1192 Anal. Chem. 1984, 56, 1192-1194

Table 111. Determination of 20 pg of Si/mL in Aqueous Standard Solution Addition of Various Concentrations of Si Standard Solutionsa

C,O added, pg/mL IP, nA CXo found, fig/mL 5.00 -2.45 f 0.03 18.9

10.0 -1.63 i 0.02 19.6 20.0 -0.1 b 20.6 40.0 3.34 t 0.06 20.0

a Transient intensities are averages of three measure- This ments at Din” = 4.0 and Im = 3.33 i 0.01 nA.

measurement is an approximate value.

Table IV. Determination of Si in 85% Phosphoric Acid Sample concn of sample concn of Si in initial concn of in solution, g/L solution, pg/mL Si, in sample, pg/g

57.802 0.341 5.90 * 0.23 100.01 0.565 5.65 f 0.20 289.01 1.350 4.70 z 0.12

to support the above speculations for achieving higher accu- racy. It may be concluded that accuracy is enhanced by the choice of high injection volumes, up to a value of Din” of ca. 4, and that a ratio C,O/C,O between 2 and 2.5 is adequate.

The precision was examined by running within-day ex- periment of an aqueous solution containing 20 pg of Si/mL to which 40 pg of Si/mL standard solution was added at D = 3.3. The relative standard deviations for P and IP were 1.2 and 1.9% (two series, 17 measurements each). The mean values were then used to calculate the concentration of the analyte yielding results which deviated by 0.1% and -0.3% for series I and 11.

As stated above the standard addition method is not ex- pected to compensate spectral and chemical interferences, such as those that may be exhibited by practical samples. This work mainly examined the validity of eq 13 with standard solutions. However, the influence of viscosity on the results obtained by the present method was also investigated. The

results for the determination of Si a t various dilutions of concentrated phosphoric acid (85%) are summarized in Table IV. The mean values obtained decrease with increasing sample viscosity. This phenomenon reflects the change in nebulization efficiency with sample viscosity which was not compensated for using standard addition method but should be minimized if an internal reference were measured simul- taneously with the silicon.

ACKNOWLEDGMENT We appreciate the loan of the Fiatron instrument from

Baird Corp., Spectrochemical Products Division, Bedford, MA. Registry No. Si, 7440-21-3; phosphoric acid, 7664-38-2.

LITERATURE CITED (1) Ruzicka, J.; Hansen, E. H. “Flow Injection Analysis”; Wiiey: New

York, 1981; pp 146-176, pp 15-17. (2) Betteridge, D. Anal. Chem. 1978, 50, 832A. (3) Tyson, J. F.; Idris, A. B. Analyst (London) 1981, 106, 1125. (4) Tyson, J. F. Anal. R o c . 1981, 78, 542. (5) Tyson, J. F.; Appleton, J. M. H.; Idris, A. B. Analyst (London) 1983,

108, 153. (6) Tyson, J. F.; Appleton, J. M. H.; Idris, A. B. Anal. Chim. Acta 1983,

145, 159. (7) Greenfield, S. Spectrochhn. Acta, Parts 1983, 388, 93. (8) Ruzlcka, J.; Hansen, E. H. Anal. Chlm. Acta 1978, 99, 37. (9) Vandersllce, J.; Stewart, K. K.; Rosenfeld, A. G. Talanta 1981, 28, 11.

( I O ) Mahanti, H. S.; Barnes, R. M. Anal. Chem. 1983, 55, 405. (1 1) Cave, M.; Barnes, R. M.; Denzer, P. 1982 Winter Conference on Phs-

ma Spectroscopy, Orlando; ICP Information Newsletter: Amherst, MA, 1982; Abstract 23.

‘ On leave from I M I Institute for Research and Development, Inc., Haifa

Yecheskel Israel’ Ramon M. Barnes*

31002, Israel.

Department of Chemistry GRC Towers University of Massachusetts Amherst, Massachusetts 01003-0035

RECEIVED for review October 14, 1983. Accepted February 15, 1984. Supported in part by Department of Energy Con- tract DE-AC02-77EV-0432.

Band Broadening in Solid-Phase Derivatization Reactions for Irreversible First-Order Reactions

Sir: The use of solid-phase reactors in flow-through ana- lytical systems has been recently discussed (1). In liquid chromatography, this type of reactor is used to improve the sensitivity and/or selectivity of detection systems. Due to the low concentration of analytes detected, many derivatization reactions obey first-order kinetics with rate constant k,

k, A-D

If a narrow pulse of analyte, A, is introduced into the re- actor, separation of derivative, D, from the pulse of A may occur. Therefore, the solid-phase reactor behaves as a so-called chromatographic reactor (2). The resulting peak of D is skewed and fused with the peak of A.

This phenomenon, which restricts the use of solid-phase reactor in HPLC and FIA, has been called “reaction band broadening” and treated on the basis of a simple mathematical model (I). Usual band broadening mechanisms are not taken into account in this model derived for first-order kinetics.

For a skewed chromatographic peak, an exponentially modified Gaussian (EMG) defined mathematically as a con- volution of Gaussian with exponential decay represents a suitable model (4-7). The response curve is given by eq 2

where the essential parameters are as follows: A, peak area; 7, time constant of the exponential decay; t ~ , center of the gravity of Gaussian; and u, standard deviation of Gaussian. The quantity t ’ is a dummy variable of integration.

Also the reaction chromatogram of a first-order irreversible reaction is supposed to be a result of two independent pro- cesses: Gaussian band broadening and exponential decay. This fact led to the idea of treating the reaction chromatogiam as an EMG.

The aim of this paper is to supplement our previous paper (1) and demonstrate that a reaction chromatogram of a.fast

0003-2700/84/0356-1192$01.50/0 0 1984 Amerlcan Chemical Soclety

ANALYTICAL CHEMISTRY, VOL. 56, NO. 7, JUNE 1984 1193

9 ‘

? I J N I L

4 6

i l i’ i\,

8 I 4 t YEtnI iVE R E l E N i l O l l T IME

Figure 1. Derivatlve peaks calculated by means of a plate model (eq 2-4). Run numbers and essentlal parameters are identical with those glven In Table I.

and irreversible first-order reaction can be approximated by use of the exponentially modified Gaussian (EMG).

EXPERIMENTAL SECTION A Model 3600 Data Station (Perkin-Elmer, Norwalk, CT) was

used as a microcomputer programmed in BASIC. Response curves of the derivative formed in a first-order reaction were simulated by means of eq 3-5; the integral of error function in eq 3 was calculated by means of a polynomial approximation (3). All curves were evaluated according to a procedure proposed by Foley and Dorsey (4). The coordinates of curve maxima and the values of peak asymmetry (B/A) at 10% of the peak height were estimated numerically with precision of about f0.5% rel.

RESULTS AND DISCUSSION

A plate model of the chromatographic reactor derived by Kallen and Heilbronner (8) has been used for the simulation of reaction chromatograms. The model, valid for first-order kinetics, takes into consideration chemical reaction, separation, and Gaussian band broadening. The response curve of D is given by

where A A is the amount of analyte A introduced and t is a dummy variable of integration. Dimensionless parameters p, cp, and r are given as

p = k $ A p = 1 - ( t A / t D ) r = t / t A (4)

where t A and tD are retention times, k, is the rate constant, and N is the number of plates. Constraints a and /3 are defined as

a = r ( l - ( P ) ( I V / ~ + P / ~ N / ~ ) - N1j2 (5)

p = r(N1l2 + p / p W I 2 ) - N112

A family of curves were calculated according to eq 3-5 for various values of parameters p, p, and r , as shown in Figure 1. The curves have been subsequently evaluated as EMG; the fraction of A converted to D at the reactor output

x = 1 - exp(-p) (6)

exceeds 99.99% in all cases. Comparing the initial values of parameters p and cp with the estimates of time constant T given in Table I, one can deduce that

-p /P = T / t D (7)

and therefore

Thus, the values of tD , u, and r are obtained With a reasonable accuracy as it is evident from Table I.

Relationship 8 is almost identical with the equation derived for the “reaction band broadening” in the previous paper (1). For an immediate conversion of A to D (K, = m ) or the lack of separation ( tA = tD), the reaction-broadening phenomenon does not occur (T = 0).

The described approach makes it possible to separate the Gaussian component of band broadening from the reaction broadening characterized by the time constant 7. Conse- quently, the performance of HPLC or FIA derivatization reactors packed with a solid catalyst or reagent can be dis- cussed more exactly, e.g., in terms of relative plate loss or relative system efficiency (4) .

ACKNOWLEDGMENT

The assistance of StBptin KrupiEka in computer program- ming is greatly appreciated.

Table I. Essential Parameters of Derivative Peak

input valuesa run no. P I @

1 201-3 2 301-3 3 201-2 4 301-2 5 20/- 1 6 101-1 7 301-1 8 1 O l - I l 3

t A = 1 s; = 1 x io3. ..

tD, s

0.250 0.250 0.333 0.333 0.500 0.500 0.500 0.750

1 0 4 ~ , s 103?, s

0.791 3.00 0.791 2.50 1.054 3.33 1.054 2.22 1.581 2.50 1.581 5.00 1.581 1.67 2.371 2.50

peak asymmetry

BIA 3.32 2.86 2.86 2.12 1.74 2.86 1.38 1.38

t D , s

0.251 0.250 0.332 0.333 0.500 0.499 0.500 0.749

EMG estimates 1 0 4 ~ , s

0.797 0.799 1.066 1.067 1.610 1.599 1.630 2.404

1 0 3 ~ ,

2.89 2.49 3.32 2.24 2.51 4.99 1.63 2.51

1194 Anal. Chem. 1984, 56, 1194-1196

LITERATURE CITED (8) Kallen, J.; Heilbronner, E. Helv. Chim. Acta 1960, 43 , 489.

LuboiS Nondek (1) Nondek, L.; Brinkman, U. A. Th.; Frei, R. W. Anal. Chem. 1983, 55,

(2) Langer, S. H.; Patton, J. E. "New Develooments in Gas Institute Of Chemical Process Fundamentals 1466.

Chromatography"; Wiley: New York, 1973; pp 294-367. (3) Abramowitz, M., Stegun, I . A, , Eds. "Handbook of Mathematical

Functions"; National Bureau of Standards: Washinaton. DC. 1964: Czechoslovak Academy of Sciences 165 O2 Prague 6, Suchdol, Czechoslovakia

Applied Mathematics No. 55, p 932. (4) Foley, J. P.; Dorsey, J. G. Anal. Chem. 1983, 55, 730. (5) Yau, W. W. Anal. Chem. 1977, 49 , 395. (6) Grushka, E. Anal. Chem. 1972, 44 , 1733. (7) Pauls, R. E.; Rogers, L. B. Anal. Chem. 1977, 49, 625.

RECEIVED for review November 14,1983. Accepted February 16, 1984.

AIDS FOR ANALYTICAL CHEMISTS

Determination of Airborne Free Chlorine in the Presence of Ammonia by Capillary Column Gas Chromatography

John M. Cheplen,' Craig Barrow,* and Earl L. White2 Analytical Services Unit, Department of General and Biochemical Toxicology, Chemical Industry Institute of Toxicology, P.O. Box 12137, Research Triangle Park, North Carolina 27709

Chlorine ((21,) is a potent respiratory tract irritant. Acute exposure of mice and rats to high concentrations of Clz (1000 ppm) caused death in 28 and 53 min, respectively (1). Rats exposed to 9 ppm C12 (6 h/day, 5 days/week, for 6 weeks) developed severe inflammatory reactions in the upper and lower respiratory tract (2).

Interpretation of toxicity studies of C12 is complicated be- cause microbial degradation of urine and feces of animals generates ammonia (NH,) that is released into the air of inhalation chambers (3). NH3 and C12 react rapidly to produce monochloramine (NH,Cl) (4 ) which can alter the concentra- tion of free C12. Due to the formation of chloramines, de- termination of C1, in the presence of NH3 can yield falsely high values for free C12 using methodology which does not differentiate between free and combined Cl,.

Numerous methods for the analysis of C12 in air have been reported. Many of these involve trapping the C12 in a solution containing a chromophore that is reactive with Cl,, resulting in a change in the spectral properties of the solution (5). These methods lack the sensitivity needed for sub-part-per-million determinations of Cl, without resorting to very long sampling times. Another complication is the possibility of the further formation of chloramines from the presence of NH3 during one or more of the steps of some analytical procedures. Gas chromatographic procedures that use thermal conductivity detectors are available for determining free C1, in air directly, but they also lack the sensitivity necessary for sub-part- per-million determinations (6). Other methods available determine total Cl,, both free and combined, by reaction with potassium iodide to produce iodine proportional to the Cl2 species. The relative amounts of iodide and iodine are then measured with ion-selective electrodes (7). Recently, a technique has been published which discriminates between free and combined C12 in water based upon the chlorination

Present address: Union Chemicals Division, Union Oil Company of California, Solvent Technical Service Center, 8901 Research Drive, P.O. Box 26009, Charlotte, NC 28213.

Present address: Department of Chemistry, University of North Carolina, Chapel Hill, NC 27514.

of the para position of 2,6-dimethylphenol by free C12 (8). The present paper describes a modification of this technique for specifically determining gaseous C12 at low concentrations in the presence of NH3.

EXPERIMENTAL SECTION Reagents. Cylinders of chlorine (-105 ppm) and ammonia

(-105 ppm), both diluted with nitrogen, were obtained from Matheson Gas Co. (Morrow, GA). The 2,6-dimethylphenol (2,6-DMP) and 4-bromo-2,6-dimethylphenol(4-Br-2,6-DMP) were obtained from Aldrich Chemical Co. (Milwaukee, WI), and 4- chloro-2,6-dimethylphenol(4-C1-2,6-DMP) from Crescent Chem- ical Co. (Hauppauge, NY). n-Hexane (Burdick and Jackson, Muskegon, MI), distilled in glass grade, was used without further purification and C12-free water was obtained by distillation from KOH/KMn04. The 2,6-DMP stock solution was prepared by dissolving (sonicated for 30 min, then stirred for 1.5 h) 300 mg of 2,6-DMP in 1 L of C12-free water. The stock solution of 4- Br-2,6-DMP was prepared by dissolving 180 mg of 4-Br-2,6-DMP in 1 L of water as described for 2,6-DMP. NH&l was prepared as described by Corbett et al. (9).

Apparatus. Mass spectral data were collected on a Finnigan Model 4023GC/MS (San Jose, CA) system equipped with an Incos data system. A Hewlett-Packard Model 5880A (Palo Alto, CA) gas chromatograph equipped with capillary injection and a flame ionization detector was used for the 4-C1-2,6-DMP determinations. The capillary column (25 m X 0.3 mm i.d.) was fused silica (Hewlett-Packard, Avondale, PA) coated with OV-1. Helium was used as the carrier and makeup gas. Carrier gas pressure at the head of the column was 10 psi resulting in an average linear velocity of 35 cm/s. Splitless injections were used with a split vent delay of 45 s. Injector and detector temperatures were set at 250 OC and 300 "C, respectively. Column temperature was held at 40 O C for 2 min and then programmed to 200 "C at 10 OC/min for a 20-min sample analysis time. The packed column was a 1.8 m, 2 mm i.d. glass column packed with 5% SP 2250 on lOO/l20 mesh Supelcoport (Supelco, Inc., Belleforte, PA). Injector and detector temperatures were the same as for capillary with a helium flow rate of 35 mL/min. The column oven was held constant at 130 "C for a lO-min sample analysis time.

Generation of Test Atmospheres. Clz or C12-NH3 test at- mospheres were generated under conditions of dynamic air flow. Clz or NH3 was metered from cylinders through calibrated

0003-2700/84/0356-1194$01.50/0 0 1984 American Chemical Society