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Home , Kovats retention index, Partition coefficient, Separation process, Van Deemter equation

Separation

• Samples are usually complex . In order to identify and quantify the components of a Ch. 23 Fundamentals of Analytical , we have to separate the components in Separations the mixture. • Separation methods – – –

Solvent Extraction Extraction Efficiency • The transfer of an analyte from one phase to a second • A solute S has a partition coefficient of 3 between based on the relative of the analyte in two toluene and . If you have 100 mL of a 0.010 M immiscible liquids. of S in water.(1)What fraction of the solute remains in H O after a 500 mL extraction with toluene? []S 2 − /)1( Vmq 2 2 K == (2) What fraction of the solute remains in H2O after a 5- []S 1 /Vqm 1 100 mL extractions with toluene? n ⎛ V ⎞ 100 q = ⎜ 1 ⎟ q = ≈= %6062.0 ⎜ ⎟ + )500)(3(100 ⎝ + KVV 21 ⎠ 5 At equilibrium: K: the partition coefficient for distribution of ⎛ 100 ⎞ q = ⎜ ⎟ ≈= %1.000098.0 S between the two phases; q: the fraction of S remaining in ⎝ + )100)(3(100 ⎠ phase 1; n: the # of extractions. It is more efficient to do several small extractions If q = 1/4, then 1/4 remains in phase 1 after one extraction than one big extraction.

pH Effects pH Effects • The charge changes of an acid or base is dependent on pH. • K for an amine B is 3.0 and the Ka for BH+ is 1.08×10-9. If • Distribute coefficient (D): an alternate form of the 50.00 mL of 0.010 M aqueous amine is extracted with 100 partition coefficient. mL of , calculate the % remaining the in aqueous phase in M at (1) pH 10.00; (2) pH 8.00. 2 phasein conc. Total conc. phasein 2 C D = = 2 1 phasein conc. Total conc. phasein 1 C 1 KKa ×× 100.10.3 −9 pH = :00.10 D = + = −9 −10 = 73.2 B][ 2 KKa + HKa ][ ×+× 100.1100.1 D = + = + = Kα B 1 + BHB 1 + HKa ][][][ V1 50 + q = = ⇒= %1515.0 1 HB ][][ B][ 2 (Ka = + ; K = ) + KVV 21 ×+ 10073.250 BH ][ 1 B][ 1 KKa ×× 100.10.3 −9 + HA][ HK ][ pH :00.8 D == + = −9 −8 = 273.0 D = 2 = = Kα + HKa ][ ×+× 100.1100.1 + AHA − ][][ + HKa + ][ HA 1 1 V 50 HA +− ][][ HA][ q = 1 = ⇒= %6565.0 (Ka = 1 ; K = 2 ) α: fraction of the species (P.191) + KVV 21 ×+ 100273.050 HA][ 1 HA][ 1

1 Extraction with a Chelator Extraction with a Metal Chelator

•Usually neutral complexes can be extracted into organic •Commonly used: dithizone, 8-hydroquinoline, and . Charged complexes (e.g. MEDTA2-) are not very cupferron. soluble in organic solvents. •Crown ethers can extract alkali metal and can bring •Commonly used: dithizone, 8-hydroquinoline, and them into non-polar solvents. cupferron.

Chromatography Extraction with a • A separation process based on the various partitioning Metal Chelator coefficients of different solutes between the two phases.

•Each ligand can be presented • Involving the interaction of solute(s) and two phases as a weak acid, HL. • Mobile phase: A gas or liquid that moves through the column. •Mn+ is in the aqueous phase • Stationary phase: A or liquid that remains in place. and MLn is in the organic phase •The distribution coefficient (D) for metal extraction depends on pH and [ligand]. •By select a pH, you can bring the metal into either phase.

Type of Chromatography Type of Chromatography • Based on the mechanism of interaction of the solute • Based on the mechanism of interaction of the solute with the stationary phase with the stationary phase

(2) Partition chromatography (1) chromatography - Solute is adsorbed on the surface of -GC the stationary phase (solid). - The stronger a solute adsorbs, the - the partitioning of solutes between a mobile phase (gas) longer it takes to travel through the chromatography column and bonded liquid stationary phase

2 Type of Chromatography Type of Chromatography • Based on the mechanism of interaction of the solute • Based on the mechanism of interaction of the solute with the stationary phase with the stationary phase

(3) Ion-exchange chromatography (4) Molecular Size exclusion chromatography - ionic interactions to separate ions. - a stationary phase of anions will -size exclusion, , or gel separate cations and vice versa. permeation chromatography -separate by size -large molecules pass through faster (they do not get caught up in pores)

Type of Chromatography The Chromatogram • Based on the mechanism of interaction of the solute •A plot of detector response with time. with the stationary phase •Volume flow rate (flow rate): vol. of solvent pass through the column (5) -Specific interactions of one kind of solute to a second •Linear flow rate: the length of the column passed though by the molecular that is covalently attached to the stationary phase solvent -Most selective (e.g. use antibodies to select out one protein from a •t : unretained mobile phase travels through the column in the mixture of hundreds) m minimum possible time

•tr: retention time, the time for each component needed after injection of the mixture onto the column until that component reaches the detector

•tr’: adjusted retention time, tr’=tr-tm •Vr: retention volume, volume of mobile phase required to elute a

solute to a maximum from a column. Vr= tr*flow rate

The Chromatogram Retention Parameters

• Adjusted retention time ' −= ttt mrr - Time spent in the stationary phase (or ts) • Relative retention - ratio of adjusted retention times for any two components - the greater the relative retention, the greater the separation ' tr 2 α = ' tr1 • Capacity factor (or retention factor): - the longer a component is retained by the column, the greater is the capacity factor. − tt k ' = mr tm

3 • Example: Calculate the adjusted retention time and Retention Time and Partition Coefficient capacity factor for benzene and toluene in the GC experiment? Methane (as a solvent) peak is at 42 s; • The capacity factor is equivalent to the time the solute spends benzene at 251 s and toluene at 333 s. in the stationary phase over the mobile phase and can be related to the partition coefficient: VC V − tt t ' −VV k ' ss K s k ' =⇔== mr r == r m

VC mm Vm tm tm Vm For Benzene For Toluene • Relative retention can be related to retention time, capacity ' ' ttt mrr =−=−= 20942251 s ttt mrr =−=−= 29142333 s factor, and/or partition coefficient ' ' tr 2 k2 K 2 α ' ' === tr1 k1 K1 − tt − 42251 ' − tt − 42333 k ' = mr = = 0.5 k = mr = = 9.6 • Physical basis of chromatography: the greater the ratio of t 42 tm 42 m partition coefficients between mobile and stationary phases, the greater the separation between two components of a mixture

• Example: If use the open tubular chromatography column, Scaling Up where methane (as a solvent) peak is at 42 s and benzene peak at 251 s. Calculate the partition coefficient (K) for •Analytical and preparative benzene between stationary and mobile phases and the •Keep column length constant fraction of the time benzene spends in the mobile phase. •Cross-sectional area of column ~ mass of column of area sectional-Cross area of column analyte ~ volume flow rate (if maintain 2 2 4 2 constant linear flow rate) ~ sample volume m rV 1 ππ ×=== 1083.4)124( μm applied to column coating of area sectional-Cross area of coating 2 2 •If change the column length, then the mass of s 2πrV 2 ×= thickness = π ×=× 108.71)5.124(2 μm sample can be increased in proportion to the ' − tt − 42251 V k = mr = 0.5 K s K =⇒== 310 increase in length tm 42 Vm − tt t k ' = mr s =⇒= 'tkt s m Scaling equation: tm tm :phase mobilein timeofFraction timeofFraction mobilein :phase Mass 2 Radius 2 2 t t 1 1 ⎛ ⎞ m m = ⎜ ⎟ = ' = ' = = 17.0 + tt ms + mm kttk +1 +10.5 Mass 1 ⎝ Radius 1 ⎠

Diffusion

•One main cause of band broadening is diffusion. •Diffusion coefficient (D): measures the rate at which a substance moves randomly from a region of high to a region of lower concentration. •Std deviation of diffusive band spreading: σ = 2Dt

4 Efficiency of Separation Efficiency of Separation

Solutes moving through a column can spread into a Gaussian distribution with a standard deviation, σ (K is a constant). Resolution A resolution of 1.5 gives an essentially complete separation of A and B. of two peaks: Δt ΔV 589.0 Δt Δt ΔV 589.0 Δt Resolution = r = r = r Resolution = r = r = r

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Column Efficiency-Theoretical Plates (N) • Example: A solute with a retention time of 407

2 s has a base width of 13 s on a 12.2 m column. Plate Height σ H = Find the plate height and number of plates. L Number of Theoretical Plates 2 2 L tr )407)(16(16 4 N = N 2 == 2 ×= 1057.1 L H w 13 L=x • Martin & Synge (1941): L 16LLx 2 N === L 2.12 m Treated a chromatographic H σ 2 w2 H == = 78.0 mm column as if it were similar N ×1057.1 4 to a column made σ =w/4 up of numerous discrete but 16t 2 2 55.5 tt 2 contiguous narrow layers N rr === r (theoretical plates). 2 2 2 w σ w 2/1

Factors Affecting Resolution Factors Affecting Resolution - Column Length

⎛ N ⎞ Resolution = ⎜ ⎟ γ − )1( ⎝ 4 ⎠ γ : separation factor

Increase resolution: – Increase column length (Square root of N) – Change phase interaction – Increase capacity factor (Increase fraction of time solute spends in stationary phase) Doubling the column length increases resolution by (2)1/2

5 Column Efficiency-

• van Deemter (Dutch, 1956): B AH ++≈ Cux ux

- H is plate height - u is the flow rate through the column - A, Multiple paths (Eddy diffusion) -B/u, Longitudinal diffusion (molecular diffusion) -Cu, Equilibration time (resistance to )

Multiple Paths (Eddy Diffusion) Longitudinal Diffusion

•Solute diffuses from the high concentration within the band to regions of lower concentration on the edges of the band. •Is inversely proportional In a packed column, analyte can diffuse through with flow rate many different paths around the stationary phase.

Equilibration Time Van Deemter Plot for

•Some solute is stuck in the •A minimal plate height of ~3 stationary phase, which falls mm is obtained with flow rate of behind the solute in the ~35 mL/min. moving forward mobile •Because longitudinal diffusion phase. in a gas is much faster than •Resulting in spreading the diffusion in a liquid, the overall zone of solute optimum linear flow rate in gas chromatography is higher than in •Is propotional to flow rate liquid chromatography.

6 Asymmetric Bandshapes Asymmetry and K • Theoretically, the band coming off a column should be Gaussian but this is not always the •Isotherm: a graph of Cs case vs Cm at a given temperature •Overloading produces a • This usually occurs when the partition gradual rise and an coefficient, K (C /C ) changes during the run abrupt fall of the s m chromatographic peak – K can become either bigger or smaller (load less solute). – K becomes bigger when too much solute has been •A long tail occurs when put into the column (overloading)-so much solute is some sites retain solute dissolved that the stationary phase acts like the solute more strongly than other sites (silanization to – K becomes smaller due to tailing-this is when the block –OH). solute binds strongly to some sites on the column

GC Process •In gas chromatography, vapor-phase analyte is swept through the column by a gaseous mobile phase (carrier gas) – Gas-liquid chrom (liquid stationary phase) Ch. 24 Gas Chromatography (GC) – Gas-solid chrom (solid stationary phase) – The mobile phase is usually He, N2, or H2 depending on the application

• The analyte is a volatile liquid or gas that is injected through a septum (rubber disk)

Schematic Diagram of GC Open Tubular Columns

•Fused silica (SiO2) coated with a polyimide that can withstand 350°C. •Typically, inner diameters are 0.10-0.53 mm and lengths are 15- 100 m. •Compared to packed columns: give higher resolution, shorter Gaseous analyte is transported through the column by a analysis time, greater sensitivity, lower sample capacity gaseous mobile phase.

7 Effect of Inner Diameter on Resolution Effect of Column Length on Resolution

Effect of Stationary Phase Thickness on Open Tubular Columns Resolution

•Wall-coated: liquid stationary phase on inside wall of column •Supported-coated: liquid stationary phase coated on solid support attached to inside wall of column •Porous-layer: solid stationary phase on inside wall of column (higher surface area, handle larger samples)

Stationary Phases

• Chosen based on the rule that “like dissolves like”. • The silica backbone and the polarity. • Strongly polar columns are best for strongly polar solute. • As a column ages, stationary phase bakes off and Si-OH groups become exposed (tailing peaks).

8 Retention Time The (I) • Retention index relates the retention time of a solute to the retention times of linear • For a linear , I = 100×# of C (ex. for octane I=800; for nonane, I=900)

' ' ⎡ tr − r nt )(log)unknown(log ⎤ ⎢ −+= nNnI )(100 ' ' ⎥ ⎣ r − r ntNt )(log)(log ⎦

Non-polar stationary phase: compounds elute mostly based on boiling point. N: # of carbon atoms in larger alkane n: # of carbon atoms in smaller alkane Polar stationary phase: strongly retains the polar solutes (alcohols are strongly retained).

• Example: If retention times for methane, octane, and nonane in a GC run are 0.5, 14.3, and 18.5 minutes respectively, what is the retention index for an unknown that elutes at 15.7 minutes?

⎡ − 8.13log2.15log ⎤ I ⎢ −+= )89(8100 ⎥ = 836 ⎣ − 8.13log0.18log ⎦

Temperature Programming • The temperature of the column is raised during the Carrier Gas separation to increase solute vapor pressure • Decreases retention time • Helium is the most common • Sharpens peaks carrier gas. • The choice is mostly dependent on the type of detector used.

•H2 provides the fastest separations and a better resolution, but limited by it’s reactivity

9 Sample Injection Sample Injection

•Split injection: analytes are > 0.1% of the sample; impurities do not •“Sandwich” injection technique get onto the column in large . •The air bubble before the sample: preventing sample from volatilizing in the injector oven before you inject it. •Splitless injection: trace analyses < 0.01% of the sample. •On-column injection: go straight onto the column rather than through •The air bubble behind the sample: prevent sample and solvent from an injector oven; for samples that thermally decompose. mixing.

Detectors Thermal Conductivity Detector (TCD) • Most common: – Thermal conductivity detector (TCD) – Flame detector (FID) • Other detectors: – Mass spectrometer (MSD) – Infrared spectrometer (IRD) •Measures how much a substance can transport heat – Electron capture (ECD) from a hot to cold region. – Nitrogen-phosphorous (NPD) •Helium is the commonly used carrier gas (has a 2nd highest thermal conductivity after H ) – Atomic emission (AED) 2 •When an analyte emerges from the column with it, conductivity will decrease. •Response to all analytes, but sensitivity is not very good.

Flame Ionization Detector (FID) Detector Figures of Merit

•The most common detector for GC •Response nearly all analytes (insensitive to nonhydrocarbons) •Has greater sensitivity than a TCD.

•Eluate is burned in a mixture of H2 and air. Most carbon atoms (except C=O) produce radicals that produce CHO+ in the flame: eCHOO CH +→+ eCHOO −+ •Measure the electron current produced, which is proportional to the number of molecules present.

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