Salt Effects on the Titration of Neutral Bases SIR: To characterize the sharpening of weak-base titration end points by large concentrations of salts ( 2 ) ,Rosenthal and Dwyer (9, 10) introduced the factor QBH into the equilibrium expression for the dissociation of BH+ (the protonated form of the base B) :
12w
(
+ 20a + 150a2 + 500d + 625a4
1
)fB
(2)
This formula is obtained by substituting the mole fraction of free H30+ [Expression 11 of ref. (S)]into the equilibrium constant for the simple reaction
B
+ H30'
=
BH+
+ HzO
(3)
and comparing with Equation 1 above. v is the number of ions per molecule of the salt, C its molarity, and a is the water activity, which can be calculated (after conversion of C to the molal scale) from tables of osmotic coefficients (8). The numerical coefficients in the denominator represent the products of the successive hydration constants of the H30+ ion and are all generated from 20 for the first stage on the assumption that subsequent constants only differ from the first by a simple statistical factor (6, 15). The number 1296 ensures that QBH = 1 when a = 1: similarly 55.5 multiplies (1 - a) to cancel VCas a approaches unity. The activity coefficient of the un, either to be detercharged base, f ~has mined separately or allowed for in some empirical way-e.g., by assuming the known salting-out parameters for aniline to apply approximately to other bases for which salting-out data are not available. From the practical point of view it is of interest to be able to predict the effect of a salt on the end point of a titration, and this is conveniently done in terms of Smith's sharpness index qmsx (1, 1 4 ) . In this application a very precise knowledge of the activity coefficient of the base is fortunately not required, since vmax involves not QBH itself but its square root.
KBH is the thermodynamic dissociation constant and the quantities in brackets are molar concentrations. Because Q B H remains constant throughout a titration in a given salt solution, K'BH can be used as a simple concentration equilibrium constant, the value of which can be calculated from KBHonce QBH is known. We were working on a hydration explanation of this phenomenon ( 6 ) , in terms of a model developed previously (15) when Rosenthal and Dwyer's further discussion in these terms appeared (12). We differ from them in adopting a specific quantitative model (which is admittedly oversimplified) for the hydration of the hydrogen ion, and in ignoring for the present complicating effects such as the hydration of the indicators used in fixing the acidity scale. (These complications are probably compensated for roughly by using somewhat fictitious values for the equilibrium constants of the successive hydration stages of the proton). An advantage of the simple model is that it leads to the following explicit formula for &BE:
In the derivation of Equation 2, the activity coefficients of the species BH+ and free (unhydrated) H30' are assumed to cancel on the usual electrostatic grounds. For charged bases this convenient cancellation is not justified and some form of Debye-Hiickel extension has then to be introduced to cover the more complicated activity coefficient factor which then replaces f~ in QBH (11). As it stands Formula 2 therefore only applies to uncharged bases. EXPERIMENTAL
The base activity coefficients, f ~ , were calculated from the salting-out parameter (kJ by the formula 4 1ogKlfB =
hc,
(4)
where C is the salt molarity. Solubility measurements were made to find k, for aniline in CaC12 solutions since this was not recorded in the literature. Riedel reagent grade aniline was purified twice by distillation and kept in a dark bottle in an atmosphere of nitrogen. Its purity was checked by the Kappenschaar method (3). A 25ml. sample of the CaC12 solution (2 or 4M) was subjected to a stream of purified nitrogen in a 50-ml. dark ampoule for 10 to 15 minutes, after which 2 ml. of pure aniline was added and the bulb was sealed. The mixture was shaken in a thermostat a t 25' f 0.05' C. for 72 hours and then kept in the bath for a t least a further 48 hours to ensure that a complete separation of the phases had been achieved before withdrawing samples for analysis. From the following solubilities a salting-out parameter of 0.167 1. mole-' was obtained for aniline in CaCl2 solutions a t 25' C.: in water 35.91 grams per liter, in 2M CaC12 16.58 grams per liter, and in 4M CaC12 7.87 grams per liter.
~
Table I.
Base p-Nitroaniline
Test of Formula 2 for QBH against the Rosenthal and Dwyer (R and D) Data
Salt LiCl 2M
3M
4M
5M 6M 7M
o-Nitroaniline 4-Chloro-2-
KC1 4M NaCl 4M LiCl 4M
8M 9M CaCh 4M
nitroaniline Aniline
LiCl 8M LiCl 4M
2-Aminopyrimidine
LiCl 4M
1068
8M
8M CaCL 4M
ANALYTICAL CHEMISTRY
LOgioQBH R and D (9) Calcd.
PK'BH
Titr. error % from QBHof R and D (9) Calcd.
R and D (9)
Calcd.
(Using f~ anil)
0.48 0.74 1.05 1.30 1.64 1.98 0.58 0.82 1.05 2.49 2.84 2.03
0.40 0.67 0.96 1.28 1.65 2.05 0.45 0.74 0.97 2.48 2.92 1.90
1.47 1.73 2.04 2.29 2.63 2.97 1.57 1.81 0.76 2.20 2.55 1.74
1.39 1.66 1.95 2.27 2.64 3.04 1.44 1.73 0.68 2.19 2.63 1.61
1.37 1.62 1.90 2.21 2.56 2.96 1.84 2.05 0.62 2.08 2.50 1.73
32.7 24.5 17.2 13.0 8.7 5.9 29.8 22.5 74.4 14.3 9.6 24.4
36.2 26.4 19.1 13.2 8.6 5.5 34.4 24.7 84.5 14.5
2.49 0.87 2.13 1.15 2.60 2.30
2.69 0.91 2.36 0.91 2.36 2.10
1.46 5.47 6.73 4.79 6.24 5.94
1.66 5.51 6.96
1.34 5.51 6.96 4.55 6.00 5.74
33.7 0.97 0.23 0.21 0.40 0.56
26.4 0.93 0.17 0.28 0.53 0.69
...
'
8.8
28.3
Other salting-out parameters used were : for p-nitroaniline, 0.082 in LiC1, 0.030 in KC1 ( 5 ) ,0.080 in KaCl ( 7 ) ; for o-nitroaniline, 0.084 in LiCl, 0.12 in CaClz [assumed to be the same as for p-nitroaniline (6)] ; for 4-chloro-2-nitroaniline, 0.11 in LiCl (10); for aniline, 0.07 in LiCl (4);and for 2-aminopyrimidine the values were assumed to be the same as for aniline. All values are in liters per mole.
LITERATURE CITED a t the point ApH before or after the end point, and qmax is the sharpness (1) Bruckenstein, S., Kolthoff, I. hl., “Treatise on Analytical Chemistry,” index, given here by ( l / a ~ / K ’ ~ ~ ) / 4 . 6 , in I. 11. Kolthoff, P. J. Elving, eds., where aT is the concentration of the acid Yol. 1, Part 1, p. 469, Interscience, and base titrated. New York. 1959. Table I also includes (as ~ K ’ B H , ~ B ( 2 ) Critchfieid, F. E., Johnson, J. B., ANAL.CHEM.30, 1247 (1958). anil.) the values that would be cal(3) Kolthoff, I. hl., Belcher, K., “Voluculated for pK’gH if solubility data were metric Analvsis,” Vol. 111. PI). 537lacking and f~ values appropriate to 43, Interscience, New York,‘l9$7. (4) Long, F. A,, McDevit, W.F., Chem. aniline had to be used throughout as an Rw. 51. -119 - - 119,521. approximation. That this procedure ( 5 ) - L o i i , F. A., AIcIntyre, D., J . -Am. would give a fair estimate of the titraChem. SOC.76, 3243( 1934). tion error to be expected is shown by the (6) Ojeda, X, Wyatt, P. A. H., J . Phys. Chem. 68, 1857 (1964). figures for 2-amino-pyrimidine for which 17) Paul. AI. A.. J . Am. Chem. SOC.76. we had no solubility data. ‘ 3236 (1954). ’ The basis of the hydration explana(8) Robinson, R. A., Stokes, R. H., tion is that the salt reduces the hydra“Electrolyte Solutions,” 2nd ed., Butterworths, London, 1959. tion of the hydrogen ion (and thereby (9) Rosenthal, D., llwyer, J. S.,AKAL. increases its activity a t a fixed acid CHEM.35, 161 (1963). concentration) merely by reducing the 110) Rosenthal, D., Dwyer, J. S.. J . water activity of the solution. ProtonaPhvs. Chem. 66. 2687 11962’1. ’ (11) ?bid., 67, 774 (1963). tion equilibria are then displaced to the (12) Rosenthal, I]., Dwyer, J. S., Can. right: J . Chem. 41, 80 (1963). (13) Rosenthal, D., Oiwa, I. T., Saxton, Hs0+ * nHzO B = A. I).. Lieto. L. R.. J . Phvs.Chem. 69. BH+ ( n 1) HzO ( 5 ) 1588 (1965).’ (14) Smith, T. B., “Analytical Processes,” 2nd ed., p. 204 ff., Edward Arnold and Sufficiently soluble nonelectrolytes Co., London, 1940. should therefore have a similar effect, (15) IYyatt, P. A. H., Discussions Faraprovided that they are not comparable day SOC.24, 162 (1957). with water in basic strength or solvating MARIOOJEDA RENATO P~REZ power. I n confirmation of this, we have P. A. H. W Y A T T ~ been able to produce a similar sharpenFacultad de Quimica y Farmacia ing of the end point in the aniline-HC1 Universidad de Chile, titration by the addition of sugars, the Santiago, Chile effects of which are being investigated 1 Present address, Sheffield University, further. England. I
RESULTS A N D DISCUSSION
As Table 1 shows, values of log&BH calculated directly from Equation 2 are in substantial agreement with those quoted by Rosenthal and Dwyer (9). For practical purposes the percentage titration error gives the most direct indication of the salt effect in sharpening the end point, and here again the formula reproduces the effects of the Rosenthal and Dwyer & B E figures reasonably well. To estimate the titration error the formulae of T. B. Smith were used (1,14): ApH
=
loglo 14.6 7mxAZ’) for ApH = 0.5
and ApH
= 7,,,AT for ApH = 0.2 (in the case of aniline and 2-amino-pyrimidine) .
AT is the fraction under- or over-titrated
+
\ - - - - I
+ +
Study on a Detector for Gaseous Components Using Semiconductive Thin Films SIR: In earlier papers (5, 7 ) , the authors reported a new type detector for gaseous components, whose principle is based on the fact that the adsorption and desorption of gases causes a change in electrical conductivity of semiconductors. This is valid because the rates of adsorption and desorption of gas are increased a t high temperatures and the change in electrical conductivity is intensified by using a thin film of semiconductor. The authors will call this detector the semiconductive thin film detector. In this paper, the relationship between the electrical conductivity of the thin film of metal or metallic oxide, the adsorption of gases, and the characteristics of the detector are reported. EXPERIMENTAL
Preparation of Thin Films. A fused silica plate ( 5 mm. X 30 mm. X 1 mm.) was used as a substrate. A t both ends of this silica plate, a platinum wire was welded. A platinum film electrode was prepared around
the junction by the method previously reported ( 5 ) . The distance between the electrodes was about 10 mm. The metal was deposited in vacuum (below mm. Hg) onto the substrate. The deposited metal film was used without further treatment for the case where a thin metal-film detector was used. When a thin oxide-film was required, the deposited metal was oxidized a t 500’ C. in air. To obtain stable thin oxidefilms, thermal treatment a t 55O0-7OO0 C. was necessary. The appropriate thickness of the film was determined to be about 1000-10,000 A. The resistance of the obtained thin films was of the magnitude of a few megohms. Apparatus. A thin film was positioned a t the center of a borosilicateglass tube, 400 mm. in length and 10 mm. in inner diameter, and the leads were extracted from it as shown in Figure 1. The temperature of the thin film was adjusted within & l oC. with a thermister temperature regulator. Gaseous samples were passed through the tube using nitrogen or dry air as the carrier gas and the change in electrical conductivity was recorded.
The electric circuit for measuring electrical conductivity was the same as described in the previous paper ( 7 ) . A variable resistance, R,, was connected in series with the thin film and the electric current flowing through the film was measured as the potential drop across R, with a potentioniecric recorder. As a source of direct current, a 6-volt battery was used. Reagents. Gaseous samples were obtained from commercial sources and the purities were guaranteed t o be above 95%. -1 sample of ethanol vapor was prepared by the following method. l q u e o u s ethanol solution of an appropriate concentration was maintained a t 25’ C. in a thermostatic bath and the equilibrium vapor was collected in a 1- or 5-ml. gas pipet. The concentration of ethanol was determined from the equilibrium vapor pressure of the aqueous ethanol solution. Although the vapor contained some water, it was ascertained experimentally that the detection of ethanol was hardly affected by the existence of this water vapor. For liquid samples, reagents above extra pure grade were used. VOL. 38, NO. 8, JULY 1966
1069
