 6.393 6.390 6.295 6.294 25 6.399 6.339 6.244 6.243 30 6.349 6.347 6.342 35 6.300 6.298 6.294 6.290 6.195 6.195 6.245 6.150 6.149 40 6.254 6.252 6.248 6.202 6.107 6.106 45 6.212 6.209 6.205 6.160 6.065 6.066 6.169 6.163 50 6.171 a Values in these four columns are for the indicated molalities of potassium chloride. b paH(calc) = 6.2943 - 0.01045(f - 25) 0.000053(r - 25)5; standard deviation, 0.0013.
+
and HA-
e H+ + Az-
and the condition for mass balance is
+ p H + ] = [A2-] + [HA-]
[BHz2+]
respectively. Then kl = 1"
PH+I 9 [BH22+l
k2 =
[H+l [A2-] [HA-]
where the square brackets indicate concentrations. The activity coefficients can be omitted for the purpose of this discussion. The condition for electrical neutrality is 2 PHz2+1
+ [BH+l + ["I
= 2 [A2-]
+ [HA-] + [OH-]
It follows then that [HA-]
+ [H+] = [BH+] + [OH-]
and [BHz'+l
+ [H+l
=
[A"]
+ [OH-]
It may be seen that, at pH values greater than 6, [H+] is negligible in comparison with the concentrations of each of the 4 ions concerned in fixing the pH of 0.02m and 0.05rn piperVOL. 40, NO. 3, MARCH 1968
* 635
azine phosphate solutions, and [OH-] is, of course, even smaller. Hence, [BHz2+] = [A2-] =
[BH+] = [HA-I
=
ion (8),respectively, it can be shown that the value of [BH+]/ [BHzz+] and [HA-]/[A*] is 8.55 at 25" C. The total ionic strength of the solution is therefore 1.314m. The ratio is 5.59 at 0" C and 13.9 at 50" C. The equation [H+Iz = klkz predicts that the hydrogen ion concentration of the buffer solution should be dependent on the concentration of piperazine phosphate only because activity coefficients have been neglected. If activity coefficients are introduced and the thermodynamic dissociation constants (K) are used, it can be shown that (aH+)z=
[H+] = d k i k z and [BH+]/@3H22+]= [HA-]/[A2-] = d k x
YBH~ YBH+YA* The symmetrical arrangement of the activity coefficients indicates that the change in paH value with concentration should be small.
for piperazinium ion Introducing the kl value (4.64 X (7) and the kz value (6.34 X lo-*) for dihydrogen phosphate
RECEIVED for review October 30, 1967. Accepted December
(7) H. B. Hetzer, R. A. Robinson, and R. G. Bates, J. Phys. Chem.,
(8) R. G. Bates and S . F. Acree, J. Res. Natl. Bur. Std., 30, 129
in press.
13, 1967.
(1943).
Infrared Determination of Trace Amounts of Polyatomic Inorganic Ions James R. Lawson and Ralph L. Barnett, Jr.' Department of Physics,
Fisk University, Nashville, Tenn.
COMPILATIONS of the spectra of inorganic compounds in the 2- to 15-micron region ( I ) and the 15- to 36-micron region (2) have demonstrated the feasibility of qualitative analysis by infrared spectrometry. Although not competitive with the higher accuracy and precision of standard gravimetric techniques, infrared methods offer rapid quantitative determinations with an accuracy to roughly 1%. Such determinations are of particular value at very low concentrations of sample. The contour and intensity of the absorption bands in the spectrum of an inorganic ion or compound are functions of the temperature and of the environment. It is possible to change appreciably the environment, and thus the absorption characteristics, by putting the ion or molecule into a solid solution. The advantages of this technique were first shown by Hiebert and Hornig in their study of HC1 (3), and have been amply illustrated at low temperatures by more recent papers (4). Large ions, or polyvalent ions, may not form solid solutions. In these cases the solute is uniformly distributed as very small crystals in the solute matrix. It has been observed (5) that an increased absorption results from smaller crystal size. The following characteristics indicate the existence of a solid solution rather than a mixture of host and solute compounds: frequency shifts are observed for the solute ion in 1 Present address, Florissant Valley Community College, Ferguson, Mo.
(1) F. A. Miller and C . H. Wilkins, ANAL.CHEM., 24, 1253 (1952). (2) F. A. Miller, G. L. Carlson, F. F. Bentley, and W. H. Jones, Spectrochim. Acta, 16, 135 (1960). (3) G. L. Hiebert and D. F. Hornig, J. Ckem. Pkys., 27, 752 (1957). (4) G . C . Pimentel, Spectrochim. Acta, 12, 94 (1958). ( 5 ) J. Bonhomme, Ibid., 7 , 32 (1955).
636
ANALYTICAL CHEMISTRY
different solvents ; selection rules arising from the existence of the unit cell in the pure solute crystal no longer hold in solid solution; and at high concentrations of solute, either the solubility will be exceeded and a spectrum characteristic of the pure solute will be obtained, or deviations from Beer's law due to the solute-solute interaction will be observed. Solid solutions in alkali halide crystals are stable at room temperature. They may be formed by the process of adding a small quantity of the appropriate inorganic salt to a molten alkali halide and cooling to form crystals, or a single crystal, in which the solute ions are trapped in the host lattice (6, 7). The use of molten alkali halides requires temperatures of 700" to 800" C, at which many ionic species decompose or react with traces of oxygen. Thus, cyanide becomes cyanate ion and nitrate partially decomposes to the nitrite ion. Solid solutions have also been produced by heating a mixture of salts under pressure (8), and by warming disks pressed from mixtures (9), relying upon diffusion in the solid state. These methods allow observation of species not stable at higher temperatures. In the majority of observed spectra, the fusion technique led to appreciable increases in the absorption peak heights of certain fundamental bands. This indicated that the sensitivity of inorganic infrared analysis might be increased. Three ions (OCN-, Sod2-,and COa2- were chosen for study in KBr, KC1, and NaC1. These represent neither the best nor (6) A. Maki and J. C . Decius, J. Chem. Pkys., 31, 772 (1959). (7) H. W. Morgan, Symposium on Molecular Structure and Spectroscopy, Ohio State University, June 1957. (8) J. A. A. Ketelaar, and J. van der Elsken, J. Ckem. Phys., 30, 336 (1959). (9) W. C. Price, W. F. Sherman, and G. R. Wilkinson, Proc. Royal SOC.(London), ,4255, 5 (1960).
