# Are Values for KОW Useful to Predict Breakthrough in RP-SPE?

The capacity factor for an RP-SPE cartridge when pure water is used, *k _{w},* discussed earlier, has been found to be closely related to

*K*and is related by (p. 52)

_{QW}^{95}and by (p. 95)

^{s3}

Hence, merely obtaining octanol-water partition coefficient values from various tabulations in the literature can yield a predictive value for *k' _{w}* because we have shown that

*k'*is directly related to the breakthrough volume,

_{w}*Vr.*

# Where Can One Obtain KОW Values?

The resources cited are available in most university libraries in order to find these values, as well as to obtain good introductions. Leo and colleagues published a comprehensive listing and follow'ed this with a more systematic presentation.^{94}-^{97} Even earlier, Hansch and colleagues published their findings.^{98} Lyman and colleagues have published a handbook on the broad area of physico-chemical property estimations.^{96} These reference sources also provide detailed procedures for calculating and estimating *K _{ow}.*

# Can Breakthrough Volumes Be Determined More Precisely?

A more precise way to determine the *breakthrough volume* for a particular *analyte* on a given SPE sorbent, *Vr,* is to use reversed-phase HPLC. The SPE sorbent is efficiently packed into a conventional HPLC column. The analyte of interest is injected into the instrument, while the mobile-phase composition is varied. This is accomplished by varying the percent organic modifier, such as acetonitrile or methanol, and measuring the differences in analyte retention time. Extrapolation of a plot of *k'* vs. percent organic modifier to zero percent modifier yields a value for the capacity factor for that analyte at 100% water. This capacity factor is represented by *k _{w} spe hplc*’ where the subscript refers to 100% water. The breakthrough volume is related to the capacity factor in 100% water according to

**FIGURE 3.46**

*V _{0}* is the void volume of the SPE column and

*k'*(SPE, HPLC) is the capacity factor of the analyte eluted by water. This capacity factor should theoretically be the same for any technique used, as

_{w}*V*is found by knowing the porosity of the sorbent and the geometry of the SPE column or sorbent bed in the cartridge. The capacity factor of a given analyte,

_{Q}*k'*(SPE, HPLC), is generally obtained from HPLC. From an HPLC chromatogram,

*k'*(SPE, HPLC) is obtained by taking the ratio of the difference in the retention time between an analyte and its void retention time to the void retention time. Expressed mathematically,

where ^{1}r represents the *retention time for the analyte of interest* under the HPLC chromatographic conditions of a fixed mobile-phase composition. * ^{{}o* refers to the retention time for an analyte that is

*not retained*on the stationary phase.

^{f}o also relates to the void volume in the column.

Log *k _{w SPEHPLC}* is obtained by extrapolation of a plot of log

*k'*vs. percent MeOH to zero. This plot is shown in Figure 3.46. A linear relationship exists between the logarithm of the capacity factor,

*k'*(SPE, HPLC), and the percent MeOH concentration for a specific organic compound in HPLC. Because

*k'*has also been shown to be related to the octanol-water partition coefficient,

_{w SPE HPLC}*K*, and hence the

_{(m}, k’_{w SPEHPLC}*breakthrough volume Vr,*can be obtained for a given RP-SPE sorbent by this approach.

# Does an SPE Cartridge or Disk Have a Capacity Factor and If So, How Do We Calculate It?

Yes and it can be shown (see below) that the extent to which any analyte, initially dissolved in water, can be isolated on an octydecyl- or an octyl siloxane chemically bonded silica sorbent (either in a 3 cc sorbent barrel cartridge or a disk format) can be mathematically related to a ratio of chromatographic capacity factors provided secondary equilibrium effects are ignored.

A capacity factor k’ can be related to the ratio of analyte sorbed to that of the total amount of analyte present in a given sample according to:

where

n_{s}—#millimoles of analyte adsorbed/partitioned onto and/or into the sorbent or disk n_{0}—#millimoles of analyte in the volume of water or sample passed through k'—capacity factor for the cartridge or disk.

The capacity factor k' for a specific RP-SPE cartridge or disk can in turn be related to the partition or distribution constant for a specific analyte according to:

where

V_{s}—volume of reversed-phase of sorbent or disk V —void volume of sorbent or disk

m

(3—phase ratio, V_{s}/V_{m }K_{D}—distribution constant.

To achieve a 90% recovery (n_{s}/n_{0} x 100) chemical analyte from, for example, an environmental drinking water sample, requires a capacity factor k' = 9. Table 3.19 uses Equation (3.44) to calculate what value p must have given a knowledge of K_{D}. For example: A 40 pm, 60 A (angstrom) length pure octyldecylsiloxane chemically bonded silica of mass 250 mg has a V_{m} = 300 pL. Assuming a 20 A length for a C_{|8} ligate and a 350 m^{2}/g surface area, this same 250 mg sorbent can be estimated to have a V_{s} = 175 pL. We can roughly estimate a phase ratio p (175/300) = 0.6."