Partitioning of Pollutants Between Phases

Introduction

After a pollutant enters a river, some may remain dissolved, some may move into air and some may attach to sediment or organic matter. A molecule's destination is influenced by equilibrium preferences, but water volume, sediment mass, air exchange and reaction rates matter too. Partition coefficients make these tendencies quantitative when their definitions and units are stated carefully.

Core explanation

Henry's law has several conventions. In this page use H = p/Cw, where p is the compound's partial pressure in air and Cw is its dissolved molar concentration in water. If p is in Pa and Cw in mol m⁻³, H has units Pa m³ mol⁻¹. At equilibrium, p = H Cw. Some sources instead define the inverse, Cw/p, so copying a numerical value without its convention can reverse an interpretation. For ideal dilute gases, Ca = p/(RT) in mol m⁻³ of air. Hence the dimensionless air–water coefficient is Kaw = Ca/Cw = H/(RT). EPA's fate-transport guidance gives this conversion and stresses using values at a consistent temperature. A larger Kaw under this convention indicates a greater equilibrium concentration in air relative to water, but real volatilization speed also depends on mixing and mass-transfer resistance.

The octanol–water partition coefficient , Kow = Coctanol/Cwater at equilibrium, is dimensionless if both concentrations use the same units. Octanol serves as a laboratory surrogate for an organic-rich phase, not a literal biological membrane. High Kow often suggests a neutral organic compound prefers nonpolar material over water. It can inform hypotheses about sorption and bioaccumulation, but ionization, metabolism and binding details limit simple predictions. A weak acid may have very different apparent distribution at different pH values because the ionized fraction behaves differently; one neutral-species Kow does not by itself describe all species.

The organic-carbon-normalized sorption coefficient Koc relates a compound's sorption to organic carbon in soil or sediment to its dissolved concentration. For a neutral organic compound where organic carbon dominates sorption, Kd ≈ foc Koc, where Kd is the solid–water distribution coefficient and foc is the mass fraction of organic carbon in the solid. Kd and Koc often carry L kg⁻¹ units depending on the concentration convention. This relation is an approximation: mineral surfaces, black carbon, pH, salinity and nonequilibrium processes can matter. The USGS fate-properties table distinguishes air–water, octanol–water and organic-carbon-normalized distribution measures.

Fugacity provides a common language for partitioning among compartments. It is an effective escaping tendency, expressed in pressure units. In a simple equilibrium model, the same chemical has equal fugacity in phases that can freely exchange and have reached equilibrium. Each phase can hold a different concentration at that equal fugacity because its capacity differs. A schematic relation is Ci = Zi f, where Ci is concentration in phase i, Zi is its fugacity capacity and f is fugacity. The idea avoids a mistaken claim that equilibrium requires equal concentrations in air and water. Actual environmental compartments may never reach global equilibrium because rivers flow, reactions proceed and barriers slow transfer.

Partitioning is distinct from fate . A compound that strongly sorbs to sediment may be transported with eroded particles; a volatile compound may undergo atmospheric reaction after release; a water-soluble compound may biodegrade. Henry's law, Kow and Koc alone do not determine persistence, toxicity or total mass in each compartment. To calculate masses, combine concentration with compartment volume or sorbent mass. A tiny air volume and vast water volume can produce more total mass in water even if the equilibrium air concentration is higher.

Temperature and composition change the coefficients. H can vary substantially with temperature. Salts may alter water solubility, organic carbon types differ, and chemical species change with pH. The EPA aquatic exposure reference connects Henry's law and Koc to possible pollutant pathways, while also recognizing biotic and abiotic transformation. Good use of a coefficient therefore names the chemical species, temperature, phase definitions and measured or estimated value.

Step-by-step reasoning

First decide which phases can exchange: air–water, octanol–water, or soil–water. Write the coefficient definition with numerator and denominator rather than relying on its symbol alone. Convert all concentrations into compatible units. Determine whether the pollutant is neutral or ionized under the system pH, and whether equilibrium is plausible on the timescale of interest. Then combine the ratio with compartment sizes or solid mass if asked about total inventory. Finally consider degradation and transport processes before making an environmental-risk conclusion.

Visual explanation

Draw a water box between an air box above and a sediment box below. A double arrow air↔water is labeled Kaw = Ca/Cw. A double arrow water↔organic carbon in sediment is labeled Koc; a small laboratory beaker at the side contains water and octanol, labeled Kow. Put different-sized boxes around the phases to represent volume or mass. The diagram separates concentration ratios from the amount stored in each phase and shows that a measured laboratory ratio is only one part of environmental distribution.

Real-world analogy

Imagine guests choosing between two rooms. A preference ratio tells how crowded one room is relative to the other at balance, but it does not tell how many guests are in each room unless you know their sizes. Likewise, a partition coefficient relates concentrations; phase volumes and masses determine total pollutant inventory. The analogy omits degradation and continuous inflow, which keep environmental systems away from simple equilibrium.

Real-world example

Suppose a pesticide enters a pond containing suspended organic-rich particles. A measured high Koc suggests a significant fraction may associate with those particles. If particles settle, bottom sediment can become a reservoir; if a flood resuspends them, the attached pesticide can move again. Koc identifies a sorption tendency, but settling, sediment disturbance and degradation govern the actual history.

Why?

Why can an organic contaminant with high Kow still remain in water? Kow compares concentrations in a model octanol phase and water at equilibrium. The environment may contain little available organic phase, the compound may be ionized, or transfer may be slow. Even a strong preference for one phase does not mean all molecules instantly leave water. A mass balance requires phase amounts and exchange kinetics.

Common misconception

“Henry's constant always has one definition and one set of units.” Some conventions use p/Cw, others Cw/p, and some report a dimensionless Ca/Cw. The number and trend reverse under an inverse definition. Another misconception equates high Koc with permanent immobilization: sorbed material can be transported as particles or desorb when environmental chemistry changes.

Worked example

At 298 K, a neutral compound has H = 250 Pa m³ mol⁻¹ under the p/Cw convention. Using R = 8.314 Pa m³ mol⁻¹ K⁻¹, the dimensionless air–water ratio is Kaw = H/(RT) = 250/(8.314 × 298) ≈ 0.101 . Thus equal volumes of equilibrium air and water would have air concentration about one-tenth the water concentration in mol m⁻³. If the air and water volumes differ greatly, their masses need not be in that ratio.

Quick check

1. A compound has Kd = 20 L kg⁻¹ in soil with foc = 0.02. Estimate Koc under the organic-carbon model. Answer: Koc ≈ Kd/foc = 20/0.02 = 1,000 L kg⁻¹ of organic carbon. The result assumes organic carbon dominates sorption.

Exam focus

Define every coefficient before using it. For Henry's law, specify p/Cw or its inverse and reconcile units with RT if a dimensionless ratio is needed. Kow is an octanol–water ratio; Koc normalizes sorption to organic carbon. Do not equate equilibrium concentration ratios with total mass ratios or with degradation half-lives. A sketch with the phases and arrows can prevent direction errors.

Advanced insight

Fugacity models can combine partitioning and transport by assigning each compartment a capacity Zi and a volume Vi, so equilibrium mass would be Mi = Zi Vi f. When exchange or degradation is represented as a rate process, distinct compartment fugacities can persist; their difference drives net transfer. This framework explains why a field system with continuous emissions may have different air, water and soil fugacities even though local interfaces approximate equilibrium.

Summary

Henry's law relates gas and dissolved concentrations, Kow compares octanol and water, and Koc describes sorption normalized to organic carbon. Fugacity expresses a shared tendency to escape at equilibrium, while each phase can store a different concentration and mass. Definitions, units, temperature, pH, phase sizes and kinetic processes are necessary for sound environmental interpretation.

Practice questions

1. What additional quantity is needed to turn a water concentration into the mass of pollutant in the water compartment? Answer: The water volume, with compatible units, is needed because mass equals concentration times volume.

2. Why might a weak acid's apparent partitioning change with pH? Answer: pH changes the fraction ionized, and the ionic and neutral species can have very different affinities for water and organic phases.

3. Does equal fugacity at equilibrium mean equal air and water concentration? Answer: No. Each phase has its own capacity, so equal fugacity can correspond to unequal concentrations.

4. What assumption is implicit in Kd ≈ foc Koc? Answer: Sorption is mainly proportional to the soil or sediment's organic-carbon fraction, with other surfaces and chemistry having limited effect.