Supplemental material for:

A pH-based method for measuring gaseous ammonia

Sasha D. Hafner, John J. Miesinger, Walter Mulbry,

and Shannon Kondrad Ingram

USDA Agricultural Research Service

sasha.hafner@ars.usda.gov, sdh11@cornell.edu

Nutrient Cycling in Agroecosystems

January 8, 2012

1

This supplement to the manuscript provides additional details on the pH-based citricacid trap (CA-pH) method, specifically: additional experimental results (Section 1), detailson method calculations (Sections 2, 3, and 4), selection of operating conditions (Section 5),and details on interferences (Section 6).

1 Additional experimental results

0 50 100 150 200 250 300

Total NH3 (mmol kg−1)

(mm

ol k

g−1 )

−2

−1

0

1

2

−20

−10

0

10

(% o

f tot

al N

H3)

Figure S-1: Error in the calculation of total ammonia from measured pH for titration of 100mmol kg−1 citric acid with NH3. The smooth line is a fifth-order polynomial fit to data fromall three trials, with equal weight given to each trial.

2

−15

−10

−5

0

5

10

15

Cal

c. e

rror

(%

)0.01 0.1 1

−15

−10

−5

0

5

10

15C

alc.

err

or (

%)

0.1 1 10

−15

−10

−5

0

5

10

15

Cal

c. e

rror

(%

)

1 10 100

Difference in total NH3 (mmol kg−1)

Figure S-2: Error in the calculation of the increase in total ammonia between all pairs ofpoints for titration of 1 (top), 10 (middle), and 100 (bottom) mmol kg−1 citric acid with NH3.Filled circles are from pairs where the total NH3 concentration to citric acid concentrationratio is < 0.25:1. Dashed lines enclose about 90% of the values (excluding filled circles), andthe solid line shows the median.

3

0 5 10 15

0.00

0.05

0.10

0.15

Time (h)

Cum

ulat

ive

emis

sion

(m

ol m

−2 )

NH

3 flu

x (m

mol

m−

2 h−

1 )

0

5

10

15

20

Flux

Emission

Figure S-3: Ammonia emission from dairy cattle manure (5.8% dry matter, total ammonia48 mmol kg−1, initial pH 7.18) over 15 hr, measured using the CA-pH method, with a 10mmol kg−1 citric acid solution, at 21◦C. A 140 g sample was held in a 250 mL jar, with 240mL min−1 of air flow through the headspace. Two sets of flux calculation results are shown,based on a 10 min and 30 min sampling interval. The increase in acid trap solution totalNH3 at each step ranged from 150 to 540 µmol kg−1 for the 10 min interval and from 450to 620 µmol kg−1 for the 30 min interval. Residual standard error from a polynomial fit tototal NH3 concentration vs. time was 15 µmol kg−1.

4

0.0 0.5 1.0 1.5 2.0 2.5

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Time (h)

Cum

ulat

ive

emis

sion

(m

mol

)

10−3

10−2

10−1

100

Cumulative Rate

Em

issi

on r

ate

(mm

ol h

−1 )

Figure S-4: Ammonia emission from a 2.0 g sample of solution containing NH4Cl (100 mmolkg−1) and NaOH (1 mol kg−1) measured using the CA-pH acid trap method, with a 1mmol kg−1 citric acid solution, and a 2 min sampling interval. Cumulative emission wasdetermined from acid trap solution pH, and emission rate was calculated from consecutivemeasurements of cumulative emission by difference. Actual quantity of total NH3 in thesample jar was 0.199 mmol, while measured final cumulative emission was 0.197 mmol. Linesshow predictions from a first-order model, with the rate constant fit to cumulative emission,and maximum emission fixed at 0.199 mmol. Residual standard error from the model was12 µmol kg−1. The right axis has a logarithmic scale. The first point for emission rate isoff-scale.

5

0 1 2 3 4 5 6

Time (hr)

Tota

l aqu

eous

NH

3 (m

mol

kg−

1 )

10−3

10−2

10−1

100

101

657

375

422

63

19

21

48

7

35

22

17

16

4

12

9

1−2 −4

28

9

11

7 2 2

64

15

10

1112 12

21

6

1

22 2

2

5

0

32 7

6

10

8

77 7

D C

BA

Citric, pHCitric, salicylatePhosphoric

Figure S-5: Field evaluation results for four trials, showing total aqueous NH3 in acid trapsolutions, measured by the CA-pH method or the salicylate method in citric acid, or thesalicylate method in phosphoric acid. Each set of two or three lines (A, B, C, or D) representsresults from a single trial. Details for each trial are in Table S-1. Phosphoric acid was not usedfor all trials; of those shown, it was used in B and D (and is indistinuishable from salicylateresults for citric acid in trial D). Vertical lines show ± one standard deviation (n=3), and arenot included for phorophoric acid for clarity (they were generally similar to those for citricacid, with differences for some samples). Each point is labeled with apparent error (differencebetween mean CA-pH and salicylate results, as a percentage, shown as lower number) andcoefficient of variation among three replicates for CA-pH result (as a percentage, shown asthe upper number).

6

0 1 2 3 4

Time (hr)

Gas

eous

NH

3 (m

g m

−3 )

5

8 32

18

31

7 −25−18

166

11

22 94

895

14

0

10

20

30

0

10

20

Citric, pHCitric, salicylatePhosphoric

5

64 33 31

5 0 22 6

Figure S-6: Gaseous NH3 concentrations from the pH-based acid trap method for a singlefield trial (trial D). The upper data (which correspond to the left y axis) show results basedon the increase in aqueous NH3 and the interval air volume for each step (consecutive calcu-lation). The time interval in minutes used for each point is given as the upper-most number,printed vertically. The lower data (which correspond to the right y-axis) were calculatedusing cumulative aqueous NH3 and cumulative air volume (cumulative calculation). Verticalbars show ± one standard deviation. Numbers printed below the error bars are the apparenterror (difference between mean pH-based and salicylate results, as a percentage), and num-bers printed just above the error bars are coefficients of variation among the three replicatesfor pH-based results (as a percentage).

Table S-1: Operating conditions for field trials shown in Figs. S-5 through S-7.Trial Location Acid conc. Solution Gas flow Gaseous NH3

(mmol kg−1) mass (g) (L min−1) (mg m−3)A Barn 1 70 1, 1, 1, 1.5, 5 0.33B Barn 1 75 5 0.52C Manure pit 10 80 5 9.9D Manure pit 10 75 5 13

Notes: The multiple flow rates given for A correspond to each sampling interval.Solution mass is the initial value.

7

0 1 2 3 4 5 6

Time (hr)

Gas

eous

NH

3 (m

g m

−3 )

4

499

36

108 9 9

656

70

449

−163

1 22

20

35

60

60 60 115

0.0

0.5

1.0

1.5

2.0

0.0

0.5

1.0

1.5

2.0

Citric, pHCitric, salicylate

4

8217

3 4 6

656 386 424 83 28 25

Figure S-7: Measured gaseous NH3 concentrations from the pH-based acid trap method fora single field trial (trial A). See caption for Fig. S-6 for a description.

2 Calculation of activity coefficients

In the CA-pH method, activity coefficients are calculated from the extended Debye-Huckelequation [1],

log γi =Az2i

√I

1 +Bai√I

(S-1)

where γi = activity coefficient of species i, zi is the caharge of species i, I = ionic strength(molal scale), and ai = a parameter based on the hydrated ion size (Table S-2).

Table S-2: Values of the parameter ai, used in Eq.(S-1). All values are from Kielland et al. [2].

Species aiH2A

– 3.5

HA 2 – 4.5A 3 – 5NH+

4 2.5H+ 9OH – 3.5

Parameters A and B are functions of the dielectric constant (ǫ, unitless) and density (d,kg m−3) of water, and temperature (T , K). To calculate ǫ and d, we used the expressionsgiven by Truesdell and Jones [3], which are used in the speciation programs WATEQ [4] andPHREEQC [5].

A =1.82483 · 106d 1

2

(ǫT )3

2

(S-2)

8

B =50.2916d

1

2

(ǫT )1

2

(S-3)

The dielectric constant and density of water are both temperature-dependent, and are alsocalculated from the expressions used in WATEQ4F and PHREEQC,

ǫ = 2727.586+ 0.6224107T − 1075.112 logT − 52000.87

T(S-4)

d =1 + 0.1342489c

1

3 − 0.003946263c

3.1975− 0.3151548c1

3 − 0.001203374c+ 7.48908 · 10−13c4(S-5)

where T is temperature in K, and

c = 647.26− T (S-6)

9

3 Calculation of equilibrium constants

Expressions for calculating equilibrium constants as a function of temperature, and theirsources, are given in Table S-3.

Table S-3: Equations for calculation of thermodynamic equilibrium con-stants.Reaction logK† Source‡R1 0.09049+ 2729.299

Ta

R2 −280.78128− 0.09572T + 6194.857T

+ 115.3451 logT b

R3 −303.45133− 0.11955T + 5394.464T

+ 126.5393 logT b

R4 −359.86316− 0.16034T + 5223.334T

+ 151.90019 logT b

R5 § −4.21958+ 2915.139T

c

†T is in K, log is base 10.‡Sources. a. Transformed from expression given by Clegg and Whitfield [6],which was fit to the data given in Bates and Pinching [7]. b. Recalculatedfrom expressions given by Crea et al. [8], which were fit to the data givenin Bates and Pinching [9] c. Calculated from equilibrium constant andenthalpy given in Martell et al. [10] using the van’t Hoff equation.§H2O −−⇀↽−− H+ +OH –

4 Example speciation calculations

Examples calculations are given for a single solution composition to clarify the use of theequations given in the paper, and to provide values for testing algorithms. The final point inFig. S-4 is used. Given: 99.0 g of a 0.996 mmol kg−1 citric acid solution in the acid trap ata temperature of 23.1◦C, and a pH of 5.471. Equilibrium constants at this temperature aregiven in Table S-4. The activity of H+ is estimated from pH as 10−5.471 = 3.38 · 10−6. Giventhese values, along with the total citric acid concentration, the activity of H3A is calculatedusing Eq. (1), giving 5.32 · 10−7 mol kg−1. Ionic strength is calculated (by iteratively solvingthe complete system of equations) to be 0.00310. With values for these variables, Eqs. (2)through (4) are used to calculate the activity of the remaining citric acid species, which arelisted in Table S-5. Species concentrations are then calculated from activities and activitycoefficients. With values for the concentration of all citric acid species, the concentration ofNH+

4 is calculated from Eq. (7), giving 1.99 mmol kg−1. The estimate of the quantity oftotal ammonia in solution is then calculated as the product of the NH+

4 concentration andthe mass of water in the solution, resulting in 0.197 mmol NH3.

Table S-4: Equilibrium constants at 23.1◦C, cal-culated from the equations given in Table S-3.

Reaction log KR1 9.302R2 -3.133R3 -7.897R4 -14.290R5 -14.058

10

Table S-5: Citric acid speciation calculated for an example solution (citric acidconcentration = 0.996 mmol kg−1, pH = 5.471, T = 23.1◦C).Species Activity coeff. (γi) Activity (ai) Concentration (mi, mol kg−1)

H+ 0.946 3.38 · 10−6§ 3.57 · 10−6 (6)H3A 1.00 5.32 · 10−7 (1)† 5.32 · 10−7 (6)H2A

– 0.941 1.16 · 10−4 (2) 1.23 · 10−4 (6)

HA 2 – 0.786 5.91 · 10−4 (3) 7.52 · 10−4 (6)A 3 – 0.584 7.07 · 10−5 (4) 1.21 · 10−4 (6)NH+

4 0.940 1.87 · 10−3 (6) 1.99 · 10−3 (7)OH – 0.941 2.59 · 10−9 (5) 2.75 · 10−9 (6)

†Numbers in parentheses indicate the equation used to calculate the given value.All activity coefficients were calculated using Eq. (S-1).§aH was calculated from measured pH as 10−pH .

5 Selection of operating conditions

When selecting the conditions that will be used for a measurement trial, the most importantparameters are:

1. Ratio of gas flow rate to acid solution mass (volume),

2. Gas-phase NH3 concentration, total mass, or emission rate,

3. Citric acid concentration,

4. Sampling interval.

The citric acid concentration determines the quantitation limit. Once three of these param-eters have been fixed, the fourth can be calculated from

∆totNH3=

Qg

MH2O

cNH3∆t (S-7)

where ∆totNH3the change in total NH3 concentration (e.g., mmol kg−1) in the acid trap over

the time interval ∆t (e.g., min), Qg= gas flow rate (e.g., m3 min−1), MH2O = the mass ofH2O in the acid trap (≈ total acid solution mass), and cNH3

= the gas-phase concentrationof NH3 in the sample gas.

Use of this approach is probably best shown by example. Assume one wants to measure agas-phase NH3 concentration that is approximately 5 mg m−3 (0.3 mmol m−3). The samplematrix is air, so acidic gases are not a concern. A sampling interval of about 30 min is desired.These requirements fix two of the four parameters listed above. Because the sensitivity ofthe method is limiting in many cases, and the desired sampling interval is small, it makessense to select the most sensitive (i.e., lowest) citric acid concentration possible. In this case,because acidic gases are not a significant concern, we should start with 1 mmol kg−1 andadjust if necessary. This leaves one parameter, the gas flow:acid solution mass ratio, to bedetermined.

To determine this ratio, we need to consider what the sampling interval means. In thiscase, we need to have a sufficient change in captured NH3 every 30 min to allow for a suffi-ciently precise estimate of that change. Titration results described in the paper showed thata difference of 20 µmol kg−1 could be measured with error generally < 10%, but field resultswere reliably accurate only above 300 µmol kg−1, which we will take as the quantitation limit

11

here. This quantity is the minimum concentration change that must take place every 30 minin order to meet this sampling interval. Rearranging Eq. (S-7),

Qg

MH2O

=∆totNH3

cNH3∆t

soQg

MH2O= 0.3

0.3·30= 0.033 m3 kg−1 min−1 = 33 L kg−1 min−1. So, if the acid solution mass

was fixed at 100 mL (e.g., simply because of the size of available glassware) the gas flow ratewould have to be at least 3.3 L min−1. Or, if our gas pump flow rate was fixed at 1 L min−1,an acid solution of about 30 mL would be required.

Continuing with this example, assume we decide that 10 mmol kg−1 citric acid is necessary,to avoid interferences from acidic gases. Because sensivity will be lower, we may want toincrease our gas flow rate–assume that we can use a maximum of 50 L min−1 kg−1 (0.05m3 kg−1 min−1). Our question now is, what is the minimum sampling interval? Based onthe field trials described in the paper, let’s assume a quantitation limit of 1 mmol kg−1.Rearranging Eq.(S-7),

∆t =∆totNH3

cNH3

MH2O

Qg

so ∆t = 1.0.3·0.05

= 67 min. Continuing with these settings, how long would it take to reachthe capacity of the acid trap? Using Eq. (5), and setting ∆totNH3

= 25 mmol kg−1 gives1700 min, or approximately 25 measurements. Of course, since we selected ∆t to provide achange of 1 mmol kg−1, we can see that the capacity allows for 25

1= 25 measurements.

Operating parameters can be determined in a similar way for other scenarios. Whenmeasuring NH3 emission rate, the gas-phase NH3 concentration is not directly limiting. Inthese cases, the following equation can be used.

∆totNH3=

QNH3∆t

MH2O

(S-8)

where QNH3= emission rate of NH3 (e.g., mmol min−1). For example, assume that we are

interested in measuring emission from a manure sample with an emission rate of about 0.3µmol min−1, and want to use a 10 min sampling interval, and a 10 g (0.01 kg) acid trapsolution. What change will we see in total aqueous NH3 after one sampling interval? FromEq. (S-8), ∆totNH3

= 0.3·100.01

= 300 µmol kg−1. With this change, we could use 1 mmol kg−1

citric acid, or increase the sampling interval to about 30 min and use 10 mmol kg−1 citricacid.

6 Interferences

In the absence of any attempts to correct it, simulations showed that relative error dueto inaccurate determination of citric acid concentration is largest at the lowest total NH3

concentrations and approaches the relative error in citric acid concentation at higher totalNH3 concentrations. As described in the manuscript, calibration with the initial citric acidsolution as the low buffer reduces this error. In the absence of compensation through pHcalibration, strong acids that might be present in the acid trap solution (but not accountedfor) will cause a negative error approximately equal to the concentration of the acid, andstrong bases will cause an analogous positive error. These constant absolute errors willtranslate into large relative errors at low total NH3 concentrations. Error in the determinationof total NH3 concentration (actually NH+

4 concentration) is approximated by

ǫmNH4≃

n∑

i

mcaizcai

−m∑

j

manjzanj

, (S-9)

12

where ca represents additional base cations, an additional acid anions, and z the charge ofthese species. This source of error is significantly reduced if the initial citric acid solution isused as the low pH buffer for calibration; in this case Eq. (S-9) no longer applies.

Contamination present in the (NH4)2C6H6O7 used to make the high pH buffer may alsocontribute error to the method. Slightly inaccurate determination of (NH4)2C6H6O7 concen-tration in the high pH buffer has a negligible effect on pH calibration and ultimate determi-nation of captured NH3. Contamination of (NH4)2C6H6O7 with a strong acid or base causesa relative error < the relative concentration of the contaminant (mole basis). Contamina-tion with acid would cause a positive error NH3 determination, and the opposite is true forcontamination with a base.

As with contamination by strong acids, the absolute error caused by acidic gases is relatedto the concentration of the acid anions in solution, i.e., HCO –

3 , CH3COO – , and HS – (foracidic solutions, CO 2 –

3 concentrations are ≪ HCO –

3 and S –

2 ≪ HS – ). Error can be approx-imated by Eq. (S-9). At equilibrium, the concentration of an acid anion can be calculatedfrom the partial pressure of the acidic compound in the gas phase:

man =KHKaPanH

aHγan(S-10)

where man = concentration of the acid anion, KH = Henry’s law constant (mol kg−1 atm−1),Ka = dissociation constant for reaction anH ⇀↽ an – + H+, PanH = partial pressure of gasanH , and γA = activity coefficient of A – .

As described in the manuscript, the presence of interferences from acidic gases can bedetermined by sparging the final acid trap solution with a non-reactive gas. We tested thistechnique using a 1 mmol kg−1 (NH4)2C6H6O7 solution. Bubbling pure CO2 through thesolution (15 mL solution, 300 mL min−1 flow), caused a drop in pH from 5.48 to 4.58 (about−30% error in NH3 at pH 4.58) that took place over about 5 min. (The final pH predictedfrom our complete speciation model using PHREEQC was 4.57.) Sparging with air (300 mLmin−1) increased the pH to the initial value after about 10 min.

Acid trap solution pH is dependent on the concentration of citric acid. Because of this,water loss through evaporation will affect the measured pH and therefore the estimate ofcaptured NH3. This source of error can be eliminated by avoiding water loss, replacing lostwater, or determining the water loss and the resulting change in citric acid concentration andsolution mass. However, simulation results show that changes in water mass can generallybe ignored, as long as the total quantity (moles) of citric acid remains constant. The relativeerror in calculated captured ammonia caused by ignoring water loss decreases as citric acidconcentration and pH increase, and so for the scenarios we analyzed, is greatest at 1 mmolkg−1 citric acid with low concentrations of captured ammonia. Figure S-8 is a contour plotshowing relative error as a function of water loss and measured pH for the lowest concentrationaddressed in the paper, 1 mmol kg−1. As long as significant evaporation does not occur earlyon, its effects will be negligible. Ignoring the loss of 10% water, for example, causes an errorin calculated total NH3 of less than 10% at all pH values above pH 3.43, when the capturedammonia concentration is 0.42 mmol kg−1 (about 17% of the total capacity). For highercitric acid concentrations, the same error occurs at lower pH values (pH of 2.78 and 2.23,or total ammonia of 1.9 and 7.2 mmol kg−1 for 10 and 100 mmol kg−1 citric acid solutions,respectively). Avoiding significant water evaporation early on in a trial is a simple way toprevent this interaction from causing significant error.

13

Measured pH

Wat

er lo

ss (

frac

tion)

3.2 3.4 3.6 3.8 4.0 4.2

0.0

0.1

0.2

0.3

0.4

0.5

0.0 0.5 1.0

Total NH3 at 0 loss (mmol kg−1)

−50

−40

−30

−20

−10

−50

1.0

1.2

1.4

1.6

1.8

2.0

Tota

l citr

ic a

cid

(mm

ol k

g−1 )

Figure S-8: Predicted relative error in calculated total ammonia (as a percentage of thetotal NH3 concentration) caused by ignoring evaporation of water from a 1 mmol kg−1 citricacid solution at 25◦C. Lines are isolines of constant error, as a percentage of the total NH3

concentration. The bottom and left axes are linear. The right axis shows the citric acidconcentration resulting from the water loss shown in the left axis. The top axis shows thetotal NH3 concentration that corresponds with the pH values on the bottom axis, and is onlyaccurate in the absence of water loss.

References

[1] Zemaitis, J. F. Handbook of Aqueous Electrolyte Thermodynamics: Theory & Application

(Design Institute for Physical Property Data sponsored by the American Institute ofChemical Engineers, New York, N.Y, 1986).

[2] Kielland, J. Individual activity coefficients of ions in aqueous solutions. Journal of the

American Chemical Society 59, 1675–1678 (1937).

[3] Truesdell, A. H. & Jones, B. F. WATEQ, a computer program for calculating chemicalequilibria of natural waters. Journal of Research of the US Geological Survey 2, 233–243(1974).

[4] Ball, J. & Nordstrom, D. WATEQ4F (2010). URL http:// wwwbrr.cr.usgs.gov/

projects/ GWC chemtherm/ software.htm.

[5] Parkhurst, D. PHREEQC: a computer program for speciation, Batch-Reaction,One-Dimensional transport, and inverse geochemical calculations (2010). URLhttp://wwwbrr.cr.usgs.gov/ projects/ GWC coupled/ phreeqc/.

[6] Clegg, S. L. & Whitfield, M. A chemical-model of seawater including dissolved ammoniaand the stoichiometric dissociation-constant of ammonia in estuarine water and seawaterfrom -2C to 40C. Geochimica et Cosmochimica Acta 59, 2403–2421 (1995).

14

[7] Bates, R. G. & Pinching, G. D. Acidic dissociation constant of ammonium ion at 0 to50 c, and the base strength of ammonia. J. Res. Nat. Bur. Stand 42, 419430 (1949).

[8] Crea, F., De Stefano, C., Millero, F. & Crea, F. Dissociation constants for citric acidin NaCl and KCl solutions and their mixtures at 25 degrees c. Journal of Solution

Chemistry 33, 1349–1366 (2004).

[9] Bates, R. G. & Pinching, G. D. Resolution of the dissociation constants of citric acid at0 to 50, and determination of certain related thermodynamic functions. Journal of the

American Chemical Society 71, 12741283 (1949).

[10] Martell, A., Smith, R. & Motekaitis, R. Database 46: NIST critically selected stabilityconstants of metal complexes (2004).

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[12] Hafner, S. D. & Bisogni, J. J. Modeling of ammonia speciation in anaerobic digesters.Water Research 43, 4105–4114 (2009).

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[14] Martensson, L., Magnusson, M., Shen, Y. & Jnsson, J. . Air concentrations of volatileorganic acids in confined animal buildings-determination with ion chromatography. Agri-culture, Ecosystems & Environment 75, 101–108 (1999).

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