# Mass Transport of Gases across the Air–Water Interface: Implications for Aldehyde Emissions in the Uinta Basin, Utah, USA

## Abstract

**:**

## 1. Introduction

^{1/2}or D

^{2/3}scaling laws [44,45,46,47,48,49,50,51,52]. There have also been generalizations that allow both for irreversible [37,53] and reversible [54,55] aqueous phase reactions. However, to the best of my knowledge, no one has ever studied models that allow for reactions in both phases and for both forms to cross the interface.

## 2. Description of the Models

## 3. Definition of Variables

_{t}= F

_{1}+ F

_{2}is the total flux. The subscripts “0” and “∞” attached to concentration variables indicate interfacial and far-field concentrations, respectively. A generic expression valid for either phase or for either compound can appear in this paper without the relevant subscripts.

_{12}and k

_{21}are pseudo-first order, since variations in water concentration are negligible. k

_{12}refers to the rate of 1 → 2 and vice versa. Enhancement factors appear in models A2 and A3 as multipliers of certain transfer coefficients. As defined, enhancement factors are always greater than 1, so these models predict that reactions can accelerate transfer. Because diffusivities of small molecules agree better than an order of magnitude, we can usually expect that $Q\approx 1$. Because compounds 1 and 2 usually do not have the same mass, molar concentrations are used throughout. The equilibrium constants are defined as K = [diol]/[aldehyde]. I use the dimensionless air-over-water form of Henry’s constant.

_{1}and H

_{2}as they are used here are intrinsic. H

_{1}is the ratio of aldehyde concentrations only, excluding the gem-diol form. H

_{2}is the ratio of only the gem-diol concentrations. Effective Henry’s constants blur the distinction between the aldehyde and the gem-diol forms:

## 4. Justification of the Whitman Model

^{p}is determined only by fluid-dynamic properties of the solvent; no property of the solute, including D, is assumed to enter. Rather, the coefficient of the term in z

^{p}is assumed to depend only on three parameters, solvent viscosity η, solvent density ρ, and friction velocity at the interface, u* [42]. For any given p, there is only one combination of these three parameters that yields the correct units. The resultant scaling laws for L′ and k are:

## 5. Properties of the Models

#### 5.1. Independent Concentration Variables and Equilibrium Conditions

#### 5.2. Converting Model A1 to A1E

#### 5.3. Properties of the Models

_{A}and R

_{W}satisfy ${R}_{A}+{R}_{W}=1$ (see the supplementary information) and indicate the extent of control by one side or the other. When ${R}_{A}\cong 1$, the system is under air-barrier control; when ${R}_{W}\cong 1$, it is under water barrier control.

_{A3}< f

_{A4}always, but they often agree well. Good agreement occurs, for example, whenever flux of 2 through the interface is negligible. However, poor agreement is also observed, indicating that there are conditions in which models A2 or A3 are inadequate. The passage of both forms through the interface should not generally be ignored.

_{1}, d

_{2}, and d defined in Table 1 measure the typical distance over which molecules diffuse before they react. The dimensionless ratio Λ distinguishes between systems with fast or slow reactions: if Λ << 1, then molecules do not interconvert as they diffuse through the film, while if Λ >> 1, they interconvert many times.

## 6. Aldehyde ↔ Gem-Diol Reactions

_{2}O, by organic and inorganic acids, by bases, and by the hydroperoxyl radical. The reaction is probably also autocatalytic [22,58,59,60]. Calculations also indicate that the acid and radical catalysts may be more efficient than water, although the relative abundance of water still means that it is the most important catalyst.

_{12A}and k

_{21A}are then expected to be strong functions of the concentrations of any catalysts and to be slower than the equivalent reactions in the aqueous phase where the catalyst concentration is larger. The air film at the interface is expected to be water saturated, which translates into a strong temperature dependence for k

_{12A}and k

_{21A}arising from the dependence of absolute humidity on temperature. The aqueous reactions are also catalyzed by H

_{3}O

^{+}and OH

^{−}so that k

_{12W}and k

_{21W}are pH dependent, and their values are lowest at about pH 7.

_{2}O ↔ diol is written in terms of the partial pressures of each gas as

_{0}is a reference pressure of 1 atm. The expression we use for K

_{A}is

_{A}for the formaldehyde reaction is essentially independent of temperature, as shown in Figure 4. The effect of relative humidity on K

_{A}is also displayed in Figure 4. Of course, in the air film at the air–water interface, 100% relative humidity can be assumed.

_{1}for the aldehydes have been retrieved from Sander’s compilation [67]. H

_{2}for the gem-diols does not appear in his compilation, but it is constrained by the values of H

_{1}, K

_{A}, and K

_{W}. Henry’s constants are often difficult to measure, and there is usually considerable scatter in Sander’s compilation for any one compound, often by more than an order of magnitude. Here, I take the median Henry’s constants from the compilation, which appear to be good consensus values. Sander tabulates effective Henry’s constants, H

_{e}, for formaldehyde and acetaldehyde. Therefore, his entries must also be converted to intrinsic constants.

_{W}, k

_{12W}and k

_{21W}have been extensively measured and calculated theoretically. For these quantities, Table 4 and Table 5 report ranges of values equal to the middle half of datasets of independently measured or computed values. The value of the formaldehyde K

_{A}is taken from Figure 4 at 100% relative humidity.

_{12A}and k

_{21A}have never been measured for either system, but their ratio is constrained by K

_{A}. Therefore, the only available constraints on k

_{12A}and k

_{21A}are ${k}_{21A}\lesssim {k}_{21W}$ and ${k}_{12A}\lesssim {k}_{12W}$, as explained above. In calculations reported below, I have allowed k

_{12A}and k

_{21A}to vary by about four orders of magnitude while enforcing these constraints.

## 7. Results

#### 7.1. Numerical Results for Formaldehyde and Acetaldehyde

_{21A}was allowed to vary from ${10}^{-6}{\text{}\mathrm{s}}^{-1}$ to ${10}^{-2.5}{\text{}\mathrm{s}}^{-1}$, but the final results for f are insensitive to this variation. Neither the air- nor the water-side dominates in either system (R

_{A}= 0.544 or 0.234). f

_{A1E}is 87% and 58% larger than f

_{A4}for formaldehyde and acetaldehyde, respectively, so model A1E is not accurate in these cases. The ratios ${f}_{A2}/{f}_{A4}$ and ${f}_{A3}/{f}_{A4}$ are, respectively, 0.935 and 0.984, so model A3 is adequate for formaldehyde and acetaldehyde.

_{A}and K

_{W}throughout the air and water films. Similarly, Figure 6 displays concentration profiles in the $m\to \infty $ limit (corresponding to zero far-field concentration in the water side). Then, the [diol]/[aldehyde] ratios fall below K

_{A}and K

_{W.}

#### 7.2. Sensitivity to Parameter Variations

_{1}, D

_{1W}, D

_{2W}, D

_{1A}, D

_{2A}, k

_{12W}, k

_{21W}, K

_{A}, L

_{W}, and L

_{A}were sampled independently from log-normal distributions

_{21A}was allowed to vary subject to the constraints k

_{21A}< k

_{21W}and k

_{12A}< k

_{12W}. The variables K

_{W}, k

_{12A}, and H

_{2}were then calculated to enforce constraints given in Table 2. When σ = 0.15, 95% of the log-normal distribution lies within the range $0.5\times {10}^{\mu}$ and $2\times {10}^{\mu}$. Because K

_{A}for formaldehyde is not well known, its σ has been set at 0.5, which places 95% of the distribution between one order of magnitude below and one order of magnitude above ${10}^{\mu}$. Other less well-constrained variables have been assigned σ’s of 0.2 or 0.3.

_{A1E}, f

_{A2}, f

_{A3}, and f

_{A4}for both the formaldehyde and acetaldehyde models. The results obviously satisfy the inequalities f

_{A2}< f

_{A3}< f

_{A4}< f

_{A1E}, although the f

_{A2}, f

_{A3}and f

_{A4}curves are almost completely superimposable. Figure 8 shows the distributions of R

_{A}for both models. These rather broad distributions, with R

_{A}occurring over much of the available range 0 < R

_{A}< 1, indicate that neither model has exclusively air- or water-barrier control. Both models are near a tipping point: modulations of less than an order of magnitude in the model parameters significantly shift the balance between air- and water-control. Figure 9 shows the distributions of the ratios f

_{A1E}/f

_{A4}, which confirms the inequality f

_{A4}< f

_{A1E}. f

_{A1E}is on the order of 20% and 50% higher than f

_{A4}for the two respective models. Figure 10 displays the distribution of f

_{A3}/f

_{A4}and f

_{A2}/f

_{A4}for the formaldehyde and acetaldehyde models. The f

_{A3}and f

_{A2}curves are indistinguishable because f

_{A2}is very near f

_{A3}for these models. For acetaldehyde, f

_{A2}and f

_{A3}are typically 94.5% of f

_{A4}, but distributed broadly, while for formaldehyde, the ratio is about 99.7%.

#### 7.3. Comparison with Experiment

_{g}is the gas-phase concentration, equivalent to ${C}_{1\infty A}+{C}_{2\infty A}$. In the limit $m\to \infty $ of model A4, $F=-{C}_{1\infty A}{f}_{A4}/{H}_{1}$. Therefore, the connection between the two notations is ${f}_{A4}={H}_{1}\left(1+{K}_{A}\right){K}_{g}.$ (2) Liu et al. [85] measured H

_{e}for formaldehyde at 23 °C to be in the range ($0.896\text{}\mathrm{to}\text{}1.23)\times {10}^{-5}$, near the consensus value, $1.3\times {10}^{-5}$, reported by Sander [67]. They also measured water-to-air fluxes of formaldehyde. In their notation, $F={K}_{0L}{C}_{L}$, with ${C}_{L}={C}_{1\infty W}+{C}_{2\infty W}$. Compare this with the notation $F={C}_{1\infty W}{f}_{A4}$ in the $m\to 0$ limit of model A4. The connection between the two notations is ${f}_{A4}=\left(1+{K}_{W}\right){K}_{0L}$.

_{10}, the wind speed at 10 m above the water surface, using the 1/7-th power law [86]. As expected, the data display variations due to variable wind speed or agitation of the water phase. However, the model predictions are all consistent with the experiment, especially at lower wind speeds. In Section 4, we saw that L

_{A}or L

_{W}are effective film thicknesses, free to be chosen to give agreement with experiment. Therefore, the agreement displayed in Table 8 is mainly a testament to the ability of Schwarzenbach et al. [43] to estimate good L

_{A}and L

_{W}values.

## 8. Summary

## Supplementary Materials

## Funding

## Conflicts of Interest

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**Figure 1.**Four different models can be defined. A1 treats a single compound that does not react. Models A2, A3, and A4 assume that compound 1 reacts to form compound 2, either only in the water phase or in both phases. Model A4 also assumes that both forms, 1 and 2, are able to cross the interface. A1 is equivalent to Whitman [33], and A2 is equivalent to Hoover and Berkshire [54].

**Figure 3.**The red rectangle and blue curve are 1/E(z) for E(z) as given in Equations (3) and (4), respectively. They are drawn with the same area under the curves. L’ is the width at half-height of the blue curve; the area under the blue curve scales as L′/D. The red rectangle has area L/D.

**Figure 4.**Temperature dependence of the formaldehyde K

_{A}. Data are from Detcheberry et al., Bryant and Thompson, and from Iliceto and Hall and Piret as quoted by Bryant and Thompson [64,65]. The saturation vapor pressure of water was calculated according to [66]. The red and blue traces were also calculated assuming three different values of relative humidity.

**Figure 5.**Concentration profiles through the films as calculated in model A4 with m = 0 and corresponding to the calculations summarized in Table 6. All concentrations are normalized to ${C}_{1\infty W}=1$. Red = aldehyde concentration, blue = diol concentration. Intercepts at z = 0 and L are shown.

**Figure 6.**Concentration profiles through the films as calculated in model A4 with $m\to \infty $ and corresponding to the calculations summarized in Table 6. All concentrations are normalized to ${C}_{1\infty A}=1$. Red = aldehyde concentration, blue = diol concentration. Intercepts at z = 0 and L are shown.

**Figure 7.**Distributions of f

_{A1E}, f

_{A2}, f

_{A3}, and f

_{A4}when model parameters are selected according to Table 7. The curves for f

_{A2}, f

_{A3}, and f

_{A4}are practically identical at the resolution of the figure. Results for k

_{21A}between ${10}^{-6}{\mathrm{s}}^{-1}$ and ${10}^{-2.5}{\mathrm{s}}^{-1}$ have all been included, but also cannot be resolved.

**Figure 8.**Distributions of R

_{A}when model parameters are selected according to Table 7. Individual curves for k

_{21A}between ${10}^{-6}{\mathrm{s}}^{-1}$ and ${10}^{-2.5}{\mathrm{s}}^{-1}$ have all been drawn but lie on top of each other at the resolution of the figure.

**Figure 9.**Distribution of the ratio f

_{A1E}/f

_{A4}for the formaldehyde and acetaldehyde models. Curves for k

_{21A}between ${10}^{-6}{\mathrm{s}}^{-1}$ and ${10}^{-2.5}{\mathrm{s}}^{-1}$ are all displayed, but except for acetaldehyde at ${k}_{21A}={10}^{-2.5}{\mathrm{s}}^{-1}$, they are practically indistinguishable; 1.8% and 0.6% of the probability density, for formaldehyde and acetaldehyde respectively, are in the tails at f

_{A1E}/f

_{A4}> 4.

**Figure 10.**Distributions of f

_{A3}/f

_{A4}and f

_{A2}/f

_{A4}for the formaldehyde and acetaldehyde models. Curves for eight different values of k

_{21A}have been plotted but are indistinguishable, as are the curves for f

_{A2}and f

_{A3}.

Notation | Description | Units |
---|---|---|

SYSTEM VARIABLES | ||

${D}_{1A},{D}_{2A},{D}_{1W},{D}_{2W}{}_{}^{}$ | Molecular diffusivities | ${\mathrm{cm}}^{2}{\text{}\mathrm{s}}^{-1}$ |

${k}_{12A},{k}_{21A},{k}_{12W},{k}_{21W}{}_{}^{}$ | Reaction rate constants | ${\mathrm{s}}^{-1}$ |

${K}_{A},{K}_{W}{}_{}^{}$ | Equilibrium constants | dimensionless |

${H}_{1},{H}_{2}{}_{}^{}$ | Intrinsic Henry’s constants | dimensionless |

${H}_{e}$ | Effective Henry’s constant | dimensionless |

${L}_{A},{L}_{W}{}_{}^{}$ | Film thicknesses | cm |

${F}_{1},{F}_{2},{F}_{t}{}_{}^{}$ | Fluxes through the interface | ${\mathrm{mol}\text{}\mathrm{cm}}^{-2}{\text{}\mathrm{s}}^{-1}$ |

${f}_{1},{f}_{2},{f}_{t}{}_{}^{}$ | Mass transfer coefficients | ${\mathrm{cm}\text{}\mathrm{s}}^{-1}$ |

CONCENTRATION VARIABLES | ||

${C}_{1\infty W},{C}_{1\infty A},{C}_{2\infty W},{C}_{2\infty A}{}_{}$ | Concentrations at specific depths | ${\mathrm{mol}\text{}\mathrm{cm}}^{-3}$ |

${C}_{10W},{C}_{10A},{C}_{20W},{C}_{20A}{}_{}$ | ||

DERIVED VARIABLES | ||

$Q=\frac{{D}_{1}}{{D}_{2}}$ | Diffusivity ratios | dimensionless |

$m={\frac{{C}_{1\infty A}}{{H}_{1}{C}_{1\infty W}}}_{}^{}$ | Equilibrium indicator | dimensionless |

${d}_{1}={\left(\frac{{D}_{1}}{{k}_{12}}\right)}^{1/2}{}_{}$ | Reaction–diffusion distances | cm |

${d}_{2}={\left(\frac{{D}_{2}}{{k}_{21}}\right)}^{1/2}{}_{}^{}$ | ||

$d={\left({d}_{1}^{-2}+{d}_{2}^{-2}\right)}^{-1/2}{}_{}^{}$ | ||

$\mathsf{\Lambda}={\frac{L}{d}}_{}^{}$ | Reduced film thickness | dimensionless |

$\begin{array}{c}{\zeta}_{A}=\frac{{D}_{2A}}{{L}_{A}},{\zeta}_{W}=\frac{{D}_{2W}}{{L}_{W}}\\ {Q}_{A}{\zeta}_{A}=\frac{{D}_{1A}}{{L}_{A}},{Q}_{W}{\zeta}_{W}=\frac{{D}_{1W}}{{L}_{W}}\end{array}$ | Zeta-notation | ${\mathrm{cm}\text{}\mathrm{s}}^{-1}$ |

$E=\frac{\mathsf{\Lambda}\left(Q+K\right)}{\mathsf{\Lambda}Q+K\mathrm{tanh}\mathsf{\Lambda}}$ | Enhancement factors | dimensionless |

RELATIONSHIP | JUSTIFICATION |
---|---|

${K}_{A}={\frac{{k}_{12A}}{{k}_{21A}}}_{}^{}$ | Equilibrium constants are ratios of forward and reverse rate constants. |

${K}_{W}={\frac{{k}_{12W}}{{k}_{21W}}}_{}^{}$ | |

${H}_{2}{K}_{W}={H}_{1}{K}_{A}{}_{}^{}$ | Required by detailed balance. |

${C}_{2\infty W}={K}_{W}{C}_{1\infty W}{}_{}^{}$ | Assumption of far-field chemical equilibrium. |

${C}_{2\infty A}={K}_{A}{C}_{1\infty A}{}_{}^{}$ | |

${C}_{10A}={H}_{1}{C}_{10W}{}_{}^{}$ | Assumption of rapid exchange through the interface and local equilibrium across the interface. |

${C}_{20A}={H}_{2}{C}_{20W}{}_{}^{}$ |

Limiting Value | Air-Side Control ${\zeta}_{W}\gg {\zeta}_{A}$ | Water-Side Control ${\zeta}_{W}\ll {\zeta}_{A}$ | ||
---|---|---|---|---|

${f}_{A1E}\cong $ | ${\zeta}_{A}{H}_{1}\left({Q}_{A}+{K}_{A}\right)$ | ${\zeta}_{W}\left({Q}_{W}+{K}_{W}\right)$ | ||

${f}_{A2}\cong $ | ${\zeta}_{A}{H}_{1}{Q}_{A}$ | ${\zeta}_{W}{Q}_{W}{E}_{W}$ | ||

$\begin{array}{c}\left({\mathsf{\Lambda}}_{W}\ll 1\right)\\ {\zeta}_{W}{Q}_{W}\end{array}$ | $\begin{array}{c}\left({\mathsf{\Lambda}}_{W}\gg 1\right)\\ {\zeta}_{W}\left({Q}_{W}+{K}_{W}\right)\end{array}$ | |||

${f}_{A3}\cong $ | ${\zeta}_{A}{H}_{1}{Q}_{A}{E}_{A}$ | ${\zeta}_{W}{Q}_{W}{E}_{W}$ | ||

$\begin{array}{c}\left({\mathsf{\Lambda}}_{A}\ll 1\right)\\ {\zeta}_{A}{H}_{1}{Q}_{A}\end{array}$ | $\begin{array}{c}\left({\mathsf{\Lambda}}_{A}\gg 1\right)\\ {\zeta}_{A}{H}_{1}\left({Q}_{A}+{K}_{A}\right)\end{array}$ | $\begin{array}{c}\left({\mathsf{\Lambda}}_{W}\ll 1\right)\\ {\zeta}_{W}{Q}_{W}\end{array}$ | $\begin{array}{c}\left({\mathsf{\Lambda}}_{W}\gg 1\right)\\ {\zeta}_{W}\left({Q}_{W}+{K}_{W}\right)\end{array}$ | |

${f}_{A4}\cong $ | ${\zeta}_{A}{H}_{1}\left({Q}_{A}+{K}_{A}\right)$ | ${\zeta}_{W}\left({Q}_{W}+{K}_{W}\right)$ |

**Table 4.**Data relevant to the $\mathrm{HCHO}\leftrightarrow {\mathrm{CH}}_{2}{\left(\mathrm{OH}\right)}_{2}$ reaction at ≈ 300K and pH 7.

Variable | Value or Range | Source |
---|---|---|

${H}_{1}$ | 0.025 | Median from [67], corrected to intrinsic. |

${H}_{2}$ | $\approx {10}^{-7}$ | Never measured, but constrained by H_{1}, K_{A}, K_{W}. |

${D}_{1W}$ | $1.87\times {10}^{-5}{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [68,70,71] |

${D}_{2W}$ | $1.57\times {10}^{-5}{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [68,70,71] |

${D}_{1A}$ | $0.155{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [69,71] |

${D}_{2A}$ | $0.124{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [69,71] |

${K}_{A}$ | 0.045 | Figure 4. |

${K}_{W}$ | 1800 to 2270 | Middle seven of thirteen independent datapoints (experimental and theoretical) [63,64,72,73,74,75,76] |

${L}_{A}$ | 0.3 cm | [43] |

${L}_{W}$ | 0.02 cm | [43] |

${k}_{12W}$ | $9.8{\mathrm{s}}^{-1}\text{}\mathrm{to}\text{}10.6{\text{}\mathrm{s}}^{-1}$ | Middle four of six independent datapoints (experimental and theoretical) [74,75,77] |

${k}_{21W}$ | $\left(4.5\text{}\mathrm{to}\text{}5.3\right)\times {10}^{-3}{\text{}\mathrm{s}}^{-1}$ | Middle four of six independent datapoints (experimental and theoretical) [59,75,78] |

${k}_{12A}$ | Unknown | Never measured, but ratio ${k}_{12A}/{k}_{21A}$ is constrained. |

${k}_{21A}$ | Unknown | Never measured, but ratio ${k}_{12A}/{k}_{21A}$ is constrained. |

**Table 5.**Data relevant to the ${\mathrm{CH}}_{3}-\mathrm{COH}\leftrightarrow {\mathrm{CH}}_{3}-\mathrm{CH}{\left(\mathrm{OH}\right)}_{2}$ reaction at ≈ 300K and pH 7.

Variable | Value or Range | Source |
---|---|---|

H_{1} | $7.0\times {10}^{-3}$ | Median from [67] corrected to intrinsic. |

H_{2} | $\approx {10}^{-5}$ | Never measured, but constrained by H_{1}, K_{A}, K_{W}. |

${D}_{1A}$ | $0.119{\text{}\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [69,71] |

${D}_{2A}$ | $0.103{\text{}\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [69,71] |

${D}_{1W}$ | $1.46\times {10}^{-5}{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [68,70,71] |

${D}_{2W}$ | $1.29\times {10}^{-5}{\mathrm{cm}}^{2}{\mathrm{s}}^{-1}$ | [68,70,71] |

K_{A} | $\approx 0.005$ | Poorly constrained. See text. |

K_{W} | 1.19 to 1.35 | The middle thirteen of 27 independent datapoints (experimental and theoretical) [73,76,79,80,81,82] |

L_{A} | 0.3 cm | [43] |

L_{W} | 0.02 cm | [43] |

k_{12A} | Unknown | Never measured, but ratio ${k}_{12A}/{k}_{21A}$ is constrained. |

k_{21A} | Unknown | Never measured, but ratio ${k}_{12A}/{k}_{21A}$ is constrained. |

k_{12W} | $\left(0.005\mathrm{to}0.015\right){\mathrm{s}}^{-1}$ | Middle four of eight independent datapoints (experimental and theoretical) [75,77]. |

k_{21W} | $\left(0.0041\mathrm{to}0.012\right){\mathrm{s}}^{-1}$ | Middle four of eight independent datapoints (experimental and theoretical) [75,80]. |

**Table 6.**Sample calculations. k

_{21A}was allowed to assume eight different values as indicated. Each of these generated eight different values for k

_{12A}, d

_{A}, and Λ

_{A}, but all remaining variables were insensitive to these variations, at least to the number of significant figures given.

Variable | Formaldehyde | Acetaldehyde |
---|---|---|

H_{1} | 0.025 | $7.0\times {10}^{-3}$ |

${D}_{1W}/\left({\mathrm{cm}}^{2}{\text{}\mathrm{s}}^{-1}\right)$ | $1.87\times {10}^{-5}$ | $1.46\times {10}^{-5}$ |

${D}_{2W}/\left({\mathrm{cm}}^{2}{\text{}\mathrm{s}}^{-1}\right)$ | $1.57\times {10}^{-5}$ | $1.29\times {10}^{-5}$ |

${D}_{1A}/\left({\mathrm{cm}}^{2}{\text{}\mathrm{s}}^{-1}\right)$ | 0.155 | 0.119 |

${D}_{2A}/\left({\mathrm{cm}}^{2}{\text{}\mathrm{s}}^{-1}\right)$ | 0.124 | 0.103 |

${k}_{12W}/{\mathrm{s}}^{-1}$ | 10.0 | 0.01 |

${k}_{21W}/{\mathrm{s}}^{-1}$ | $5.0\times {10}^{-3}$ | 0.008 |

K_{A} | 0.045 | 0.005 |

L_{W}/cm | 0.02 | 0.02 |

L_{A}/cm | 0.3 | 0.3 |

${k}_{21A}/{\mathrm{s}}^{-1}$ | $\left\{{10}^{-X}\right\}$^{a} | $\left\{{10}^{-X}\right\}$^{a} |

K_{W} | 2000 | 1.25 |

${k}_{12A}/{\mathrm{s}}^{-1}$ | $0.045\times \left\{{10}^{-X}\right\}$^{a} | $0.005\times \left\{{10}^{-X}\right\}$^{a} |

H_{2} | $5.625\times {10}^{-7}$ | $2.8\times {10}^{-5}$ |

d_{A}/cm | {6.15, 10.9, 19.5, 34.6, 61.5, 109, 195, 346} | {5.69, 10.1, 18.0, 32.0, 56.9, 101, 180, 320} |

d_{W}/cm | $1.37\times {10}^{-3}$ | $2.77\times {10}^{-2}$ |

Q_{A} | 1.25 | 1.16 |

Q_{W} | 1.19 | 1.13 |

Λ_{A} | $\text{{}488,\text{}274,\text{}154,\text{}86.7,\text{}48.8,\text{}27.4,\text{}15.4,\text{}8.67\text{}}\times {10}^{-4}$ | $\text{{}527,\text{}296,\text{}167,\text{}93.7,\text{}52.7,\text{}29.6,16.7,\text{}9.37\text{}}\times {10}^{-4}$ |

Λ_{W} | 14.6 | 0.723 |

${H}_{e}$ | $1.3\times {10}^{-5}$ | $3.1\times {10}^{-3}$ |

${\zeta}_{A}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | 0.413 | 0.343 |

${\zeta}_{W}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | $7.85\times {10}^{-4}$ | $6.45\times {10}^{-4}$ |

R_{A} | 0.544 | 0.234 |

${f}_{A1E}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | 0.0133 | $9.91\times {10}^{-4}$ |

${f}_{A4}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | $7.08\times {10}^{-3}$ | $6.25\times {10}^{-4}$ |

${f}_{A3}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | $6.62\times {10}^{-3}$ | $6.15\times {10}^{-4}$ |

${f}_{A2}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | $6.62\times {10}^{-3}$ | $6.15\times {10}^{-4}$ |

^{a}$X\in \left\{2.5,3.0,3.5,4.0,4.5,5.0,5.5,\text{}6.0\right\}$.

Variable | Formaldehyde | Acetaldehyde | ||
---|---|---|---|---|

μ | σ | μ | σ | |

H_{1} | −1.6 | 0.15 | −2.2 | 0.15 |

${D}_{1W}/\left({\mathrm{cm}}^{2}{\mathrm{s}}^{-1}\right)$ | −4.7 | 0.15 | −4.8 | 0.15 |

${D}_{2W}/\left({\mathrm{cm}}^{2}{\mathrm{s}}^{-1}\right)$ | −4.8 | 0.15 | −4.9 | 0.15 |

${D}_{1A}/\left({\mathrm{cm}}^{2}{\mathrm{s}}^{-1}\right)$ | −0.8 | 0.15 | −0.9 | 0.15 |

${D}_{2A}/\left({\mathrm{cm}}^{2}{\mathrm{s}}^{-1}\right)$ | −0.9 | 0.15 | −1.0 | 0.15 |

${k}_{12W}/\left({\mathrm{s}}^{-1}\right)$ | 1.0 | 0.2 | −2.0 | 0.3 |

${k}_{21W}/\left({\mathrm{s}}^{-1}\right)$ | −2.3 | 0.2 | −2.1 | 0.3 |

K_{A} | −1.3 | 0.15 | −2.3 | 0.5 |

L_{W}/cm | −1.7 | 0.15 | −1.7 | 0.15 |

L_{A}/cm | −0.5 | 0.15 | −0.5 | 0.15 |

k_{21A} | Unconstrained, except to enforce ${k}_{21A}<{k}_{21W}$ and ${k}_{12A}<{k}_{12W}$ | |||

K_{W} | $={k}_{12W}/{k}_{21W}$ | |||

k_{12A} | $={K}_{A}{k}_{21A}$ | |||

H_{2} | $={H}_{1}{K}_{A}/{K}_{W}$ |

Seyfioglu and Odabasi [84]; Formaldehyde; Air → Water Experiments; Model A4. | |||
---|---|---|---|

Experimental conditions | ${U}_{10}/\left({\mathrm{m}\text{}\mathrm{s}}^{-1}\right)$ | ${K}_{g}{H}_{1}\left(1+{K}_{A}\right)/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | ${f}_{A4}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ |

Laboratory | 8 | $\left(15.1\pm 5.5\right)\times {10}^{-3}$ | $\left(5\mathrm{to}10\right)\times {10}^{-3}$ |

Field | 4 | $\left(6.3\pm 3.1\right)\times {10}^{-3}$ | |

Liu et al. [85]; Formaldehyde; Water → Air Experiments; Model A4. | |||

Experimental conditions | ${U}_{10}/\left({\mathrm{m}\text{}\mathrm{s}}^{-1}\right)$ | ${K}_{0L}\left(1+{K}_{W}\right)/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ | ${f}_{A4}/\left({\mathrm{cm}\text{}\mathrm{s}}^{-1}\right)$ |

Without stirring | 0.4 | $4.66\times {10}^{-3}$ | $\left(5\mathrm{to}10\right)\times {10}^{-3}$ |

$4.51\times {10}^{-3}$ | |||

With stirring | 0.4 | $5.61\times {10}^{-3}$ | |

$6.06\times {10}^{-3}$ | |||

$6.06\times {10}^{-3}$ |

© 2020 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Mansfield, M.L.
Mass Transport of Gases across the Air–Water Interface: Implications for Aldehyde Emissions in the Uinta Basin, Utah, USA. *Atmosphere* **2020**, *11*, 1057.
https://doi.org/10.3390/atmos11101057

**AMA Style**

Mansfield ML.
Mass Transport of Gases across the Air–Water Interface: Implications for Aldehyde Emissions in the Uinta Basin, Utah, USA. *Atmosphere*. 2020; 11(10):1057.
https://doi.org/10.3390/atmos11101057

**Chicago/Turabian Style**

Mansfield, Marc L.
2020. "Mass Transport of Gases across the Air–Water Interface: Implications for Aldehyde Emissions in the Uinta Basin, Utah, USA" *Atmosphere* 11, no. 10: 1057.
https://doi.org/10.3390/atmos11101057