Lesson 10 of 10 · 16 min
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Must-know facts
19 facts
- 01Molality, mole fraction, mass % and ppm are temperature-independent; molarity is not.
- 0235% (V/V) ethylene glycol lowers water's freezing point to 255.4 K (−17.6 °C).
- 03Fluoride: 1 ppm prevents tooth decay; 1.5 ppm mottles teeth.
- 04Henry's law: p = K_H x; larger K_H means lower solubility.
- 05Gas solubility falls as temperature rises (K_H rises).
- 06Scuba tanks: 11.7% He, 56.2% N₂, 32.1% O₂, to avoid the bends.
- 07Raoult's law: p_i = p_i° x_i; p_total = p₁° + (p₂° − p₁°) x₂.
- 08Vapour is richer in the more volatile component: y_i = p_i / p_total.
- 09Ideal 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
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.