NuclearNotes · Chapter 06 — Separation Techniques

1 Chapter overview

In analytical chemistry you almost never measure the analyte in its original matrix. A drug tablet, a river-water sample, a food extract — each is a mixture, and the detector cannot tell your analyte apart from everything else. So before the measurement comes a separation: break the mixture into its components, then quantify them one by one. This chapter is about the separation techniques that dominate modern analytical work.

The centrepiece is chromatography: band broadening (why peaks spread), column efficiency (how many theoretical plates the column gives), and resolution (how well two peaks are separated) — with the numerical problems these generate. Then the two great instruments built on these principles: gas chromatography (GC) and high-performance liquid chromatography (HPLC). Finally, a chemistry turn: ionic liquids (synthesis, properties, applications) and the wider family of green solvents.

📖 Definition — chromatography

Chromatography is a separation method in which the components of a sample are carried by a mobile phase through a stationary phase. Each component partitions between the two phases to a different extent, so components travel at different speeds and elute (exit the column) at different times. A plot of detector signal against time is a chromatogram.

Roadmap: §2 builds the principles — retention, capacity factor, selectivity, the three band-broadening mechanisms, GC and HPLC hardware, ionic liquids and green solvents. §3 derives the working equations: van Deemter, plate number, HETP and the Purnell resolution equation. §4 turns them into exam numericals. Note: no question from this chapter appeared in the 2020–2024 papers — so §6 carries an honest empty state, and the whole chapter is built directly from the reference books.

2 Core concepts

2.1 · The chromatographic experiment

A small volume of sample is injected into a flowing mobile phase (a gas in GC, a liquid in HPLC), which sweeps it through a column containing the stationary phase (a coated liquid film or solid particles). Solute molecules repeatedly partition between the two phases. A solute that prefers the mobile phase races through; one that prefers the stationary phase lingers. Each solute therefore has a characteristic retention time $(t_R)$ : the time between injection and the peak maximum at the detector.

⏱ Retention vocabulary — learn this cold

Hold-up (dead) time $(t_M)$ : time an unretained species (one that never enters the stationary phase) needs to cross the column. Adjusted retention time $(t_R' = t_R - t_M)$ : the extra time the solute actually spends in the stationary phase. Capacity (retention) factor $(k = t_R'/t_M)$ : the number of column volumes of mobile phase needed to elute the solute — equivalently the ratio of time the solute spends in the stationary vs mobile phase. Selectivity (separation) factor $(\alpha = k_B/k_A = t_{R,B}'/t_{R,A}')$ , with $(k_B > k_A)$ : how differently two solutes are retained.

Rule of thumb from Harris and Skoog: keep $(1 < k < 10)$ — below 1 the solute barely retains and separation is hard; above 10 you wait forever for little extra resolution. Selectivity $(\alpha)$ must exceed 1 for any separation at all; values near 1.05–1.2 are the hard cases where efficiency (plates) has to do the heavy lifting.

2.2 · Band broadening: why peaks spread

An injected band starts as a sharp plug, but by the detector it has spread into a broad, roughly Gaussian peak. Two theories explain it. Plate theory (Martin–Synge) treats the column as stacked equilibrium stages — "theoretical plates" — and gives the counting tools (N, HETP). Rate theory (van Deemter) asks why the band spreads and gives the optimisation tool: the van Deemter equation. Three in-column mechanisms matter:

Term	Name	Physical origin	Velocity dependence
$A$	Eddy diffusion	Packed particles force molecules along paths of different lengths — some short cuts, some detours.	Constant (independent of $u$ ). $A = 2\lambda d_p$ : smaller, uniform particles help.
$B/u$	Longitudinal (axial) diffusion	Molecules diffuse along the column axis, from the concentrated band centre outward, while migrating.	Falls as $u$ rises — slow flow gives diffusion time to act. $B = 2\gamma D_m$ .
$Cu$	Resistance to mass transfer	Partition between phases is not instantaneous; molecules in the two phases get out of step with each other.	Grows with $u$ — fast flow leaves no time for equilibrium. Thinner films and smaller particles help.

In open-tubular (capillary) columns there is no packing, so the $A$ term vanishes — the governing form is the Golay equation, $(H = B/u + (C_s + C_m)u)$ , with separate mass-transfer terms for stationary and mobile phases.

⚠️ Extra-column broadening — beyond van Deemter

The column is not the only band-spreader. Broadening from the injector (finite injection volume), connecting tubing, and detector cell volume adds to the column's own. Variances add: $\sigma_{\text{total}}^2 = \sigma_{\text{col}}^2 + \sigma_{\text{ext}}^2$ . This is why instruments use low-volume injectors, short narrow tubing, and small detector cells — a 10 000-plate column is wasted if the detector smears the bands.

2.3 · Gas chromatography

In GC the mobile phase is an inert carrier gas — He (best, safest), N₂ (cheaper, needs lower optimum flow), or H₂ (fastest, flammable) — and the sample must be volatile and thermally stable (typically bp < ~350 °C, or made volatile by derivatisation). Solutes partition between the gas and a liquid stationary phase coated on the column walls.

Column type	Dimensions	Notes
Packed	2–6 m × 2–4 mm i.d., 60/80–100/120 mesh particles	High sample capacity; modest plates (~10³–10⁴); being replaced by capillaries.
Capillary / WCOT (wall-coated open tubular)	10–100 m × 0.1–0.53 mm i.d., 0.1–5 µm film	Standard today: up to ~10⁵ plates, no $A$ term; small capacity (~ng per component).

Because retention in GC is driven by vapour pressure, the column sits in a temperature-controlled oven and wide-boiling mixtures are run with temperature programming: start cool to resolve the volatiles, then ramp (typically 5–20 °C/min) to elute the heavies in a reasonable time — sharp peaks throughout instead of the broad late peaks of an isothermal run.

Detector	Selectivity	Destructive?	Typical detection limit
FID — flame ionisation	Almost universal for organics (C–H); blind to H₂O, CO₂	Yes	~10⁻¹² g/s (mass-sensitive)
TCD — thermal conductivity	Universal (anything differing from carrier gas)	No	~10⁻⁷ g/mL (concentration-sensitive)
ECD — electron capture	Selective: halogens, nitro groups, peroxides, organometallics	No	~10⁻¹³ g/mL (the pesticide detector)
MS — mass spectrometry	Universal + structural ID via m/z and library spectra	Yes	~10⁻¹² g (pg range; instrument-dependent)

2.4 · High-performance liquid chromatography

HPLC swaps the gas for a liquid mobile phase pumped at high pressure through a short column of fine particles. No volatility requirement — the workhorse for drugs, biomolecules, polymers, and anything thermally fragile. The hardware chain:

Pump — reciprocating (dual-piston) pump delivering pulse-free flow ~0.1–10 mL/min at up to ~400 bar (6000 psi). Injector — a loop (Rheodyne-type) valve that drops a fixed µL volume into the high-pressure stream without stopping flow. Column — stainless-steel, typically 3–25 cm × 4.6 mm, packed with 3–5 µm silica-based particles; efficiency follows the van Deemter terms, and smaller particles cut both $A$ and $C$ . Detectors — UV-Vis (254 nm fixed or diode-array; the default, ng sensitivity, needs a chromophore), refractive index (RI) (universal but insensitive, no gradient use), fluorescence (the most sensitive, ~pg, but only for fluorescing analytes).

Mode	Stationary phase	Mobile phase	Elutes first
Normal phase	Polar (bare silica, amino)	Non-polar (hexane, chloroform)	Least polar analytes
Reversed phase	Non-polar (C18, C8 bonded silica)	Polar (water–methanol/acetonitrile)	Most polar analytes — the ~75% default

Elution strategy: isocratic (constant mobile-phase composition — simple, fine when $\alpha$ values are similar) vs gradient (composition ramps from weak to strong solvent during the run — the LC analogue of temperature programming; sharp peaks for both weakly and strongly retained analytes). The RI detector cannot be used with gradients (its baseline drifts with composition).

	GC	HPLC
Mobile phase	Inert gas (He, N₂, H₂)	Liquid (water–organic mixtures)
Sample requirement	Volatile, thermally stable	Soluble; no volatility needed
Typical columns	10–100 m capillaries	3–25 cm packed columns
Plates	Up to ~10⁵ (capillary)	~10³–2×10⁴
Selectivity lever	Stationary-phase chemistry + temperature	Mobile-phase composition (gradient)

2.5 · Ionic liquids

🧂 Definition — ionic liquid

An ionic liquid (IL) is a salt that is liquid below 100 °C (many are liquid at room temperature — RTILs), e.g. 1-butyl-3-methylimidazolium hexafluorophosphate, [bmim][PF₆]. Bulky, asymmetric organic cations (imidazolium, pyridinium, ammonium, phosphonium) frustrate crystal packing, so the lattice energy stays low enough for the salt to melt near room temperature.

Synthesis is a two-step classic: (1) quaternisation (Menshutkin reaction) — an amine or phosphine attacks an alkyl halide, e.g. 1-methylimidazole + 1-chlorobutane → [bmim]Cl; (2) anion metathesis/exchange — the halide is swapped for the target anion, e.g. [bmim]Cl + HPF₆ → [bmim][PF₆] + HCl, or with NaPF₆/NaBF₄. The anion largely sets the properties: halides give water-miscible hydrophilic ILs; PF₆⁻, NTf₂⁻ give hydrophobic ones.

Properties — the exam list: negligible vapour pressure (no VOC emissions, no evaporative loss); wide liquid range (often liquid from below 0 °C to decomposition above 200–300 °C); tunability ("designer solvents" — swap cation/anion to dial polarity, miscibility, acidity); good thermal stability; intrinsic ionic conductivity; non-flammability of most common ILs.

Applications: green solvents replacing volatile organics in synthesis and liquid–liquid extraction; separations (extractive distillation, e.g. aromatics/aliphatics; CO₂ capture; metal-ion extraction); catalysis (immobilising homogeneous catalysts in a separate IL phase for easy product decantation — biphasic catalysis); electrolytes for batteries and electrodeposition (wide electrochemical window).

2.6 · Green solvents

Green chemistry's solvent problem: solvents are the bulk of chemical waste. The replacement family, in the order the syllabus (and Tundo's Green Chemistry framing) presents them:

Water — the greenest solvent: non-toxic, non-flammable, cheap; enables aqueous biphasic catalysis (e.g. the Ruhrchemie/Rhône-Poulenc hydroformylation). Limitation: most organics are insoluble; workarounds include surfactants and "on-water" rate accelerations. Supercritical CO₂ (scCO₂, T_c = 31 °C, P_c = 74 bar) — gas-like diffusivity with liquid-like density, tunable by pressure, leaves zero residue on depressurisation; used for extraction (decaffeination), chromatography (SFC), and polymer processing. Ionic liquids — above. Deep eutectic solvents (DES) — mixtures like choline chloride + urea (1:2) that melt far below either component (Abbott et al., 2003): cheap, biodegradable, easy to prepare — the "poor man's ionic liquid".

✅ Solvent selection guides

Industry codifies greenness in solvent selection guides (GSK, Pfizer, Sanofi): each common solvent is scored red/amber/green on waste, environmental impact, health, flammability/reactivity and life-cycle. Exam point: the guides exist to drive substitution — e.g. replace dichloromethane and DMF (red) with 2-MeTHF, ethyl acetate or water (green) where the chemistry allows.

3 Key derivations

3.1 · The van Deemter equation

Rate theory adds the three broadening variances per unit column length. Each is a plate-height contribution — a length (mm) — so they simply add:

Eddy diffusion $(A)$ . Molecules taking different paths through the packing arrive at different times. $(A = 2\lambda d_p)$ , with $(d_p)$ the particle diameter and $(\lambda)$ a packing-uniformity constant — velocity-independent, so it is a floor under the curve.

Longitudinal diffusion $(B/u)$ . In time $(t)$ a band diffuses $(\sigma^2 = 2D_m t)$ ; residence time is $(t \propto 1/u)$ , so the plate-height contribution is $(B/u)$ with $(B = 2\gamma D_m)$ . Dominant at low flow — the left arm of the curve.

Mass-transfer resistance $(Cu)$ . Partition lags equilibrium; the lag grows with flow, so the contribution is linear in $(u)$ . Dominant at high flow — the right arm of the curve.

Assemble. Adding the three contributions gives the van Deemter equation — and because $(B/u)$ falls while $(Cu)$ rises, the sum has a minimum at an optimum velocity.

(1)

H = A + \frac{B}{u} + Cu \qquad \text{(van Deemter equation)}

Differentiate and set to zero: $(dH/du = -B/u^2 + C = 0)$ . Solving gives the optimum velocity, and substituting back gives the minimum plate height:

(2)

u_{\text{opt}} = \sqrt{\frac{B}{C}}

(3)

H_{\text{min}} = A + 2\sqrt{BC}

🔬 Read the curve like an examiner

Below $(u_{\text{opt}})$ you lose plates to diffusion (B term); above it you lose plates to mass-transfer lag (C term). Practical GC runs at roughly 2× $(u_{\text{opt}})$ — the "optimum practical gas velocity": plate height rises only slightly, but analysis time drops a lot. Capillary columns kill $(A)$ ; smaller particles and thinner films shrink $(A)$ and $(C)$ .

3.2 · Column efficiency: plates and HETP

Peak shape. A chromatographic peak is approximately Gaussian. For a Gaussian, the base width $(W)$ (between the tangents at the inflection points) spans $(4\sigma)$ and the half-height width $(W_{1/2})$ spans $(2.355\sigma)$ .

Plate count. Plate theory gives $(N = (t_R/\sigma)^2)$ . Eliminate $(\sigma)$ with $(\sigma = W/4)$ — or $(\sigma = W_{1/2}/2.355)$ for the half-height form.

Plate height. Height equivalent to a theoretical plate: $(H = L/N)$ — the column length consumed per plate. Smaller $(H)$ (or larger $(N)$ ) = narrower peaks = more efficient column.

(4)

N = 16\left(\frac{t_R}{W}\right)^2 = 5.54\left(\frac{t_R}{W_{1/2}}\right)^2

(5)

H = \frac{L}{N} \qquad \text{(HETP: height equivalent to a theoretical plate)}

⚠️ Units trap

$(t_R)$ and $(W)$ must be in the same units (both minutes, or both seconds) — the ratio is dimensionless. $(W)$ is the base width (4σ); the half-height width needs the 5.54 coefficient. Mixing them up is the classic numerical error.

3.3 · Resolution and the Purnell equation

Resolution $(R_s)$ measures how well two adjacent peaks are separated: peak spacing over average peak width. Baseline separation (≤0.3% overlap) needs $(R_s \geq 1.5)$ ; $(R_s = 1.0)$ leaves ~2% overlap.

(6)

R_s = \frac{2\,\Delta t_R}{W_A + W_B} = \frac{1.18\,\Delta t_R}{W_{1/2,A} + W_{1/2,B}}

Now the master result. Write $(N)$ via (4) for the later peak, express $(\Delta t_R)$ through $(k)$ and $(\alpha)$ (since $(t_R' = k\,t_M)$ and $(\alpha = k_B/k_A)$ ), and (6) rearranges into the Purnell (master resolution) equation — resolution factorised into its three independent levers:

(7)

R_s = \frac{\sqrt{N}}{4}\,\frac{\alpha - 1}{\alpha}\,\frac{k_B}{1 + k_B} \qquad \text{(Purnell equation)}

Lever	Factor in (7)	How to move it	Cost
Efficiency $(N)$	$(\sqrt{N}/4)$	Longer column, smaller particles, $(u_{\text{opt}})$	Weak: doubling $(R_s)$ needs 4× the plates (∝ √N)
Selectivity $(\alpha)$	$((\alpha-1)/\alpha)$	Change stationary phase, temperature, mobile-phase composition	Strongest lever — the chemist's lever
Retention $(k)$	$(k/(1+k))$	Weaker/stronger solvent, temperature	Saturates: beyond $(k \approx 10)$ gains vanish while time explodes

🔬 The examiner's moral

When peaks overlap, do not first buy a longer column — change the selectivity $(\alpha)$ . Because $(R_s \propto \sqrt{N})$ , efficiency is the most expensive way to fix a separation and selectivity is the cheapest. Retention $(k)$ is tuned only into the useful 1–10 window.

4 Worked examples

Six exam-style numericals. Every number below is worked through step by step — check each division yourself; these are exactly the calculations the paper asks for.

Example 1 · Plate number from retention time and peak width

Given: a solute elutes at $(t_R = 8.52)$ min with base width $(W = 0.52)$ min. Also measured: half-height width $(W_{1/2} = 0.31)$ min.

Base-width formula (4): $(N = 16\,(t_R/W)^2)$ . Ratio $(8.52/0.52 = 16.38)$ . Square: $(16.38^2 = 268.5)$ . Times 16: $(16 \times 268.5 = 4295)$ ≈ 4300 plates.

Half-height check: $(N = 5.54\,(t_R/W_{1/2})^2 = 5.54\,(8.52/0.31)^2 = 5.54 \times 27.48^2 = 5.54 \times 755.4 = 4185)$ ≈ 4200 plates — consistent, as it must be for the same peak.

Example 2 · HETP from plates

Given: the column in Ex. 1 is $(L = 25.0)$ cm long and gives $(N = 4300)$ plates.

$(H = L/N = 250\ \text{mm} / 4300 = 0.0581\ \text{mm})$ ≈ 58 µm. For a packed HPLC-style column this is an ordinary, realistic plate height; a capillary GC column at its optimum can reach ~0.3–0.5 mm.

Example 3 · Resolution from a chromatogram

Given: two adjacent peaks: $(t_{R,A} = 8.52)$ min, $(t_{R,B} = 9.31)$ min; base widths $(W_A = 0.52)$ min, $(W_B = 0.60)$ min.

Spacing $(\Delta t_R = 9.31 - 8.52 = 0.79)$ min. Resolution (6): $(R_s = 2\Delta t_R/(W_A+W_B) = 2(0.79)/(0.52+0.60) = 1.58/1.12 = 1.41)$ .

Verdict: $(R_s = 1.41 < 1.5)$ — the peaks overlap slightly (~1% area); not baseline-separated. Fix it by improving selectivity $(\alpha)$ , not by reflexively lengthening the column.

Example 4 · How much more efficiency to reach a target resolution?

Given: current $(R_s = 1.41)$ at $(N_1 = 4300)$ ; target $(R_s = 1.75)$ with $(\alpha)$ and $(k)$ unchanged.

From the Purnell equation, $(R_s \propto \sqrt{N})$ , so $(N_2/N_1 = (R_{s,2}/R_{s,1})^2 = (1.75/1.41)^2 = 1.241^2 = 1.54)$ . Plates must rise 54%, to $(N_2 = 4300 \times 1.54 = 6620)$ .

At constant $(H)$ , $(N \propto L)$ : the 25.0 cm column must become $(25.0 \times 1.54 = 38.5)$ cm — and analysis time rises ~54% too. This is the price of the √N law.

Example 5 · Optimum velocity from van Deemter parameters

Given: $(H = 0.025 + 0.045/u + 0.0018u)$ cm, with $(u)$ in cm/s.

Read off $(A = 0.025)$ cm, $(B = 0.045)$ cm²/s, $(C = 0.0018)$ s. Optimum (2): $(u_{\text{opt}} = \sqrt{B/C} = \sqrt{0.045/0.0018} = \sqrt{25} = 5.0)$ cm/s.

Minimum plate height (3): $(H_{\text{min}} = A + 2\sqrt{BC} = 0.025 + 2\sqrt{0.045 \times 0.0018} = 0.025 + 2\sqrt{8.1\times10^{-5}} = 0.025 + 2(0.0090) = 0.043)$ cm. Check: $(H(5.0) = 0.025 + 0.0090 + 0.0090 = 0.043)$ cm ✓.

For a 25 cm column at the optimum: $(N = L/H = 25/0.043 = 581)$ ≈ 580 plates.

Example 6 · The Purnell equation as a design tool

Given: hold-up time $(t_M = 1.20)$ min; $(t_{R,A} = 4.80)$ min, $(t_{R,B} = 5.28)$ min; later peak has $(N = 10\,000)$ plates.

Capacity factors: $(k_A = (4.80-1.20)/1.20 = 3.0)$ , $(k_B = (5.28-1.20)/1.20 = 3.4)$ . Selectivity: $(\alpha = k_B/k_A = 3.4/3.0 = 1.13)$ .

Purnell (7): $(R_s = (\sqrt{10\,000}/4)\times((1.13-1)/1.13)\times(3.4/4.4) = 25 \times 0.1176 \times 0.7727 = 2.27)$ . Baseline separation with margin.

What if the phase were changed to raise $(\alpha)$ to 1.20? $(R_s = 25 \times (0.20/1.20) \times 0.773 = 25 \times 0.1667 \times 0.773 = 3.22)$ — selectivity moves the needle far more than adding plates ever could.

✅ Number hygiene for the exam

Always use the later peak's $(N)$ and $(k_B)$ in (7); $(t_R)$ and $(W)$ in the same units; base width with 16, half-height width with 5.54. And quote $(R_s)$ to two decimal places — 1.41 vs 1.50 is a pass/fail distinction.

5 Figures

The van Deemter curve. The B/u arm dominates at low velocity, the Cu arm at high velocity; the minimum at u_opt gives the smallest plate height H_min.

Resolution in pictures. Rs = 2ΔtR/(WA + WB): at Rs ≈ 1.0 the peaks overlap; at Rs = 1.5 they return to baseline between them — the exam standard for "separated".

Block diagram of a gas chromatograph. HPLC follows the same flow of blocks with a high-pressure pump and liquid mobile phase instead of the carrier-gas cylinder.

6 PYQ bank

⚠️ Honest empty state — zero PYQs

No question from this chapter — band broadening, column efficiency, resolution, GC, HPLC, ionic liquids, or green solvents — appeared in any of the five years' papers (2020–2024). This chapter is therefore built entirely from the reference books (Skoog/Holler/Crouch, Harris, Tundo et al.). Treat it as high-probability unasked syllabus: examiners frequently rotate to long-ignored units.

The five questions below are practice questions written from the books — they are NOT PYQs and never appeared in any paper. Use them to test yourself.

P1. [Practice — not a PYQ] State the van Deemter equation. Identify the three terms, say which dominates at low and at high mobile-phase velocity, and explain why capillary (open-tubular) columns have no A term.

$H = A + B/u + Cu$ . A — eddy diffusion (multiple flow paths through packing); B/u — longitudinal diffusion; Cu — resistance to mass transfer. At low u the B/u term dominates (diffusion has time to act); at high u the Cu term dominates (no time for phase equilibrium). Capillaries have no packing, so there are no multiple paths — A = 0 (Golay equation).

P2. [Practice — not a PYQ] A peak elutes at $t_R = 6.40$ min with half-height width $W_{1/2} = 0.24$ min on a 30 cm column. Calculate N and HETP.

$N = 5.54\,(t_R/W_{1/2})^2 = 5.54\,(6.40/0.24)^2 = 5.54 \times 26.67^2 = 5.54 \times 711.1 = 3940$ plates. $H = L/N = 300\ \text{mm}/3940 = 0.076$ mm ≈ 76 µm.

P3. [Practice — not a PYQ] Two peaks: $t_R = 5.20$ and $5.85$ min, base widths $0.30$ and $0.34$ min. Calculate $R_s$ and state whether separation is baseline.

$R_s = 2(5.85-5.20)/(0.30+0.34) = 2(0.65)/0.64 = 1.30/0.64 = 2.03$ . $R_s > 1.5$ — baseline separation achieved.

P4. [Practice — not a PYQ] Chlorinated pesticide residues in river water must be determined at trace level by GC. Which detector do you choose, and why? Contrast with FID and TCD.

ECD (electron capture detector): selective for electrophores (halogens, nitro groups), detection limit ~10⁻¹³ g/mL — the most sensitive choice for chlorinated analytes. FID is near-universal for organics but not selective and less sensitive here; TCD is universal and non-destructive but far too insensitive (~10⁻⁷ g/mL).

P5. [Practice — not a PYQ] Give the two-step synthesis of [bmim][PF₆] starting from 1-methylimidazole, and state two properties that qualify ionic liquids as green solvents.

(1) Quaternisation: 1-methylimidazole + 1-chlorobutane → [bmim]Cl (Menshutkin reaction). (2) Anion metathesis: [bmim]Cl + HPF₆ → [bmim][PF₆] + HCl. Green credentials: negligible vapour pressure (no VOC emissions) and wide liquid range / tunability / non-flammability.

7 Exam Q&A

Q1. Define the capacity factor $(k)$ . What range is recommended?

$(k = (t_R - t_M)/t_M)$ — the ratio of time the solute spends in the stationary phase to that in the mobile phase. Keep $(1 < k < 10)$ .

Q2. What is the selectivity factor $(\alpha)$ , and what value must it exceed for separation?

$(\alpha = k_B/k_A = t_{R,B}'/t_{R,A}')$ , with $(k_B > k_A)$ . It must exceed 1 — at $(\alpha = 1)$ the peaks coincide.

Q3. Name the three terms of the van Deemter equation.

A — eddy diffusion; B/u — longitudinal (axial) diffusion; Cu — resistance to mass transfer.

Q4. Which band-broadening term dominates at very low flow? At very high flow?

Low flow: B/u (longitudinal diffusion). High flow: Cu (mass-transfer resistance).

Q5. Give the optimum velocity and minimum plate height.

$(u_{\text{opt}} = \sqrt{B/C})$ ; $(H_{\text{min}} = A + 2\sqrt{BC})$ .

Q6. Define the plate number $(N)$ and HETP.

$(N = 16(t_R/W)^2 = 5.54(t_R/W_{1/2})^2)$ ; HETP $(H = L/N)$ .

Q7. What resolution value corresponds to baseline separation?

$(R_s \geq 1.5)$ (≈99.7% separated). $(R_s = 1.0)$ still leaves ~2% overlap.

Q8. State the Purnell equation and name its three levers.

$(R_s = (\sqrt{N}/4)\,((\alpha-1)/\alpha)\,(k_B/(1+k_B)))$ . Levers: efficiency $(N)$ , selectivity $(\alpha)$ , retention $(k)$ .

Q9. Name the GC carrier gases and give one advantage of capillary over packed columns.

He, N₂, H₂. Capillary (WCOT) columns give up to ~10⁵ plates and have no eddy-diffusion (A) term.

Q10. Name two green solvents and state the purpose of solvent selection guides.

Any two: water, supercritical CO₂, ionic liquids, deep eutectic solvents. Guides (GSK, Pfizer) score solvents red/amber/green to drive substitution of hazardous solvents.

8 Quick revision

Boxed results — the whole chapter on one screen

Retention: $t_R' = t_R - t_M$ ; capacity factor $k = t_R'/t_M$ ; selectivity $\alpha = k_B/k_A$
(1) van Deemter: $H = A + B/u + Cu$
(2) Optimum velocity: $u_{\text{opt}} = \sqrt{B/C}$ ; (3) $H_{\text{min}} = A + 2\sqrt{BC}$
(4) Plates: $N = 16(t_R/W)^2 = 5.54(t_R/W_{1/2})^2$ ; (5) HETP: $H = L/N$
(6) Resolution: $R_s = 2\Delta t_R/(W_A+W_B)$ ; baseline needs $R_s \geq 1.5$
(7) Purnell: $R_s = (\sqrt{N}/4)((\alpha-1)/\alpha)(k_B/(1+k_B))$ — $R_s \propto \sqrt{N}$ , so doubling $R_s$ needs 4× plates
Extra-column broadening: $\sigma_{\text{total}}^2 = \sigma_{\text{col}}^2 + \sigma_{\text{ext}}^2$
Ionic liquid synthesis: quaternisation (amine + alkyl halide) → anion metathesis; properties: negligible vapour pressure, wide liquid range, tunability, conductivity

Symbols

Symbol	Meaning	Symbol	Meaning
$t_R$	retention time	$t_M$	hold-up (dead) time
$k$	capacity (retention) factor	$\alpha$	selectivity factor
$N$	theoretical plates	$H$	plate height (HETP)
$u$	mobile-phase linear velocity	$A, B, C$	van Deemter coefficients
$R_s$	resolution	$W, W_{1/2}$	base / half-height peak width
$\Delta t_R$	retention-time difference	$L$	column length