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**Fugacity Models Level 1 : Equilibrium**

Level 2 : Equilibrium between compartments & Steady-state over entire environment Level 3 : Steady-State between compartments Level 4 : No steady-state or equilibrium / time dependent

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**“Chemical properties control”**

Level 1 : Equilibrium “Chemical properties control” fugacity of chemical in medium 1 = fugacity of chemical in medium 2 = fugacity of chemical in medium 3 = …..

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**Mass Balance Total Mass = Sum (Ci.Vi) Total Mass = Sum (fi.Zi.Vi)**

At Equilibrium : fi are equal Total Mass = M = f.Sum(Zi.Vi) f = M/Sum (Zi.Vi)

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**Fugacity Models Level 1 : Equilibrium**

Level 2 : Equilibrium between compartments & Steady-state over entire environment Level 3 : Steady-State between compartments Level 4 : No steady-state or equilibrium / time dependent

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**fugacity of chemical in medium 1 = fugacity of chemical in medium 2 = **

Level 2 : Steady-state over the entire environment & Equilibrium between compartment Flux in = Flux out fugacity of chemical in medium 1 = fugacity of chemical in medium 2 = fugacity of chemical in medium 3 = …..

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**Level II fugacity Model:**

Steady-state over the ENTIRE environment Flux in = Flux out E + GA.CBA + GW.CBW = GA.CA + GW.CW All Inputs = GA.CA + GW.CW All Inputs = GA.fA .ZA + GW.fW .ZW Assume equilibrium between media : fA= fW All Inputs = (GA.ZA + GW.ZW) .f f = All Inputs / (GA.ZA + GW.ZW) f = All Inputs / Sum (all D values)

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**Fugacity Models Level 1 : Equilibrium**

Level 2 : Equilibrium between compartments & Steady-state over entire environment Level 3 : Steady-State between compartments Level 4 : No steady-state or equilibrium / time dependent

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**Level III fugacity Model:**

Steady-state in each compartment of the environment Flux in = Flux out Ei + Sum(Gi.CBi) + Sum(Dji.fj)= Sum(DRi + DAi + Dij.)fi For each compartment, there is one equation & one unknown. This set of equations can be solved by substitution and elimination, but this is quite a chore. Use Computer

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**Time Dependent Fate Models / Level IV**

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**Evaluative Models vs. Real Models**

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**Recipe for developing mass balance equations**

1. Identify # of compartments 2. Identify relevant transport and transformation processes 3. It helps to make a conceptual diagram with arrows representing the relevant transport and transformation processes 4. Set up the differential equation for each compartment 5. Solve the differential equation(s) by assuming steady-state, i.e. Net flux is 0, dC/dt or df/dt is 0. 6. If steady-state does not apply, solve by numerical simulation

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**Application of the Models**

To assess concentrations in the environment (if selecting appropriate environmental conditions) To assess chemical persistence in the environment To determine an environmental distribution profile To assess changes in concentrations over time.

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**What is the difference between**

Equilibrium & Steady-State?

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**Time Dependent Fate Models / Level IV**

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