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Must-know facts

19 facts

1Molality, mole fraction, mass % and ppm are temperature-independent; molarity is not.
235% (V/V) ethylene glycol lowers water's freezing point to 255.4 K (−17.6 °C).
3Fluoride: 1 ppm prevents tooth decay; 1.5 ppm mottles teeth.
4Henry's law: p = K_H x; larger K_H means lower solubility.
5Gas solubility falls as temperature rises (K_H rises).
6Scuba tanks: 11.7% He, 56.2% N₂, 32.1% O₂, to avoid the bends.
7Raoult's law: p_i = p_i° x_i; p_total = p₁° + (p₂° − p₁°) x₂.
8Vapour is richer in the more volatile component: y_i = p_i / p_total.
9Ideal solution: ΔmixH = 0, ΔmixV = 0; e.g. benzene + toluene, n-hexane + n-heptane.
10Positive deviation: ethanol + acetone, CS₂ + acetone; negative: phenol + aniline, chloroform + acetone.
11Minimum boiling azeotrope: ethanol-water at about 95% ethanol (V/V). Maximum boiling: 68% HNO₃, 393.5 K.
12Relative lowering of vapour pressure = mole fraction of solute.
13Kb (water) = 0.52 K kg mol⁻¹; Kf (water) = 1.86 K kg mol⁻¹.
141 mol sucrose in 1000 g water boils at 373.52 K.
15π = CRT; osmotic pressure is used for molar masses of proteins and polymers.
16Normal saline is 0.9% (m/V) NaCl, isotonic with blood cells.
17Reverse osmosis uses a cellulose acetate membrane to desalinate sea water.
18i > 1 for dissociation, i < 1 for association; KCl ≈ 2, ethanoic acid in benzene ≈ 0.5.
19Weak electrolyte AB: i = 1 + α; dimerisation: i = 1 − x/2.

Common traps

Where marks are lost

Using grams of solvent directly in the molality formula.

Molality is per kilogram: divide the solvent mass in grams by 1000, or use m = w₂ × 1000/(M₂ × w₁).

Reading a larger Henry's constant as a more soluble gas.

x = p/K_H, so a larger K_H gives a smaller mole fraction dissolved at the same pressure.

Taking the vapour over a mixture to have the same composition as the liquid.

Use y_i = p_i/p_total; the vapour is richer in the more volatile component, except at an azeotrope.

Mixing up which mixtures deviate which way.

Weaker A–B attraction means easier escape and positive deviation (ethanol + acetone); stronger A–B means negative deviation (chloroform + acetone).

Writing relative lowering of vapour pressure as the mole fraction of the solvent.

(p₁° − p₁)/p₁° = x₂, the mole fraction of the solute.

Forgetting the van't Hoff factor for electrolytes.

Multiply by i: 0.1 m NaCl behaves like nearly 0.2 m of particles, and 0.1 m K₂SO₄ like nearly 0.3 m.

Using molality in π = CRT.

Osmotic pressure uses molarity C (mol L⁻¹) and R = 0.083 L bar mol⁻¹ K⁻¹ for π in bar.

Saying solvent flows from the concentrated solution to the dilute one in osmosis.

Solvent always moves from lower solute concentration to higher, into the more concentrated solution.

Expecting association to give i > 1.

Association cuts the particle count, so i < 1 and the apparent molar mass is larger than the true one.

Formulas

11 to know

Mole fraction

x_A = n_A / (n_A + n_B) ; x_A + x_B = 1

For a binary solution.

Molarity and molality

M = moles of solute / litres of solution ; m = moles of solute / kg of solvent

Molality does not change with temperature.

Henry's law

p = K_H x

x is the mole fraction of the gas in solution; K_H rises with temperature.

Raoult's law

p₁ = p₁° x₁ ; p_total = p₁° + (p₂° − p₁°) x₂

For volatile components of an ideal solution.

Vapour composition

y_i = p_i / p_total

Dalton's law of partial pressures.

Relative lowering of vapour pressure

(p₁° − p₁)/p₁° = x₂ ≈ (w₂ × M₁)/(M₂ × w₁)

Non-volatile solute; the approximation holds for dilute solutions.

Boiling point elevation

ΔTb = i Kb m ; M₂ = (Kb × w₂ × 1000)/(ΔTb × w₁)

Kb (water) = 0.52 K kg mol⁻¹; i = 1 for non-electrolytes.

Freezing point depression

ΔTf = i Kf m ; M₂ = (Kf × w₂ × 1000)/(ΔTf × w₁)

Kf (water) = 1.86 K kg mol⁻¹.

Molal constants from solvent data

Kb = R M₁ Tb² / (1000 ΔvapH) ; Kf = R M₁ Tf² / (1000 ΔfusH)

M₁ in g mol⁻¹, temperatures in K.

Osmotic pressure

π = i C R T = i n₂ R T / V ; M₂ = w₂ R T / (π V)

R = 0.083 L bar mol⁻¹ K⁻¹ for π in bar and V in L.

van't Hoff factor

i = normal molar mass / abnormal molar mass = observed / calculated colligative property

Weak electrolyte into two ions: i = 1 + α; dimerisation: i = 1 − x/2.

Key terms

14 terms

Binary solution: A solution made of exactly two components.
Molality: Moles of solute per kilogram of solvent; unchanged by temperature.
Saturated solution: A solution in dynamic equilibrium with undissolved solute, holding the most solute it can at that temperature and pressure.
Henry's law constant (K_H): The ratio of a gas's partial pressure to its mole fraction in solution; large K_H means low solubility.
Ideal solution: A solution that obeys Raoult's law at every composition, with no heat or volume change on mixing.
Azeotrope: A mixture that boils at a fixed temperature with vapour of the same composition as the liquid.
Colligative property: A property that depends on the number of solute particles, not on their identity.
Ebullioscopic constant (Kb): The boiling point rise produced by a 1 molal solution of a non-electrolyte in that solvent.
Cryoscopic constant (Kf): The freezing point drop produced by a 1 molal solution of a non-electrolyte in that solvent.
Semipermeable membrane: A film whose pores let solvent molecules through but hold back solute particles.
Osmotic pressure: The excess pressure on the solution side that just stops osmosis.
Isotonic solutions: Solutions with the same osmotic pressure, between which no osmosis occurs.
Reverse osmosis: Forcing solvent out of a solution through a membrane by applying more than the osmotic pressure.
van't Hoff factor (i): The ratio of particles actually present to formula units dissolved, found from colligative data.

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