internal filling solution with respect to dimethyl amine, since no dimethyl ammonium salt was added to it. No indication of this type of interference was observed in the sea water and aquarium water samples studied. The discharge from sewage treatment plants where the effluent is chlorinated may contain chlorinated ammonia compounds such as NHZC1 and NHC12. These species, however, do not influence the potential of the ammonia electrode (7). Ammonia analyses in which 1 to 4 pellets of NaOH were added to distilled water showed that the pellets contributed no detectable amount of ammonia to the samples. Washing the electrode with distilled water between samples removes any membrane memory except when there is greater than a 100-fold decrease in NHJ concentration from one sample to the next. In these cases, another determination should be made of the second sample to check for an erroneously high initial result. Electrode reproducibility was evaluated using samples from different marine life display tanks a t the New England Aquarium with varying ammonia levels. The results listed in Table I1 indicate that the relative precision of these analyses was fairly constant over a wide concentration range. The high levels found in samples I and I1 are an indication of inefficient conversion of reduced nitrogen, such as ammonia and nitrite, to nitrate by the tanks' biological filters. These conditions, if unchecked, may lead to fish mortality. (7) G . Sutherland, Hercules, Inc., Wiimington, Del., personal communication, 1972.
To test the accuracy of the method and to evaluate the electrode/portable unit as a tool for on-site analysis, a series of 1-liter samples of Boston Harbor water was collected. A Dorchester Bay sample was analyzed on site using the standard procedure described above with a battery powered magnetic stirring moter. With the meter in a horizontal position to minimize needle oscillation due to rocking of the boat, six analyses of the sample gave a with a standard deviation of mean value of 92 ppb "3-N 3 ppb. Other samples were acidified to pH 3-4 with 6M HC1 to stabilize the ammonia and analyzed the same day in the laboratory by the electrode and also by the phenolhypochlorite method ( 4 ) . The results of triplicate analyses with both methods are listed in Table Ill along with similar results for marine life display tank water analyses. The data indicate that the electrode provides an accurate means of analyzing ammonia in sea water and that it is usually more precise than the spectrophotometric method. Furthermore, the performance of the electrode in the field is comparable to that observed in the laboratory, showing the technique to be well suited for field analysis.
ACKNOWLEDGMENT The authors gratefully acknowledge the technical advice of M. S. Frant, Orion Research, Inc., and the capable work of A. J. Barker in the collection of samples. Received for review October 11, 1972. Accepted March 5 , 1973.
Calculations in Programmed Temperature Gas Chromatography When Void Volume Is Not NegligibleA New Approach Robert Rowan, Jr., and E. W. Leach Department of Chemistry, New Mexico State University, Las Cruces, N.M. 88003
A number of methods have been proposed for the calculation (prediction) of retention temperature in programmed temperature gas chromatography (PTGC). They have been discussed by Harris and Habgood ( I ) . One of these which is particularly adaptable for use with a digital computer is that proposed by Rowan (2, 3 ) . This method, however, suffers from the fact that it does not take proper account of the void volume of the column. Habgood and Harris showed that performing the necessary integration over the temperature interval starting with the air peak, rather than the sample injection, does not really compensate for the use of net retention volume in place of retention volume as had been proposed. However, in the case of packed columns at any except extreme conditions (high r / F values, i.e., high tem.perature rise rates and/or low flow rates), the error caused by disregarding the void volume is negligible. (1) W. E. Harris, and H. W . Habgood, "Programmed Temperature Gas Chromatography," Wiley, New York, N.Y., 1966. (2) R. Rowan,Ana/. Chem., 33, 510 (1961). (3) R. Rowan,Ana/. Chem., 34, 1042 (1962).
In these cases, the void volume is usually only a few milliliters per gram of substrate (less than 10) and is small compared with the total retention volume. For capillary columns, however, void volume is generally of the order of several hundred milliliters per gram. Here it is, in general, not possible to disregard the void volume, since it is significantly large compared with the total retention volume. A treatment is here presented which will take account of the void volume in substantially all cases when packed columns are used and many cases in which capillary columns are employed. It will at the same time allow the use of certain techniques of calculation reported previously ( 3 ) which are especially well suited to use with a digital computer. Of course, direct numerical integration, which is the simplest method, can (and generally must) be carried out by means of a computer. The present method is not claimed to be any better, faster, or more economical than numerical integration. It is simply an alternative approach.
A N A L Y T I C A L CHEMISTRY, VOL. 45, NO. 9. AUGUST 1973
1759
Table I . Predicted Retention Temperatures Calculated in Various Ways Retention Temperature,
rlF
Vv, m l l g
Run
Calcd by this method
Numerical integration
O K
Using term 1 only
Exptl
Material
Hypothetical runs
120 180 180 180 5.0 5.0 5.0 25.0 25.0 25.0 50.0
0.097 0.097 0.146 0.293 0.1 1 .o 10.0 0.1 1 .o 10.0 0.1
385.7 388.5 402.1
385.5 388.3 403.1 434.3 365.2 434.6 545.6 366.0 442.0
NCa
365.2 434.7 545.2 366.2 442.0
380.3 380.3 391.2 411.1 365.1 432.9 530.2 365.8 432.9 530.2 365.1
NCa
367.3
367.0
365 4356 5466
Actual runs in capillary columnC
138 138 138 138 138 138
(12) (13) (14) (15) (16) (17)
0.035 0.035 0.035 0.035 0.035 0.035
315.2 317.0 319.8 322.8 323.8 333.4
315.1 316.9 319.8 322.8 323.8 333.5
311.0 312.9 315.9 319.2 320.3 330.3
314.5 316.2 319.5 321.2 323.0 329.0
No convergence. Values calculated from same data by numerical integration by Habgood and Harris ( 7 ) .
DERIVATION
Data supplied by G. Guiochon.
1 ---=
The basic equation relating the significant variables in
X + Y
FTGC at constant flow was first enunciated by Habgood
L(1 X
and Harris
1
+ (!273V,/T)dT
V,
2 methyl pentane n-hexane benzene cyclohexane 3 methylhexane methylcyclohexane
where Tr = retention temperature (OK), TO = starting temperature, Vv = void volume per gram of substrate at 273"K, T = column temperature, r = temperature rise rate, V, = specific retention volume, and F = flow rate, milliliters per minute per gram of substrate. Retention volume can be expressed in terms of the following equation
+
lnV, = (BIT) lnBg (2) where 0 = A H J R , the heat of evaporation from the solvent divided by the gas constant. B, relates to the entropy term and pertains to 1 g of solvent. Equation 2 can be written V, = BgeB/T
Y3 Y4 y n+ y )) xY + 2Y 2 - x" + jjz ... x"-l(x
(7)
It is clear that if Y > X , this series is of no interest, but if Y < X, it converges. The smaller Y J X is, the more rapidly it converges. (Obviously, the series can always be written so that the fraction, either Y / X or X / Y , is less than 1 except in the special case where X = Y.) If the terms of the fraction in Equation 4 are considered to be X and Y, then the fraction can be expressed in the form of Equation 5 and enough terms can be taken so that the last term (which includes 1 / ( X Y)) can be dropped with negligible effect. Equation 4, written in the form of Equation 5 , is as follows
+
(3)
and Equation 1 becomes
(4) An analytical solution to Equation 4 has not been presented. This work will show, however, that it can be transformed so that it can be integrated and evaluated analytically to any desired degree of accuracy. It can be shown that the fraction 1 / ( X Y) can be expressed as 1 1 Y +Y' - Y 3 + ... yn (5)
Equation 8 may be integrated by resorting to a change of variable. Let O/T = 4, then d T = -(O/4*)d@,and
r -
-@--Lql &$ "Y
2(273)V,
-+
2he-''
-
+
x+Y
x
x2
x 3
XYX
x4
+ Y)
or, in general,
1
x +Y
=
"y. E--(q r_ox*' +
y"+'(-1)"+' X"+'(X + Y )
Equation 5 can be written as 1760
A N A L Y T I C A L C H E M I S T R Y , VOL.
(6 1
All of the terms of Equation 10, including the irreducible exponential integrals, can be evaluated. By calculation
45, NO. 9, A U G U S T 1973
Table 11. Predicted Retention Temperatures Calculated in Various Ways Conditions Run
To,
8,deg
310.3 298
4726 4529
r , deg/min
0.O K
5,
F, mi/min/g
Hypothetical runs
(1)to (4) (5)to (11)
1.053X l o A 3
300 273
x 10-3
1.0
Actual runs in capillary column
(12) (13) (14) (15) (16) (17)
2852 2893 2924 3268 3263 3401
305.0 305.0 305.0 305.0 305.0 305.0
=
j
"
140-000
0
0
180-
1.699 X 1.999 x 2.625 X 1.186X 1.322 X 1.703X
10-2 10-2 10 -? IOe2
298 298 298 298 298 298
lod2
loe2
0.27 0.27 0.27 0.27 0.27 0.27
7.80 7.80 7.80 7.80 7.80 7.80
I
160-0
To 1 3 1 0 . 3
120-0
0
loo-.
0 0
80-0
e
14726.0
0
B :0.001053 0 0 0 0
Q
60-0000000
= 300.0
SUCCESS
0
o FAILURE
40-0
0
0
0 0
20-0 0 0
0.00
0 .
0 I
0
0
0
0
0 0 I
0 0 I
0 0 0 I
I
0 0 I
I
0 1
I
I
1
Figure 1. Limits of validity for calculation procedure
procedures already described ( 3 ) , 4 2 , the only unknown, can be determined and from this T,can be found. The only case where this approach would not be beneficial is one in which the ratio of void to retention volume is unity or near enough to unity so that a n impractical number of terms is required. When the indicated integrations are carried out for a sufficient number of terms (8 or 9), it becomes evident that all terms beyond the second can be described by a general equation
CALCULATIONS The existence of Equation 11 for all the higher terms made it possible to write a computer program which would compute a variable number of terms, depending upon the number necessary to reach a preset degree of convergence. Such a program was written (in Fortran) to calculate a maximum of 45 terms, the cut-off occurring when the kth term was less than 0.001 times ( r / F - term 1). Since, by ignoring void volume, one obtains
-As *2
r/F =
4"-Yn - 0 ) rn+n-l)
+
4"-*(n - l)(n - 0) n -i n--PI
+
+
...
4n;;n!)}]** @I
(11)
where n = r - 3 and Q = reference temperature. The equation is not suitable for the first two terms because they contain the irreducible exponential integral.
Bg
e-@ p-dq5 = t e r m 1
dl
the sum of all terms above the first can be looked upon as a correction of term 1 to take care of void volume. The cut-off criterion was selected a t a point where it was judged that further change in the correction terms could be neglected. In the calculation procedure, term 1 was set equal to (-&/OF) and 4 2 (the only unknown) was evaluated by a calculation procedure already described ( 3 ) . In brief out-
ANALYTICAL C H E M I S T R Y , VOL. 45, NO. 9, AUGUST 1973 * 1761
line, the method cited involves the algebraic determina/~ tion of $2 from In (* + Y) = (CZ- 114 + C I ( ~ Z ) ~CO, where is term 1 and Y is easily evaluated from the starting temperature. C1, Cz, and CO are constants. This value of $2 was then used to calculate all terms, using Equation 11, and term 1 was again evaluated as r / F (sum of terms 2 to k ) . A new value of 4 2 was calculated from the corrected term 1, and the entire process was repeated until successive values of $2 differed by less than 0.002. Usually, about 3 to 8 iterations were necessary.
+
RESULTS The calculation procedure was first tested upon various sets of synthetic data made up to study the importance of void volume and r/F. In addition, experimental data obtained with a capillary column were studied. The results are shown in Tables I and 11. In all cases the standard measurement was taken to be the value calculated by numerical integration. The difference between the value obtained by the series method (ie., the proposed method) and that using only term 1 is the error caused by neglecting the void volume. For a packed column, void volume seldom exceeds 5 ml/g of substrate and r / F is usually of the order of 0.1. This would, for example, be a packed column operating at a flow of 100 ml/min and a temperature rise rate of lo"/ min. Except under extraordinary conditions such as a very high r / F value, the error caused by neglecting void volume is generally negligible. Starting with the most usual conditions, values successively more drastic were chosen, up to a void volume of 180 ml/g with r / F = 0.1, and 5
ml/g with r / F = 10. Under these conditions, the series calculation checked the numerical integration exceedingly well. It is shown, however, that in extremely severe cases such as when both r / F and void volume are large, the series calculation does not converge. With rare exceptions, any calculation on a packed column can be done very well by the series method. In the case of the capillary column, where the void volume was 138 ml/g, temperatures by the series method checked the numerical integration values quite well and also were usually close to the experimental values. These data were obtained with exceptional care by G. Guiochon, Ecole Polytechnique, Paris, France. Here the effect of void volume was evident but errors due to its neglect would not be large. This was a 140-m squalane column, 0.25 mm, with argon as a carrier. It is clear that the series method can be used with capilllary columns as well as packed columns. The approximate limits of applicability of this method are shown by Figure 1, where r / F is plotted us. void volume. It can be seen that successful calculations (those in which the series converges) are defined by what appears to be an hyperbola. In fact, the relationship is approximately ( r / F ) V , = 35. For success, the product should probably be less than 30 for this particular set of parameters. Received for review December 6, 1972. Accepted March 16, 1973. This work was first presented at the National Meeting of the American Chemical Society, Washington, D.C., Sept. 1971. It was supported by Grant No. G.P. 8361 from the National Science Foundation.
Adsorption as a Mechanism for Separation of Nonionic Solutes by Pellicular Ion Exchange Chromatography Joseph J. Pesek and Jack H. Frost Department
of Chemistry, Northern lllinois University, DeKalb, 111. 607 75
Ion exchange chromatography has been successfully used to separate a wide variety of organic compounds. Most separations involve charged species such as acids, bases, and amino acids or charged species produced by complexing agents ( I ) . However, a significant number of separations of nonionic compounds on ion-exchange resins have been reported. Separations of such nonionic solutes as alcohols (Z),sugars (3-11), hydantoins (12), and phenacetin and caffeine (13,14) have been achieved by ion exchange chromatography. W. Rieman and H. F. Walton, "Ion Exchange in Analytical Chernistry," Pergamon Press, Oxford, 1970, pp 162-172. C. M. Wu and R. M. McCready, J. Chromatogr., 57,424 (1971). 0. Samuelson and B. Swenson, Acta Chern. Scand., 16, 2056 (1962). 0. Sarnuelson and B.Swenson, Anal. Chim. Acta, 28,426 (1963). L. I . Larsson and 0. Sarnuelson. Acta Chern. Scand., 19, 1357 (1965). R . M. Saunders, Carbohyd. Res., 7, 76 (1968). M. E. Evans, L. Long, and F. W. Parrish, J. Chrornatogr., 32, 602 (1968). 0. Samuelson and H. Stromberg, Acta Chem. Scand., 22, 1252 (1968).
1762
A N A L Y T I C A L C H E M I S T R Y , VOL. 45,
NO. 9,
The nature of the solute-resin interaction for the above solutes is not completely understood in all cases. There are several possible mechanisms which might contribute to the separation of nonionic compounds by ion exchange chromatography: (1) solvation of the solute by the resin acting as an organic solvent, (2) a sieving effect that would discriminate on the ability of the solute to penetrate into the pores of the resin, (3) adsorption of the solute a t the ion-exchange site, and (4) adsorption of the solute on the resin matrix. One or any combination of the above mechanisms may contribute to the retention of the solute. Mechanisms 3 and 4 may be evaluated by the use of pellicular ion-exchange resins. The pellicular resin con(9) 0. Sarnuelson and H. Stromberg, Fresenius' Z. Anal. Chem., 236, 506 (1968). (10) H. G. Walker and R . M. Saunders, Cereal Sci. Today. 15, 140 (1970). (11) P. Jonsson and 0. Sarnuelson,Ana/. Chern., 39,1156 (1967). (12) M. W. Anders and J . P. Latorre, Anal. Chern., 42, 1430 (1970). (13) R . A. Henry and J. A . Schmit. Chromatographia. 3, 116 (1970). (14) R. L. Stevenson and C.A . Burtts, J. Chromafogr., 61, 253 (1971).
A U G U S T 1973
