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Lecture # 20 – Analytical Separations

Chapter 23

Analytical Chemistry

Steps in Chemical Analysis

1. Formulating the Question 2. Selecting the Analytical Procedure 3. Sampling 4. Sample Preparation 5. Analysis 6. Interpretation and Reporting 7. Drawing Conclusions

Solvent Extraction

Hot Water Extraction

Solvent Extraction

Phase I (water)

Phase 2 (organic solvent)

Immiscible = don’t mix …much!

Liquid-Liquid Extraction

e.g. Separatory Funnel

S S

S S S

S S S

S S

S S

S S S S

S S

S

S = solute

Solvent Extraction Partition Coefficient

K = AS2 ≈ [S]2

AS1 [S]1

m = moles of S

q = fraction of S in “Phase 1”

1-q = fraction of S in “Phase 2”

K = (1-q)m/V2 qm/V1

Solvent Extraction Partition Coefficient

K = AS2 ≈ [S]2

AS1 [S]1

Fraction in Phase 1 = q = V1 (after one extraction) V1 + KV2

Fraction in Phase 1 = qn = V1 (after n extractions) V1 + KV2

n

2

Solvent Extraction pH and Solvent Extraction

Distribution = Total Concentration in Phase 2 Coefficient (D) Total Concentration in Phase 1

Example: Extraction of base (B)

D = [B]2 [B]1 + [BH+]1 K = [B]2/[B]1

Ka = ([H+][B]1)/[BH+]1 = K ⋅ Ka Ka + [H+]

αB = Ka/(Ka + [H+]) = K ⋅ αB

“ a neutral species is more soluble in an organic solvent and a charged species is more soluble in aqueous solution”

Solid-Phase Extraction

S K

Phase 2

Phase 1 S (in Solvent 1)

K1

K1 K1

K1

S

S

S

S

Solvent 2

S S S S

K2

K2

K2

K2

Solid-Phase Microextraction (SPME) Chromatography Solvent (Eluant)

Mixture (with analyte)

Column Packing (sorbent)

Eluate

Z

= Stationary Phase

Mobile Phase (solvent, gas)

Elu

tion

Chromatography

Packed Open Tubular

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Chromatography

Types of Chromatography (see Chapter 26)

1.  Adsorption Chromatography 2.  Partition Chromatography 3.  Ion-Exchange Chromatography 4.  Molecular Exclusion Chromatography 5.  Affinity Chromatography

Chromatography

Adsorption Chromatography

Adsorbed

Mobile Phase (solvent or gas) Stationary Phase

e.g. SiO2

Chromatography

Partition Chromatography

Mobile Phase (gas) Liquid Stationary

Phase

Solid e.g. SiO2

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Chromatography

Ion-Exchange Chromatography

Mobile Phase (solvent/water) Stationary Phase

(= Resin with cations or anions)

+ + + + + +

+ + +

+ +

+

+

+ + + +

Chromatography

Molecular Exclusion = Gel Filtration or Gel Permeation

Chromatography

Affinity Chromatography

Mobile Phase (solvent/water) Stationary Phase

with Covalent Ligand

(e.g. Antibody)

Chromatography “Column Chromatography”

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Chromatography High-Performance Liquid Chromatography (HPLC)

Chromatography

Chromatography Chromatography Flow Rate

Length

Radius (r)

1 cm

V = πr2 ⋅ (1 cm)

e.g. r = 0.46 cm V = π(0.046 cm)2(1 cm) = 0.665 mL* *1 cm3 = 1 mL

If 20% of column volume is solvent, then

0.133 mL/cm

Chromatography

Flow Rate

Volume Flow Rate (uv): “how many milliliters of solvent per minute”

e.g. 1 mL/min

Linear Flow Rate (ux): “how many centimeters are traveled in 1 minute by the solvent”

e.g. 1 mL/min / (0.133 mL/cm) = 7.52 cm/min

tr = Retention Time

t’r = Adjusted Retention Time

= tr - tm tm

Time

Det

ecto

r Res

pons

e

The Chromatogram “a graph showing the detector response as a

function of elution time”

Unretained Mobile Phase (solvent or gas)

Vr = tr ⋅ uv

uv = Volume Flow Rate

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t’r2

Time

Det

ecto

r Res

pons

e

The Chromatogram

t’r1

Relative Retentionα = t’r2/t’r1 > 1

t’r = tr - tm

Time

Det

ecto

r Res

pons

e

The Chromatogram

tm

Capacity Factor: k’ = tr – tm = t’r tm tm

k’ = time in the stationary phase time in the mobile phase

= moles of solute in stationary phase moles of solute in mobile phase

k’ = CsVs

CmVm

k’ = Vs ⋅ K

Vm = t’r tm

Cs/Cm = partition coefficient

Retention Time and Partition Coefficient

α = t’r2 = k’2 = K2 t’r1 k’1 K1

Relative retention

Efficiency of Separation

Time

Det

ecto

r Res

pons

e

Peak Width

?

½ h w1/2

=2.35σ

w = 4σ

Resolution = Δtr = ΔVr = 0.589Δtr wav wav w1/2av

Efficiency of Separation 3σ

6σ

Resolution = 0.75

Resolution = 1.5

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Efficiency of Separation

dx

x c

x + dx d - dc

J (Flux)

Flux (J) = -D dc (mol/m2 ⋅ s) dx

D = diffusion coefficient (see Table 23-1)

“a band of solute broadens as it moves through a chromatography column”

Efficiency of Separation

x = 0

c = m e-x /(4Dt)

4πDt

2

c = concentration (mol/m3) t = time x = distance from center of band

σ = 2Dt

σ2 = 2Dt

Efficiency of Separation

Plate Height

σ2 = 2Dt x = ux ⋅ t

t = x/ux σ2 = 2D x ux

σ2 = 2D x ux

σ2 = H x H = plate height

Efficiency of Separation

Plate Height σ2 = H x H = σ2/x

Number of Plates (N) = Length of Column (L) H

N = L = Lx = L2 = 16L2 H σ2 σ2 w2

σ = w/4

N = 16 tr2 = tr2 w2 σ2

N = 5.55 tr2 w1/2

2

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Efficiency of Separation

Plate Height and Resolution

Resolution = N (γ – 1) 4

γ = separation factor = uA = tB

uB tA

Resolution ∝ N ∝ L

e.g. Doubling L increases resolution by 2

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Assigned Problems in Chapter 23:

Problems: 23-1, 23-8, 23-11, 23-19, 23-21, 23-27