# Partition Coefficient

## Partition Coefficient

The partition coefficient is the equilibrium distribution of an analyte between the sample phase and the gas phase.
Samples must be prepared to maximise the concentration of the volatile components in the headspace and minimise unwanted contamination from other compounds in the sample matrix. To help determine the concentration of an analyte in the headspace, you will need to calculate the partition coefficient (K).

 K values of common solvents in air-water systems at 40°C Solvent Cyclohexane n-Hexane Tetrachlorethylene 1,1,1-Trichlormethane O-Xylene Toluene Benzene Dichlormethane K Value 0.077 0.14 1.48 1.65 2.44 2.82 2.90 5.65 Solvent n-Butylacetate Ethylacetate Methylethylketone n-Butanol Isopropanol Ethanol Dioxane K Value 31.4 62.4 139.5 647 825 1355 1618

### Calculating the Partition Coefficient

Partition Coefficient (K) = Cs/Cg

where:

Cs is the concentration of analyte in sample phase;
Cg is the concentration of analyte in gas phase

### Partition Coefficients of Common Compounds

Compounds that have low K values will tend to partition more readily into the gas phase and have relatively high responses and low limits of detection. An example of this would be hexane in water: at 40°C, hexane would have a K value of 0.14 in an air-water system.

Compounds that have high K values will tend to partition less readily into the gas phase and have relatively low responses and high limits of detection.
An example of this would be ethanol in water: at 40°C, ethanol has a K value of 1355 in an air-water system.

Partition coefficient values for other common compounds are shown in the table above.

### Changing the Partition Coefficient Sensitivity is increased when K is minimisedSensitivity is increased as the partition coefficient is decreased and volatiles can more readily enter the gas phase. This is illustrated by the graph on the left.K can be lowered by changing the temperature at which the vial is equilibrated or by changing the composition of the sample matrix. In the case of ethanol, K can be lowered from 1355 to 328 by raising the temperature of the vial from 40°C to 80°C.The partition coefficient may also be changed by adding salts or by changing the Phase Ratio. These will be examined in the next two sections.

High salt concentrations in aqueous samples decrease the solubility of polar organic volatiles in the sample matrix and promote their transfer into the headspace, resulting in lower K values. The magnitude of the salting-out effect on K, however, is not the same for all compounds.

Compounds with K values that are already relatively low will experience very little change in the partition coefficient after adding a salt to an aqueous sample matrix.

Generally, volatile polar compounds in polar matrices (aqueous samples) will experience the largest shifts in K and have higher responses after the addition of salt to the sample matrix.
Common salts used to decrease matrix effects:

• Ammonium chloride
• Ammonium sulphate
• Sodium chloride
• Sodium citrate
• Sodium sulphate
• Potassium carbonate

The value of K is also dependent on the Phase Ratio. This is discussed in the next section.

## Phase Ratio

The phase ratio (β) is defined as the relative volume of the headspace compared to volume of the sample in the sample vial.

 Calculating the Phase RatioPhase Ratio (β) = Vg / Vs where: Vs is the volume of sample phaseVg is the volume of gas phase Sensitivity is increased when β is minimised

Lower values of β (i.e. larger sample size) will yield higher responses for volatile compounds.

Decreasing the β value will not always yield the increase in response needed to improve sensitivity.

When β is decreased by increasing the sample size, compounds with high K values partition less into the headspace compared to compounds with low K values and yield correspondingly smaller changes in Cg.

Samples that contain compounds with high K values need to be optimised to provide the lowest K value before changes are made in the phase ratio.

## Combining Partition Coefficient and Phase Ratio Lower K and β result in higher Cg and better sensitivity

Partition coefficients and phase ratios work together to determine the final concentration of volatile compounds in the headspace of sample vials.

The concentration of volatile compounds in the gas phase can be expressed as:

Cg = Co / (K + β)

where

Cg is the concentration of volatile analytes in the gas phase

and

Co is the original concentration of volatile analytes in the sample.

Striving for the lowest values for both K and β will result in higher concentrations of volatile analytes in the gas phase and therefore better sensitivity.