Separation techniques — filtration, distillation, chromatography, centrifugation, sublimation: Foundations

Before you can read the parent note, you must be able to read its symbols and words without pausing. This page builds every one of them from nothing. Read top to bottom — each idea is the ladder rung for the next.

0. What is a "mixture"? (the word everything rests on)

Picture two colours of sand poured into one jar. They share the jar, but a grain of red sand is still red sand. Nothing became a new colour. That is the mental image of a mixture.

Figure — Separation techniques — filtration, distillation, chromatography, centrifugation, sublimation

Figure s01 — what "mixture" looks like. A single jar holds black grains and red (accent) grains together. The red arrow points out that a red grain is still red even while sharing the jar: the two substances coexist without becoming a new substance. This is the picture behind the word "mixture".

Why the topic needs it: if the substances were chemically bonded, no physical trick could pull them apart — you'd need a chemical reaction. Separation techniques only work on mixtures. See States of Matter and Solutions and Solubility for the deeper picture of how things mix.

1. "Dissolved" vs "colloidal" vs "suspended" — the size spectrum

The difference is particle size, and where a component sits on this spectrum decides whether filtration will work.

Figure s02 — the size spectrum decides filterability. Left beaker: dissolved particles as tiny black dots — far too small to catch. Middle beaker: colloidal particles as small red (accent) dots — bigger than molecules but still small enough to slip through ordinary filter paper. Right beaker: suspended particles as big black clumps — large enough for a filter to trap. Same liquid, but only the big clumps can be strained out by ordinary paper.

Why the topic needs it: ordinary filtration only catches suspended particles (they are large). Dissolved and colloidal particles slip through. The parent's biggest "mistake" callout — "you cannot filter salt out of water" — is the dissolved end of this same spectrum.

2. The Greek letter $μ$ and the unit "μm" (micrometre)

The parent throws numbers like "pore diameter ~2–10 μm" at you. Let's earn that symbol.

Picture a metre stick (about an adult's stride). Chop it into a million equal slivers. One sliver is $1 μ m$ . A human hair is about $70 μ m$ thick — roughly 70 of these slivers side by side.

Why the topic needs it: every filtration decision is one comparison of two sizes — and it is only valid once both sizes are in the same unit.

3. Boiling point, vapor pressure, and the symbol $P$

Distillation lives on these three. Take them slowly.

Picture a covered pot of water. Molecules keep jumping off the surface into the trapped air. The more that jump, the harder the trapped gas pushes — higher $P_{vapor}$ . Heating makes molecules faster, so more escape, so $P_{vapor}$ rises with temperature. This is the whole idea of Vapor Pressure.

Figure s03 — boiling is where two pressures meet. The red (accent) curve is the liquid's vapor pressure

P_{vapor}

climbing as temperature rises (vertical axis in kilopascals, kPa; horizontal axis in °C). The black dashed line is the fixed atmospheric pressure

P_{atmospheric} \approx 101.3 kPa

. The black dot marks the boiling point: the exact temperature where the red curve reaches the dashed line, i.e. where

P_{vapor} = P_{atmospheric}

. Both pressures are in the same units (kPa) — that is why they can be equal.

Why the different symbols matter in Raoult's Law. The parent writes: $P_{total} = P_{A}^{0} χ_{A} + P_{B}^{0} χ_{B}$ Let's define every piece (every $P$ here is a pressure in the same unit, e.g. kPa):

$A$ and $B$ are just names for the two liquids in the mixture.
$P_{A}^{0}$ — the little superscript $0$ means "pure". It's the vapor pressure liquid $A$ would have all by itself (in kPa).
$χ$ is the Greek letter "chi" (say "kie"). $χ_{A}$ is the mole fraction of $A$ : the amount of $A$ (counted in moles) divided by the total amount of everything (in moles). A mole is just a fixed, huge counting number for particles (like "a dozen" but $6.022 \times 1 0^{23}$ ) — see Stoichiometry. So if you have 3 moles of $A$ and 7 moles of $B$ , then $χ_{A} = \frac{3}{3 + 7} = 0.3$ . Because it's a fraction of the whole, $χ_{A} + χ_{B} = 1$ .
$P_{total}$ — the whole mixture's vapor pressure (kPa), built by adding each liquid's contribution.

Intuition WHY mole fraction × pure vapor pressure? (the picture behind the formula)

Picture the surface of the liquid as a crowd of molecules, some of type $A$ , some of type $B$ . Only molecules sitting at the surface can escape into the vapor. In a well-mixed ideal solution, the fraction of surface spots occupied by $A$ is just $A$ 's share of all the molecules — that is exactly the mole fraction $χ_{A}$ . So if pure $A$ (every surface spot is $A$ ) would push with vapor pressure $P_{A}^{0}$ , then a solution where only a fraction $χ_{A}$ of the surface spots are $A$ pushes with only that same fraction of the escaping — giving a partial pressure of $P_{A} = P_{A}^{0} χ_{A}$ . The single condition needed for this clean proportionality is ideal behaviour: an $A$ molecule escapes just as easily whether its neighbours are $A$ or $B$ (equal attractions). Do the identical reasoning for $B$ to get $P_{B} = P_{B}^{0} χ_{B}$ . Finally, the total push is simply the two contributions added (this adding of partial pressures is Dalton's Law): $P_{total} = P_{A} + P_{B} = P_{A}^{0} χ_{A} + P_{B}^{0} χ_{B}$ So the formula is not magic — it is "fraction of surface that is $A$ " times "how hard pure $A$ pushes", plus the same for $B$ .

Read the formula in words: each liquid pushes in proportion to how pure-it-pushes ( $P^{0}$ ) times how much of it is present ( $χ$ ). The low-BP liquid has a big $P^{0}$ , so it dominates the vapor — which is why the low-BP component comes off first. This foreshadows Colligative Properties and Raoult's Law.

4. Polarity — the "stickiness" behind chromatography

Picture a magnet (polar) versus a smooth marble (nonpolar). Magnets stick to magnetic surfaces; marbles roll on by.

Why the topic needs it: chromatography's stationary paper/silica is polar. Polar components stick to it (slow), nonpolar ones ride the solvent (fast). "Like dissolves like" — this is Intermolecular Forces in one sentence.

5. Density — the idea behind centrifugation

Centrifugation spins a tube fast so that "sinking" happens hundreds of times faster — the dense component slams to the bottom, the light liquid stays on top. Same principle as sand settling in a pond, just sped up.

6. Sublimation — skipping the liquid

Why the topic needs it: if only one component of a solid mixture sublimes, gentle heating turns just that one into vapor, which you re-freeze elsewhere — a clean separation.

How these foundations feed the topic

How to read the map below. The top box is the starting fact (a mixture is not chemically bonded). It branches into the five physical properties that components can disagree on. Each property in turn feeds the one technique that exploits it. The two lower boxes (vapor pressure, mole fraction) show which extra ideas plug into the boiling-point / distillation branch. Follow any arrow top-to-bottom to read "this idea makes that technique possible".

Equipment checklist

Read each prompt, say the answer out loud, then check yourself against the text after the ::: separator (::: just marks "flip to reveal the answer").

What "mixture" means

two-plus substances physically together, not chemically bonded, each keeping its identity

The three size regimes and their sizes

dissolved (below 0.001 μm, invisible), colloidal (0.001–1 μm, cloudy but doesn't settle), suspended (above 1 μm, visible and settles)

Why ordinary filter paper cannot clear a colloid

colloidal particles (0.001–1 μm) are far smaller than the 2–10 μm paper pores, so they pass straight through

What

μ m

means

micrometre, one millionth of a metre

The filtration size test — and its unit requirement

particle diameter greater than pore diameter implies trapped, BUT only after both diameters are put in the same unit

What happens if particle diameter exactly equals pore diameter

it's a toss-up (some pass, some jam); never design at that boundary — pick pores comfortably smaller

What vapor pressure

P_{vapor}

is, and its units

the push from molecules that have escaped the liquid surface into the gas above; measured in Pa, kPa, atm or bar

The boiling-point condition

P_{vapor} = P_{atmospheric}

, both in the same pressure unit

What the superscript

0

P_{A}^{0}

means

"pure" — the vapor pressure of that substance alone, NOT an exponent

What

χ_{A}

(mole fraction) means

moles of A divided by total moles of everything;

χ_{A} + χ_{B} = 1

Why

P_{A}^{0} χ_{A}

gives A's partial pressure

χ_{A}

is the fraction of surface spots that are A, and pure A pushes with

P_{A}^{0}

, so a fraction

χ_{A}

of that push escapes; add A and B contributions (Dalton) for the total

When Raoult's Law is valid

only for ideal solutions; real mixtures need activity coefficients and can show positive or negative deviation

Polar vs nonpolar

polar = lopsided charge (tiny magnet, like water); nonpolar = even charge (like oil)

What the fraction bar in

R_{f}

means

it is the division operator — take the numerator (component distance) and divide it by the denominator (solvent-front distance)

What

R_{f}

depends on

BOTH stationary-phase stickiness AND mobile-phase (solvent) polarity

What density decides

dense sinks, light floats — the basis of centrifugation

What sublimation is

solid turning straight into gas, skipping the liquid