| Front page | | Contents | | Previous | | Next |

Dry deposition and spray drift of pesticides to nearby water bodies

Appendix A. Calculation of the fraction of the pesticide in the gas phase in the soil

Deriviation of the equation for the fraction in the gas phase

The following set of equations is necessary to find the fraction of the pesticide in the gas phase (Smit et al., 1997).

The Henry’s law coefficient gives the relation between the concentration of the pesticide in the gas and water phase:

where:
K_H = Henry’s law coefficient (dimensionless),
c_gas = concentration of the pesticide in the gas phase in the soil (kg pesticide m^-3 air),
c_liquid = concentration of the pesticide in the water phase in the soil (kg pesticide m^-3 water).

Henry’s law coefficient can be determined directly or can be determined from the molecular weight, vapour pressure and the solubility in water of the pesticide (see section 1.3). Both the measured or calculated values can be uncertain. It is not unusual that for one compound Henry’s law coefficients are reported in the literature, which differ an order of magnitude.

Henry’s law coefficient is rather temperature dependent (see section 1.4).

The solid-liquid partitioning coefficient Kd gives the relation between the mass of pesticide adsorbed to the soil particles and the concentration in the water phase in the soil. If a linear sorption isotherm is assumed Kd the following equation is found:

where:
K_d = solid-liquid partitioning coefficient of the pesticide (kg pesticide kg^-1 solid)/(kg pesticide m^-3 water).
X = mass of pesticide adsorbed to the soil particles (kg pesticide kg^-1 solid).

Often the sorption is not linear and Kd is decreasing with increasing concentration in the water phase increases (Green and Karickhoff, 1990). Kd is not very temperature dependent (F. van den Berg, Alterra, Wageningen, personal communication, 2001).

The total concentration of pesticide in the soil (in all phases) can now be described by:

where:
c_soil = concentration of pesticide in the whole soil matrix (kg pesticide m^-3 soil) (Note: soil includes both the solid, water and gas phase of the soil),
θair = volume fraction of air in the soil (m³ air m^-3 soil),
θl_water= volume fraction of water in the soil (m³ water m^-3 soil),
ρ _soil,dry = dry bulk density of the soil, i.e. soil without water, but including air (kg solid m^-3 soil).

Equation (3) can also be written as:

with the (dimensionless) capacity factor Q:

The dimensionless fraction of the pesticide in the gas phase is then:

K_H and K_d should be known, or can be derived from other properties of the pesticide and/or the soil.

θ air and θ water are usually not given, but have to be derived from the following parameters:

• c_org = organic matter content of the solid part of the soil (% of the volume).
• ρ_{soil, mineral} = density of the mineral part of the solid phase of the soil (kg m^-3). A constant value of 2660 kg m^-3 is chosen (F. van den Berg, Alterra, Wageningen, personal communication, 2001).
• ρ_soil,org = density of the organic matter part of the solid phase of the soil (kg m^-3). A constant value of 1470 kg m^-3 is chosen (F. van den Berg, Alterra, Wageningen, personal communication, 2001).
• ρ_soil,dry = dry bulk density of the soil (without water, but including air) (kg m^-3),
• ρ_air = density of air (kg m^-3). A value of 1.25 kg m^-3 is taken, which is representative of a pressure of 1 atmosphere and a temperature of 10° C,
• c_moist = volumetric moisture content of the soil (% of the volume). The volume fraction of moisture can be found from:

Dry soil consists of organic matter and mineral parts. The density of the solid part of the soil ρ soil,solid (kg m^-3) is calculated from the information on the organic matter content and the densities of the organic and mineral parts of the soil:

As an intermediate step θair+water, the volume fraction of air and water together in the moist soil, can be found from:

When deriving this equation one should note that the difference between dry soil and moist soil is that part of the volume fraction of air of the dry soil is replaced by water in the moist soil. This means that the volume fraction of air in the dry soil is equal to the volume fraction of air and water together in the moist soil.

The volume fraction of air θ air can then be found from:

Derivation of K_d from K_om , K_oc or K_ow

Many pesticides adsorb to organic matter in the soil, but not all. If the soil contains organic matter and the pesticide adsorbs mainly to organic matter, Kd can be calculated from Kom and the organic matter content (in %):

where:

K_om = coefficient for sorption to soil organic matter (m³ kg^-1). It should be noted that K_om is often given in (l kg^-1) in the literature.

If K_om is not known it can be estimated from K_oc (Chiou, 1989):

where:
K_oc = organic carbon distribution coefficient (kg kg^-1 organic carbon)/(kg m^-3 water).
If K_oc is not known it can be found from K_ow using the following equation (Rao and Davidson, 1980):

If no value of K_d is not availabe, it may be estimated with the methods presented here, but in that case the uncertainty in K_d becomes larger.

Derivation of K_H from molecular weight, vapour pressure and solubility

The Henry’s law coefficient as defined by (A-1) can be found from the molecular weight, vapour pressure and solubility given in units that are often used:

where:
molw = molecular weight (g mol^-1)
VP = vapour pressure (mPa)
R_gas = gas constant (8314.5 Pa l K^-1 mol^-1)
T = temperature (K)
S = solubility (mg l^-1)

Temperature dependence of the vapour pressure

The Clausius-Clapeyron equation describes the temperature dependence of the vapour pressure:

where:
VP = vapour pressure at temperature T (Pa)
H_v = heat of vaporisation (J mol^-1)
R = universal gas constant (8.314 J mol^-1 K^-1)
T = temperature (K)

If it is assumed that Hv is constant with changes in temperature the following equation can be obtained (Lyman et al., 1990):

where:
VP(T) = vapour pressure at temperature T (Pa)
VP_ref = vapour pressure at reference temperature T_ref
T_ref = reference temperature (K)

There are methods to estimate Hv if it is not known, but these methods are rather uncertain (Lyman et al., 1990). The heat of vaporisation has only been determined for a limited number of pesticides. Smit et al. (1997) found an average value for Hv of 95000 J mol^-1 for about 15 pesticides. The values range from 58000 to 146000 J mol^-1. In PESTDEP model a default value for Hv of 95000 J mol^-1 is used if no values are known.

Temperature dependence of the solubility

The solubility as a function of the temperature can be found from:

where:
S(T) = solubility at temperature T  
S_ref    = solubility at reference temperature Tref
T_ref    = reference temperature (K)
Hs = differential heat of solution (J mol^-1)

Smit et al. (1997) found an average value for Hs of 27000 J mol^-1 for about 11 pesticides. The values range from -17380 to 54350 J mol^-1. In the PESTDEP model a default value for Hv of 27000 J mol^-1 is used if no values for Hs are known.

Temperature dependence of the Henry’s law coefficient

The relation for the temperature dependence of the Henry’s law coefficient is given by (Seinfeld and Pandis, 1998):

where:
H = Henry’s law coefficient (mol l^-1 atm^-1)
T = actual temperature (K)
T_ref = reference temperature (K)
R_g = gas constant (8.314 Pa m³ K^-1 mol^-1 = 8.314 J K^-1 mol^-1); note that the gas constant used here is expressed in different units than the one used in (A-14).
H_A = heat of dissolution at constant temperature and pressure (J mol^-1); H_A can be calculated from H_v and H_s using relation (A-14). A default value of –(95000 – 27000) = -68000 J mol^-1 is used in PESTDEP if no values are known.

The relation between Henry’s law coefficients K_H and H that are defined in different ways is:

From (A-15) and (A-16) the following function for KH as a function of temperature can be found:

K_H generally increases with temperature. HA will be different for different compounds.

References

Chiou, C.T. (1989) Theoretical considerations of the partition uptake of nonionic organic compounds by soil organic matter. In Sawhney, B.L., Brown, K.: Reactions and movement of organic chemicals in soils. SSSA special publication 22, Soil Science Society of America, Madison, Wisconsin, USA, 1-30.

Green, R.E., Karickhoff, S.W. (1990) Sorption estimates for modeling. In: Cheng, H.H. (ed.) Pesticides in the soil environment: processes, impacts, and modeling. Soil Science Society of America Inc., Madison, Wisconsin, USA, 79-101.

Lyman, W.J., Reehl, W.F., Rosenblatt, D.H. (eds.) (1990) Handbook of chemical property estimation methods, American Chemical Society, Washington DC, USA.

Rao, P.S.C., Davidson, J.M. (1980) Estimation of pesticide retention and transformation parameters required in nonpoint source pollution models. In: Overcash, M.R., Davidson, J.M. (eds.): Environmental impact of nonpoint source pollution. Ann Arbor Sci. Publ., Ann Arbor, USA, 23-67.

Seinfeld, J.H., Pandis, S.N. (1998) Atmospheric chemistry and physics. John Wiley, New York, USA, 342.

Smit, A.A.M.F.R., van den Berg, F., Leistra, M. (1997) Estimation method for the volatilization of pesticides from fallow soil. Report Environmental Planning Bureau Series 2, DLO Winand Staring Centre, Wageningen, the Netherlands.

| Front page | | Contents | | Previous | | Next | | Top |