Table 11. Comparison of Results Obtained by Nitrometer and Electrode __ Nitric acid, Nitrometer, Electrode, mean of eleven mean of five -. Standard devia:ion .~ determinations determinations Nitrometer Electrode 5.31
5.25
0.03
n. 14
~~
Table 111. Determination of Nitric Acid in Oletiin Nitric acid, --. -. --Found by Ditkrericc frorri Found by electrode n itromrte: nitrometer ~
5.45 6.32 5.51 6.18 5.26 5.83 7.32 5.58 5.10 5.90
5.37 6.15 5.11 6 29 5.34 5.77 7.53 5.55 5.20 5.77
-.n.os -0.17 -0.10 +O.ll +O 08 -0.06 1-0.21 -0.03 t o . 10 13
obtained which enabled a calibratiori curve to be consxucted. The bulb was broken inside a stoppered vessel which contained a known volume of standard 0 . 3 N sodium hldroxide plus a suitable quantity of water. The volume of sodium hydroxide was calculated to be abount S ml less than the total volume required to neutralize all of the oleum. The cooled solution was titrated to the equivalence point using methyl red indicator, and the total volume of standard sodium hydroxide recorded. All total acidities agreed to kO”15Zabsolute error. The titrated solutions were transferred quantitatively to 250-ml volumetric flasks and separated from broken glass at the same time. The solutions wete diluted to the mark wi?h distilled water, mixed, and transferred to polythene bottles for storage. From the weight of oleum taken, and the nitric acid content, the molarity of each standard was calculated. Millivolt readings were obtained by dipping the electrodes into the standard solutions at room temperature. Stirring the solutions was found to be unnecessary and a steady millivolt reading was obtained after 3 minutes. The millivolt readings were plotted against the logarithms of the molar concmtrations of nitrate to yield a calibration curve which was used in subsequent analyses of unknown solutions.
The analysis of ‘’unknoms’’ was , 2 1 gram of oleum was collected in the giass buib. ‘::.it? acidity was determined by titration with hydroxide solution. Following diluti sample to 250 ml, a millivolt reading was obtaia.xi using the electrode system, and this was cornparzd with &e stsnJsrds which were run ai the same time under identical cocditims. ‘The concentration of nitric acid in the sample w s obtained from the calibration curve and the perc’entage v m calciila!ed froni the sample w i g h t RESLJETSAND
wscussra?i
Fable I1 shows the resuits obained when the electrode method was compared with the nitrometer rnethc~d fnr the determination of nitric acid in oleum, Siiice this COtiipEiZy operates a test sample system (h), a common sample of oleum containing nitric acid was annlyzed indqxndently i:? 5 company laboratories equipped with its v r n r i i t r m e t ~ .~ r Tile same sample was analyzed using the clectrode method. Many determinations of nitric acid in oleum were mad typical winter production samples usink the nitrcmrirr 2;cd electrode methods. Some of these are lisred i;i Table IIT The nitrometer determines nitrososu!furic acid in tidditiur? to free nitric acid, whereas the electrode will only respoi>d IC: nitrate ion. In all of the results quoted, no correction to the nitrometer for nitrososulfuric acid was made. In mast cares its concentration would be very low. The electrode method for nitrat;. determination has the advaniages of replacing the lengthy nitrometer method acd requiring only one sample for the snalysis of both total acidity and nitrate. The two component analy.iis of the okurr needs only one standard solution (NaOH) In addition to thc: calibration standards and apparatus for the electrode mrz,surernents. Furthermore, the handling of large quant.kies c? m r cury found in the nitrometer method is obviated. RECEIVED for review December 28, 1970. Accepted h h r c h 29, 1971. (6) “Treatise on Analytical Chemistry,” I. M. Kolthoff, P. J . Elving, and F. H. Stross, Ed., Interscienc?, New York, N. Y., 1967, Part iii, Volume I , p 67.
Conductometric Determination of pK, Values-Oxa Iic and Squaric Acids Robert I. Gelb University of Massachuselts-BBaston, Boston, Mass. 021lo’
DIRECT CONDUCTANCE MEASUREMENTS may be employed to determine p K , values for weak and fairly strong acids. The direct technique is difficult for fairly strong acids where impurities along with limited solubility may yield poor results. The direct method involves conductance measurements with a series of solutions of different concentrations of an acid. Darken (1) and recently Schwartz and Howard (2) have employed this technique to determine pK, values for some fairly strong acids. (1) L. S . Darken, J . Phys. Chem., 63, 1007 (19S9). (2) L. M. Schwartz and L. 0. Howard, J . Phhys. Chem., 75, 1798 (1971). 1110
ANALYTICAL CHEMISTRY, \/OL. 43, NO. 8,JULY 1971
The method employed here involves “titrsticn” of the acid samph with perchloric acid reagent while the cirndi~zt~lnc‘c i: recorded. The conductance data are compared with l-hncse obtained by “titrating” a sample of pure water with perchloric acid. The value of pK,, is estimated from these dats. Theory. In any solution containing both completr>iy dissociated perchloric acid and the partially dissociated acid HX, the value of K , of HX is determined by
where N denotes the fraction of dissociated H X ,C t h e acid concentration, and f* the rntan ionic activity iocfk-icr?ua.
The conductance of such a solution is
where 8 is the cell constant, &4HCIO, and AHX denote the eyuivalent conductances of the acids at the appropriate ionic strength, and the other symbols have their usual significance. Ordinarily direct use of Equation 2 to find CY and subsequently pK, is precluded by lack of knowledge of AHCIO,and AHX as functions of ionic strength. Several theoretical and semiempirical equations which allow calculation of Ancio, and AHX at finite ionic strengths have been developed. Use of these equations involves complex iterative calculations which may be further complicated by a lack of knowledge of A’Hx. The semi-empirical equations sometimes fail to give accurate results at high ionic strengths. This difficulty is circumvented by the following considerations. One can always prepare a second solution containing only perchloric acid in water having the same conductance measured with the same cell as the original solution containing the two acids. Denoting the properties of this pure perchloric acid solution by asterisks, the conductance is (3) Equations 2 and 3 together yield CHCIO,* AHCIO,* = Ciicio, AHCIO,
+ ~ C HAXH X
(4)
If HX is a 1 :1 univalent electrolyte, then the ionic strengths in these two solutions do not differ significantly and there. fore A H C I O = ~ A H C I ~ , * . Even if the ionic strengths differ by as much as 5 because of differing A values for the two acids, the equality is likely to be quite accurate. Our data on the equivalent conductance of HC10, solutions indicates that a change of in k near ~1 = 0.1 results in approximately a 0.2 change in ‘i. Furthermore the useful approximation that A H C I ~=, AIIX can be based on the relation that these values depend primarily, and in common, on the equivalent conductance of the hydronium ion. This approximation is to be refined by a subsequent calculation after pK, is estimated. With these two equalities introduced into Equation 4, there results
z
z
5z
CfIClO,
+ aCnx
= CHCI04*
(5)
from which A is calculated. There only remains f+ in Equation 1 to be found before K , is determined. In most cases f.t will not be known from experiment and high ionic strengths will preclude the use of the Debye-Huckel limiting law. Consequently, f+ must normally be estimated from a semi-empirical extension of the Debye-Huckel equation such as the Davies equation (3)
where p is the ionic strength These principles allow deteimination of pK, by an elementary experimental technique. First, the conductance of a solution of the acid H X is measured during the additicn of HCIOl reagent. This procedure yields a series of values of the conductance cs. CHCIO,.Then, a sample of pure water of the same volume as the HX solution before is “titrated” with perchloric acid and the conductance recorded. The
concentration of pure HCIO,(CIICI,,*) that has the same conductance as one recorded for thz mixed acid solution is obtained by interpolation. This procedure yields a value of C H C I ~for , * each value of CHCIO,. Equation 5 determines the corresponding a. The ionic strength in the mixed acid solution is then C H ~ I O ,cuCfIxwhich in turn determines f+ from Equation 6. Finally K , is calculated from Equation 1. For example, a typical experiment involved addition of 5.53 mmoles of oxalic acid to 100 ml of water arid subsequent addition of 10.00 ml of 0.9040F HCIO?. The coiicentrations of oxalic and perchloric acids in the resulting solution were 0.0503F and 0.08218F, respectively. A solution of pure perchloric acid in water that had the same measured conductance as the mixed acid solution above was found to con-, Cain 0.1039F HCIO1. Then, from Equation 5 , uCIrx = 0.0217F. The ionic strength of the mixed acid solution is 0.1039M and Equation G yields f i* = 0.607. Substitution into Equation 1 yields pKa = 1.328 The initial approximation that AZX = i Z ~ I ~ ~ lmay i, be rzfined by considering Equation 4 in the form
+
(7) where the equality AH~1o,* = .IkfCIO, has been introduced and where /3 = A H x / A H c ~ o C . Making a more accurate estimation of /3 and then using Equation 7 in place of 5 to determine LY will yield a more accurate estimate of pK, from Equation 1. Determination of p depends on the fact that this ratio is quite insensitive to ionic strength when applied to aqueous solutions of acids. The limiting equivalent conductance of perchloric acid, ~ H C I O , ” is 418 ( 4 ) mho cm*,’equiv. The corresponding quantity for Anxo dc-pends on the nature of the anion X-. Typical AX-’ values for small or medium sized anions range from 30 to 80, which implies that with AH+’ = 350, A ~ isx typically 380 to 430. Consequently, the ratio p will be within 9 % of unity at infinite dilution for most small or medium sized X-. The variation of /3 with increasing ionic strength can be estimated by means of a semi-empirical correlation such as Shedlowky’s (5) modification of the Onsager conductance equation. Cy
A = A’
=
(cHClO,*
- (BIA” f B z ) d p
-
CHCIOi)/pCHX
.f
+ Bd(1 - B l Z / L ) p
(8) As an example, if A’HX == 380, then /3 = 0.909 at ~1 = 0. At 25 “C with B1 = 0.23 and ,E?? = 61, Equation 8 prtdicts that at an ionic strength of 0.25M, AIix = 339, AHCIO, = 374, and their ratio is 0.906. For p closer to unity than 0.909, the ratio is even less sensitive to ionic strength. The ratio p can be determined experimentally at any convenient ionic strength. Orte additional conductance measurement is made with a pure dilute HX solution in which (BIA’
1 - .( Y C H S Z i.__ iX ._ R 1000 8 where th? .value of *iis calcuhtzd rrum the initial approximate value of pK,. The conductance of a ptire perchloric acid solution where aCHx = C * : { C ~is~ ,obtained by interpolation with the original data. The ratio of the conductances of the pure HX solution and the pure perchloric acid solution yields /3 directly. This /3 leads to a new estimate of pK, via Equations 7, 6, and l . The new pK, could, in turn, be used to determine a second refinement of ,6 but this was found to be unnecessary.
R. A. Robinsor, ana i.k’ Dzvies. J , Chem. Soc., 1937, 574. (5) T. Shedlovsky, J . Arner. C h m . Soc., 54, 1405 (1932). (4)
(3) C . W. Davies, “Ion Association,” Butterworths, London, 1962.
ANALYTICAL. CHEMISTRY, YOL. 43, NO. 8,-JULY 1971
1111
__-----
I _
l l l p
Table I. Initial Estimates of pKtl foe Oxalic 2nd Squaric Acids mnioles
mtnoles HX104 taken
*
HzGaOa
9.27 5.53 3.52 2.47 A\
pxa; 1.324 k 0.306 1.337 f 0.006 1.315 i 0.012 1.29 ?t 0 . 0 3 1.32 f 0 . 0 3
taken
PKBP 0.54 f 0.02 0.53 f 0 . 0 3 0.53 f 0 . 0 2 4.49 0.55 f 0 . 0 3 Av 0.54 f 0.03
1:.2 7.55 5.20
Each entry corresponds to the average of four o r Sve data points from a single “titration.” Table 11. Refined pK,, for Oxalic and Squaris Acids P(HtC204) =: 0.95; 0iH~CiOa)= 0.98 mmoles minoles HZC20* HjC,O( taken PKLI taken PK,, 9.27 5.53 3.52 2.47
--
1.286 i 0 . 0 ; 1.297 i 0 . W 3 1.274 + 0.008 1.26 i 0.02 Av 1 . 2 8 i 0.01
11.2 7.55 5.20 4.49
0.51 0.51 0.51 0.52 Av 0.51
i 0.01 i0.01 f 0.02 f 0.02 k 0.02
_l_l-_l___I__~
Table 111. Error Analysis Error in K by measurement __ With 0.050F With 0.100F HX; 0.150F Source of error NX, 7; HClOa, % Conductance measurement 1.3 3.0
+O.l% impurities present 0 . 4 % Error in limiting equivalent conductance + O . 5x
0.b 0.4 5.2 2.3 1.5 6.3 2.9 1.9
1.7 1.5 2.5
1.2 0.6 3.1 1.5 0.8
EXPERIMENTAL
Oxalic and perchloric acids were of Analytical Reagent grade. Squaric acid (1,2-dihydroxycyclobutene-3,4-dione) was obtained through the courtesy of Professor L. M. Schwartz and Mr. L. 0. Howard. The acid, originally obtained from Aldrich Chemicals, was recrystallized from water and found to have a neutralization equivalent of57.15 (theory: 57.03). Conductance measurements were made with the aid of a Leeds and Northrup Model 4959 conductance bridge with a sensitivity of +O.l%. A 1000-cycle signal was employed throughout. A dip-type conductance cell with 0 = 20 was utilized. Solutions were maintained at 25.0’ i 0.01 ‘C with constant stirring in a thermostat cell and allowed to reach thermal equilibrium fur a t least 15 minutes after each addition of reagent. Determination of p K , , for Oxalic and Squaric Acids. Weighed samples of the pure acid were added to 100 ml of distilled water and the cmductance measured after acidition of perchloric acid. Measurements were obtained when a one- to five-fold excess of perchloric acid had been added. Additivity of volumes was assumed in calculating concentrations. The results are sntnmarized in Table I. Values of p were estimated from conductance measurements with dilute pure solutions of oxalic and squaric acid and calculations that employed pKd1values from Table I. The results were p = 0.95 and 0.98, respectively, for oxalic and squaric acids. These values provided new estimates of pKai for the acids (Table 11). New values of obtained with these new estimates of pK,k were essentially identical with the first estimates. Darken 1112
( I ) has obtained a value of pKal for oxalic acid of 1.27 + 0.01 b y a conductometric technique and Bjerrum (6) has reported a balue of 1.25. Schwartz and Howard (7)have determined pKal for squaric acid as 0.55 0.15 by electrometric titration. The effect of the second dissociation of both oxalic and squaric acids could be neglected in these calculations. The values of pKa2for these acids have been reported as 4.266 (8) and 3.48 (7), respectively. The present method employs solutions of sufficiently high acidity so that a negligible fraction of the acid exists as the dianion.
ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
ANALYSIS OF ERRORS
Table I11 compares the extent to which experimental K , values depend on various parameters for this “titration” technique and the direct method involving conductance measurements with solutions of the pure acid. In each case, theoretical ionic concentrations and conductance values were calculated from the assumed pK, value and acid concentration. For convenience, activity effects and variation of equivalent conductances with ionic strength were neglected. The first number in each entry corresponds to the error calculated for an acid with pK. = O.OO0; the second p K , = 0.500; and the bottom one for pK, = 1.00. The effect of an error in conductance measurement was evaluated by calculating apparent K, values resulting from conductances of 0.1 % higher and 0.1 % lower than theoretical. Errors in A’HX were evaluated in similar fashion. For convenience, it was assumed that A’HX = A’Hc~o,. Several different kinds of impurities were considered in evaluating the effect of sample purity. These included strong acids along with neutral ionic and non-ionic materials. For the sake of convenience, all impurities were assumed to have equivalent weights approximately equal to that of the acid HX. The limiting equivalent conductances of acidic impurities were assumed equal to A’Hx. I n each case, the sample was assumed to contain 99.6% H X and theoretical ionic concentrations and conductance values were calculated o n this basis. In each case considered, the largest error in apparent K , values resulted in the case of neutral non-ionic impurities. Impurities of this type include acids weaker than H X which are not significantly dissociated in the strongly acidic solutions encountered with either the direct or titration method, but are not readily detected by ordinary analysis. The errors found in this case appear in Table 111. The effect of limited acid solubility is accounted for in the calculations. The solubility limit of HX is assumed to be 0.100F and for each value of pK, considered, the mixed solution containing 0.050F HX and 0.150F “210, is somewhat below the solubility limit of HX. Although the acid solubility is decreased by the addi!ion of acid, measurements with the mixed solution seem less sensitive to the effect of impurities. The decreased sensitivity of K, to impurities is due to the smaller values of QI encountered with the mixed acid method. CONCLUSIONS
The utility of the mixed acid method depends o n the accuracy of estimating the point at which R = R*. Experimental precautions including temperature control t o approximately *0.02 ‘C or better seem necessary. Further(6) J. Bjerrum, G. Schwartzenbach, and G. Sillen, “Stability Constants.’’ SDecial Publication No. 7, The Chemical Society, London, 1957-58. . (7) L. M. Schwartz and L. 0. Howard, J . Phys. Clieni., 74, 4374 (1970). (8) G. D. Pinching and R . G. Bates, J . Res. Nu/.B w . Stur~d.,Sect. A , 40,405 (1948).
more, the solutions here have somewhat higher ionic strengths than those employed in a direct conductometric method, so that a greater uncertainty in activity coefficients results. For this reason, along with the assumptions required, the present method seems limited to a precision of approximately sr0.05 pK, unit for acids with pK, = 0.0. However, the lower sensitivity of calculated pK, values to sample purity seems to recommend the mixed acid method for certain practical applications.
ACKNOWLEDGMENT
The author gratefully acknowledges the assistance of ProfessorL. M.Schwartz in this work, RECEIVED for review December 7, 1970. Accepted March 19, 1971. Acknowledgment is made to the donors of The Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research.
Measurement of Atmospheric Nitrous Oxide Using a Molecular Sieve 5A Trap and Gas Chromatography Miles D. LaHue, Herman D. Axelrod, and James P. Lodge, Jr. National Center for Atmospheric Research, Boulder, Colo. 80302 The presence of nitrous oxide, NzO, in the atmosphere has not .received much publicity, because the gas is not a direct product of technological pollution. Nevertheless, the concentration of NzO is about 250-300parts per billion (ppb or Two possible sources of N 2 0 are soil bacteria and photochemical reactions. One would believe that the bacterial source would vary seasonally, while a photochemical source might produce a constant NzO level. In order to discriminate between these two possible conditions, a very reproducible method for NzOanalysis is needed. Junge (I) reviewed some of the earlier methods of NzO measurement. Most used infrared spectrometry, but the measurements suffered from large COZand water interferences. Gas chromatographs with a thermal conductivity detector typically do not have the sensitivity to measure ambient NzO (300ppb) with a 5-ml air sample. Recognizing this fact, Bock and Schutz (2) concentrated NzOon molecular sieve SA. After the sample was taken, the molecular sieve was placed under vacuum and heated to 250-300 OC. The released NzO was pulled off by a Topler pump and stored in a gas buret prior to analysis by gas chromatography. This procedure can possibly cause erroneous values; Schiitz (3) reported thermal decomposition of NzO above 300 OC, and it is conceivable that reducing the pressure prior to transfer could remove NzOadsorbed on the molecular sieve surface. LaHue et al. ( 4 ) also used a molecular sieve and a heating technique, but found the reproducibility to be poor. Leithe and Hofer ( 5 ) recommended trapping atmospheric NzO on silica gel submerged in a dry ice-acetone bath and then heating the sample to drive the NzO onto a gas chromatographic column. However, the need to use a cold bath renders this method unsuitable for field work. The use of molecular sieve offers the advantage of allowing sample collection at any location. Furthermore, a transfer technique not involving heat or evacuation would bypass the ~
~
~~~~
(1) C. E. Junge, “Air Chemistry and Radioactivity,” Academic Press, New York, N. Y., 1963, pp 81-84. (2) R. Bock and K . Schiitz, J . Anal. Chem., 237, 321 (1968).
( 3 ) K . Schiitz, Ph.D. thesis, University of Mainz, Germany, 1966. (4) M. D. LaHue, J. B. Pate, and J. P. Lodge, Jr., J . Geophys. Res., 75, 2922 (1970). ( 5 ) V. W. Leithe and A. Hofer, Allg. Prukt. Chem., 19, 78 (1968).
problems mentioned above and would be simple and inexpensive (no Topler pump or vacuum system would be required). The method described below uses a molecular sieve trap for sampling, but the transfer technique has been significantly altered. A stream of water-saturated He passed over the sieve displaces the NzO. The water-displaced NzO is trapped on a silica gel column submerged in a dry ice-isopropyl alcohol bath. The silica gel column is then heated to transfer the NzO into a gas chromatograph. EXPERIMENTAL
Sampling System. Activated molecular sieve 5A (l/16-in. pellets) was obtained directly from Linde Division, Union Carbide Corp., and used without further preparation. (The NzO content of the unexposed molecular sieve should be determined, because this commercially activated molecular sieve was found to contain about 1 pg NzO/ll grams. Fur,thermore, each batch of molecular sieve must be thoroughly mixed to ensure the same NzO background for all sample tubes.) A sampling train similar to that described by LaHue et al. (4) was used with critical orifices controlling the sampling rate. The air was first passed over C a S 0 4 (8 mesh) and Ascarite (8-20 mesh) to remove most of the atmospheric water and COa prior to reaching the molecular sieve. The molecular sieve tube was made from stainless steel */*-in. 0.d. X 8-in. L with Swagelok fittings at each end. The tube contained 11 grams of molecular sieve. Such a tube can be sealed and mailed without fear of leakage and breakage. Transfer of NnO to Gas Chromatographic Sample Loop. Prior to introducing the NzO into the gas chromatograph, the experimenter must remove the NzO from the molecular sieve. (Molecular sieve 5A has a great affinity for water and will easily displace other trapped gases.) A He flow saturated with water vapor was passed over the molecular sieve to displace the NzO and t o carry the liberated NzO past C a S 0 4 and Ascarite into a U-tube filled with activated 8-20 mesh silica gel in a dry ice-isopropyl alcohol bath (-80 “C). (The substitution of Na for He did not give satisfactory results.) Figure 1 shows the experimental system. The U-tube T was fitted with Whitey toggle valves for isolation. Initially, dry He (bypassing the sample tube) flowed through the system with T at room temperature. This allowed all the air in the system t o be purged with the He still flowing. T was then submerged in the bath and allowed t o reach bath temperature. The sample tube was then placed into the system, and V ANALYTICAL CHEMISTRY, VOL. 43, NO. 8, JULY 1971
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