Nitric acid-air diffusion coefficient: Experimental determination

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Vol. 20. No. 3. pp. 559463.

Ooo44981@6 53.M) + 0.00 Fkrgamon Press Ltd.

1986

Britain.

NITRIC ACID-AIR DIFFUSION COEFFICIENT: EXPERIMENTAL DETERMINATION J. L. DURHAMand L. STOCKBURGER Atmospheric Sciences Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711, U.S.A. (First received 8 Muy 1985 and infiwljorm

29 July 1985)

Abstract-Trace gaseous HNO, in air is removed in a laminar flow nylon tube. The HNOl deposition pattern was obtained by sectioning the tube, extracting with an aqueous solution, and measuring the concentration by ion chromatography. Mass transport analysis of the deposition pattern demonstrated the

HNO, was removed from the air stream at a rate controlled by gaseous diffusion. The HNOa-air diffusion coefficient ==0.118f0.003cm2s-’ (n = 7) for T = 298 K and P = 1 atm. It exhibited no dependence on relative humidity over the range 5-95 %. Key word index: Nitric acid, relative humidity, diffusion coefficient, denuder tube.

where C(0) = concentration of trace reactive gas at inlet, pg m- 3 a = 0.819 D = mutual diffusion coefficient, cm2 s- r Q = volume flow rate, cm3 s- ’ C = average concentration of trace reactive gas at x, pgrn-” x = axial distance from reactive tube inlet, cm.

INTRODUCTION

The deposition of nitric acid (HNO,) to the earth’s surface has been associated with ecosystem acidification (Likens et al., 1977). and particulate ammonium nitrate has been associated with the deterioration of atmospheric visibility (White and Roberts, 1977). The development of strategies to reduce such impacts requires measurements of ambient air quality to guide the formulation of rates of formation and removal to The diffusion coefficients of reactive gases may be observe the response due to changes in N-oxides determined by fitting mass penetration data to emissions. The sampling of HNO, and particulate Equation (1) (Thomas, 1955; Bennett and Adams, nitrate salts is difficult because of possible biases due to 1968; Durham and Fish, 1971). If the diffusion coefthe shifts in the equilibria of the dry and wet ficient of the trace reactive gas in air is known, then HNOs-NH3-NH,N03 systems. The equilibrium ‘perfect-sink’ conduits may be designed and operated as thermodynamics of these systems are known (Stelson ambient air samplers to deplete a predictable fraction et al., 1979; Stelson et al., 1984) but the evaporation of the gas. C(0) may be determined by measuring the kinetics are not. Such shifts may be induced in the quantity of gas that deposited to a fraction or penesampler by changes in air temperature or HNO,, trated a conduit with a perfect-sink’ wall. NH,. or water vapor concentrations, but the response Passive samplers based on Fickian diffusion may be time cannot be easily predicted due to the lack of designed to collect trace reactive gases in the presence kinetic data for evaporation from dry and wet of particles. A convenient design consists of a stagnant particles. tube with an inert inner wall, an open end (or an inert, A convenient active technique to separate reactive permeable membrane cap), and an end cap whose inner trace gas from suspended particles with diameter surface is a ‘perfect sink’ for the trace gas (Coutant and > 0.01 pm is to flow the aerosol through a conduit Scott, 1982). The average ambient concentration of the whose wall is a perfect sink for the gas (Browning and reactive trace gas is given by Ackley, 1962; Bennett and Adams, 1968; Smith er al., 1969; Durham et al., 1978). The technique takes C(0) = (mL)/(AtD) (2) advantage of the relatively large diffusion coefficients where C(0) = the average concentration at the open of reactive trace gases compared to particles. For a end, pg me3 tube with laminar flow, Gormley and Kennedy (1949) m = mass of reactive trace gas accumulated have reported the mass penetration equation for by the end cap, ~8 species diffusion to a perfect-sink’ wall (first term L = the axial length of the inert tube, cm only): A = tube’s cross-sectional area, cm2 C/C(O)=aexp(-11.49Dx/Q) I = sampling duration, s. (1) 559

560

J. L. DURHAM and t. STOCKBURGER

A common variable to the active and passive samplers is their dependence on the mutual reactive gas-air molecular diffusion coefficient. If I) is altered during the sampling period and is not accurately known, a bias is introduced into the determination of C(0). Slight variations to D during sampling may result from temperature and pressure changes. However, if the reactive trace gas forms molecufar complexes (e.g. dimers, hydrates), then the ~rformance of diffusionbased samplers will be substantially altered due to the decrease of the diffusion coefficient. It has been reported that the HN03-air diffusion coefficient decreases (from 0.12 to 0.05 cm* s- ‘) as a function of relative humidity (O-95 %) and suggested that the likely cause is the formation of the hydrates ffNO~*rzHsO (Braman et al., 1982; J&tough et al., 1985). For a typical diffusion-depletion tube 50cm long and operated in laminar flow at 16.7 cm3 s- ‘, the penetration of HNO, as the postulated hydrates would increase from 1.6 to 17.8 7; as relative humidity increased from 0 to 95 “/,. If such m~ifi~tions of the effective HNOs-air diffusion coefficients are not taken into account (e.g. sampling at constant relative humidity), then the change in penetration transmits a bias to the estimate of HNO, concentration. The response of a passive sampler of the type described above is greater, as the collected mass is directly proportional to L7.Since Eatough et al. (1985) have interpreted resuhs reported by Durham and Spiller (1982) to support the existence of gaseous hydrates of HNO,, we have reexamined the dependence of the HNO,-air diffusion coefficient as a function of relative humidity. METHOD

Theq The fractional penetration of a trace reactive gas being removed by diffusion to a ‘perfect-sink’ wall is given by Equation (1). which requires: (a) a welldeveloped Iaminar fldw in theiube, (b) that ihe gas not be generated in the tube or deoieted cxcem at the wall. and (cl that C/C(O) c 0.8I9, since the series solution has be& trur&ted. O.rn&‘he determined from Equation (I) by regressingmeasurements ofC/C(O) and x at constant Q. For a reactive wall that accumulates the trace gas, direct measurements of C/C(O) are not practical, but C/C(O) can be obtained from the measurements of the deposited mass (M)) along discrete sectionsof the tube. The cumulative deposit of mass (Fif through i discrete section is:

K = uM, [ -

where

I + exp (II.49 DAx/Q)J. 19)

Then, In (M,) = in (K) - 11.49 Dx/Q.

(101

Equation (10) is the differential form of Equation (1). It carries the condition that i > 1 which, in addition to the truncation problem previously mentioned, excludes the first section (M, ) from the regression of in M, against x to obtain estimates of If and Mr. The precision of the m~surement of the mass on the sections usually decreasesas mass decreases. Therefore, In Mj must be weighted by the variance (Bevington, 1969) to remove the improper influence of the more imprecise measurements. The weighting factor is: I+$= (Mj/sj)‘;

s = standard deviation.

0))

If MT is known, then Equation (10) may be expressed as ln (Mi/Mr)

= In r (K/MT)-

11.49Dx/Q,

(12)

and the regression determines the value of a, which has a theoretical value of 0.819 (Gormiey and Kennedy, 1949).

EXPERIMENTAL The deposition patterns of HNOl were measured in inert Teflon pipes (i.d. t 0.9 cm) 94 cm long lined with nylon fiber mats (thickness = 0.015 cm). Since well-developed laminar flow is a necessarycondition at the entrance to the reactive zone, a 47-cm bare section of Teflon was left ahead of the reactive nylon zone. Also, a 7-cm bare section of Tegon was left downstream to prevent disturbam of the flow exiting the nylon zone. A nylon filter in a Teffon holder trapped- the HNOI that oenetrated the tube. The easeous HNC& was gene&d by three different methods”depending on the relative humidity required. For the lowest relative humidity, * 5 % r.h., HNO, was generated by vaporizing 0.05 ml of 0.1 N HNOa with air from an Aadcociean air system. For the intermediate relative humidities, 30 and 40%, HN03 was venerated bv vaoorixiirr 0.05 ml of 0.1 N HNOl with fihered &lass fiber z&d kylon &ers) room air. For the highest relative humidity, _ 95 % r.h., HNO, was generated by bubbling air from theclean air system through aqueous 1 Ii4H2S04 with a small amount of concentrated HNO,. This HNO, contaminated air was pumped through the tubes at an approximate flow rate of loo0 cm’min- ‘, regulated by a Praision Flow Devices Model 101 mass flow controller [standard deviation z 2 “/. After aamphng, the nylon liner w&cut into 8 sections, each 5.00 f 0.05 cm kmg. The NO; background was 0.01 pg per section, The sectionsand the filter were each extracted in 10cm3 of an aqueous solution of 0.003 h4 NaHCO, and 0.0024 M NasCO,, wbieh was also the carrier solution for the ion chromatograph. The standard deviation for determining the NO; mass in the extractwas the larger of 0.3 fig or f 3 “/, The analytical errors dominated those due to Bow rate ffuctuations and sectioning the nylon liner. RESULTS

= M,(l -C/C(O))

(4)

= M,[l

(5)

-aexp(-11.49Dx/Q)]

where M, = total mass of trace reactive gas entering tube, and x corresponds to the end point of Mj. If the discrete sections are of uniform length Ax, then Equation (5) may be expressed as F, = M, [I -a exp (I 1.49DiAx/Q)] where

(6)

Ax = x/i

The mass of the reactive trace gas deposited on section j is Mj,;

= (Fi -Fi_ = K exp ( -

,), i >

1 11.49trx/Q)

(7) (8)

The laboratory conditions for each of the seven experiments are given in Table 1. These experiments arc paired replicates for temperature, pressure, and reIative humidity, except for No. 5, whose replicate was lost due to malfunction of the ion chromatograph. For experiment, weighted values of each the In (MI/M,) were regressed against the axial distance .Y to estimate in (K/M, ) and - 11.49 (D/Q), which are the intercept and slope, respectiveiy, of Equation (I 2). The estimates of these parameters are in Table 2. The weighted reduced chi-square (xt = X*/V) for each

561

Nitric acid-air diffusion coefficient:experimental determination Table 1. Experimental conditions ExP. No.

: 3 4 5 6 7 -

Total NO; 0%)

Flow rate (cm’s_‘)

Temperature (“C)

Pressure (atm)

Rel. humidity f %)

74.823.9 88.4k4.2 142.8k6.2 113.8fS.l 226.8k9.6 171.0i7.3 166.6k6.7

1600~0.32 17.17&O&l 17.17&0.34 1600~0.32 17.1710.34 17.17*0.34 1600*0.32

23.5 f0.2 23.5 If:0.2 22.8 f 0.2 22.8 j: 0.2 23.3 & 0.2 23.9 f 0.2 23.9 kO.2

1.005

95*5 95is 4o*s 40*5 30+5 5Lt5 5+5

I.005 0.993 0.993 1.000

1.002 1O02

Table 2. Estimates of Parameters to tit Equation (12) ExP. No.

Intercept = In (KIM,)

: 3 4 5 6 7

-0.759 + -0.828 ?I 0.048 0.056 -0.996~0040 -0.892 &O&t4 -0.905kO.036 -0.812*o.tMO -0.916+0.039

Slope = - 11.49D/Q (cm-‘) -0.0904 & -0.0834 f 0.0035 O.OO28 -0.0760+0.0020 -0.08 f I f 0.0024 -0.07~*0.~16 -0.0843 f o.OO20 -0.0780~0.0019

1 X”

V

0.8674 0.0709 1.3283 0.5184 2.2617 1.6802 1.5997

5 5 5 5 5 5

p,

(x2.

Vf ( %I+

>99 50 25 76 5 13 16

*Probability of exceeding $..

experiment was calculated from (~vington,

1969):

1 I 1~“5[hmj-lnAj]

Jft= (l/V) i

M;r[ln(MjIMT)-In(~j,MT)12

Table 3. Estimates of a and D, from fit to Equation (12)

(13)

Exp. No.

2

-(i/v)

2

where in Aj is estimated from the regression equation with the parameters in Table 1, and v is the degree of freedom (number of data points -number of coefficients estimated - 1). Except for Experiment No. 1, the values of the reduced chi-squares are contained within the 95 Y0confidence interval, which is 0.1662 c P,(x2. v) < 2.5000. The reduced chi-square is also equal to the ratio of the variance of the fit to the variance of the data. If the two uncertainties are equal, the reduced chi-square should be approximately unity. The reduced chi-square for Experiment No. 1 is much less than unity; that may be due to an overestimate of the experimental error or fortuitous fluctuations in the variance of the fit. Estimates of a were made from the intercepts In(K/Mr) in Table 2 through Equation (12). The standard deviations of a were obtained by the transformation (Bevington, 1969): s, = sin (K/M,drln(KIMT)J/d(KIMT)

(14)

= sln(KI~,)~CUUM,) exp (Kl+)l/cxp

1 2 3 4 5 6 7 Weighted average

1

(57.45 D/Q) - 11).

The estimates of a f s for each experiment are given in Table 3. The vaunt-weighty average irifX = 0.829 + 0.012, which agrees well with the theoretical value of

Do(cm2 s-i)

a

0.128i0.005 0.126~0.~ O.114+0.003 0.1 13+0.003 0.120~0002 0.127~0003 0.109+0.0O3 0.118+0.003

0.818&0.035 0.8~*0.034 0.799kO.032 0.819~0.032 0.830*0.027 0.846~0.028 0.838+0.030 0.82920.012

0.819 derived by Gormley and Kennedy (1949). The estimates of D have been made from the slopes in Table2 and scaled to the reference condition T = 298 K and P = I atm by Do = P(298/T)*,‘D.

(15)

The

variance-weighted average be&s= 0.118 4:0.003cm2s-‘. For each experiment, the fraction mass deposited is plotted as a function of y, where y = 11.49(l/~)(T/298)‘.~(S/P)x.

(16)

The ycoordinate normalizes each point to the reference temperature (298 K), pressure (l/atm), and flow rate of 1 cm’s_‘, and Equation (12) becomes In ~M~M~)

= In SKIMS)

-l&y.

(13

The regression curve with the weighted averages of a

562

J.

L. DURHAM and L. SRXKWRGER

=0.829andIf0=0.118cm2s-‘islineBinFig.l.For y 1 3.5,? and IO, the seven points cannot be resolved until y increases. Theduster ofseven pointsat A in Fig. I corresponds to an average mass percent of 45.64 1.0 at y = 3.4 + 0.1 cm- 2 s. Thus, the fraction of mass deposited on the first section is constant and reproducible for the relative humidity range S-9.5 %. 60 r

DISCUSSION The excellent fit of the HNOa deposition data to Equation (12) and the constant values of a and D over the relative humidity range 5-9.5 % indicates that the nylon-lint tube satisfies the Gorm~ey-Kenn~y condition that the wall be a ‘perfect sink.’ The values of a and D exhibit no dependence on relative humidity.

I -

50

2aI-

0 :

10

;9 :._ 9 E - 7

6

3

Fig. I. Percent massdeposited to discrete section (Ax = 5 cm) vs y. For example, the scvcn points clustered at A represent the percent mass dcpositcd to the fkst S-em section and are plotted at the section’s exit coordinate (x = 5 em t4rreJponds to y = 3.4&0.1 en~-~s). In y-eoordinatcs, the plotted lincshaveslopesof -00. LineBis theregression linec&uiated for thcdatapointsand has the weighted y and Do values contain& in Table 3. The estimate of standard deviation for each point is shown as a vertical line or is less than the dimension of the point, which is the ease for y e 15cm -*s. The lines indicated by n = 0, 1,3. 5 and 10 have DOs calculated for the hydrates

HN03 ‘nH20.

Nitric acid-air diITusion coefficient: experimental determination

That is, the deposition of HNOJ to the nylon is controlled solely by gaseous diffusion; there is no exhibited surface resistance, indicating that possible surface water films do not reduce nylon’s reactivity. Also, HNOS vapor did not change its diffusion coefficient as a function of relative humidity in the range 5-95 %; this observation agrees with Eatough et 01. (1985). The diffusion coefficients for HNOa.nHtO were calculated from Gilliland’s (1934) semi-empirical equation and the predicted deposition profilesare plotted in Fig. 1 for n = 0, 1,3,5 and 10. The calculated value of 0.113 cm* s- ’ for n = 0 corresponds well to our experimental value of 0.118 + 0.003 cm2 s- ‘, and it agrees well with the value n of 0.103cm2s-’ reported by Eatough et al. (1985) and 0.121 m* s- ’ (not referred to standard T and P) for low relative humidity reported by Braman et al. (1982). Eatough ef al. (1985) observed that Do determined in tungstic acid-lined tubes decreased as a function of relative humidity. Although Braman et al. (I 982) and Eatough et al. (1985) did not present experimental determinations of a as evidence that their sampling tubes satisfied the GormleyKennedy (1949)conditions, it is likely that the tungstic acid surface was not a ‘perfect sink’ due to exceeding surface capacity or influences of absorbed water. Our results demonstrate that gaseous HN09 does not change hydration number over the relative humidity range 5-95 %; comparison with Gilliland’s semi-empirical theory suggests that HNO, is not hydrated for that range of relative humidity. Eatough et nl. (1985) report thermodynamic calculations that indicate n varies from 0.8 to 1.2 for relative humidity from 5 to 95%. However, the hydration number of HNOJ can be established unequivocally only by examining the i.r. spectra of HNO, as a function of relative humidity. We are not aware of such a study, but Tuazon et al. (1978,1981) have observed in the Los Angeles atmosphere (= 879 cm- ‘, the ON0 angle deformation) and 2 :: (= 896 cm- I, the overtone of the HO torsion). These reported frequencies are not shifted with respect to reference spectra of the pure vapor, which has been reported by McGraw et al. (1965). FTIR (vs. 2v,) was included in an intercomparison study of HNOJ measurement methods. For 12 selected sample periods, FTIR demonstrated good correspondence with the median HNO3 concentrations determined from all the methods (Spicer et al., 1982). Thus, for these periods, it is unlikely that HNO, was hydrated; otherwise, vg and 2v, would have been shifted and not observed.

CONCLUSIONS

The diffusion coefficient of HN03 in air (T = 298K, P = I atm) is 0.118~0.003cm2s-‘. No influence of relative humidity (5-95 %) was exhibited.

563

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