Chemistry · Solutions and electrolytes · Year 1

Raoult's law, distillation and osmosis

Why is salt spread on roads in winter and antifreeze put in a radiator?

The situation

In winter salt is spread on the roads, and antifreeze rather than water is poured into a car radiator. The “physiological saline” sold in the pharmacy is exactly 0.9 % NaCl: anything stronger or weaker harms blood cells. At the Fergana oil refinery, crude oil is separated into fractions in a rectification column, while in the laboratory the molar mass of an unknown substance can be found with a thermometer. One idea links all of this: in a solution the “activity” of the solvent falls. How much ice does one kilogram of salt melt, and why can alcohol not be distilled to 100 %?

Topic

Thermodynamics of solutions: Raoult's law, distillation and colligative properties. Winter in Tashkent: salt spread on the road, antifreeze in a car radiator; 0.9% saline at the pharmacy; the rectification column of the Fergana oil refinery…

Key ideas

Raoult's law
Cryoscopy
Osmotic pressure

Formulas

p_{i} = x_{i} p_{i}^{\circ} (Raoult), p_{i} = k_{H} x_{i} (Henry)

The vapour pressure of the solvent is proportional to its mole fraction, and the pressure of a sparingly dissolved substance (a gas) is proportional to the Henry constant.

Δ T_{k r} = K_{k r} i m, Δ T_{e b} = K_{e b} i m

Cryoscopy and ebullioscopy: for water $K_{f}$ = 1.86, $K_{b}$ = 0.512 K·kg/mol; for benzene 5.12 and 2.53; $i$ is the van ’t Hoff factor.

K = \frac{R T_{0}^{2} M}{Δ H}

The constants come from the solvent itself: its heat of melting (vaporisation) and its temperature.

M = \frac{K g \cdot 1000}{Δ T G}

Molar mass: $g$ is the mass of the solute, $G$ is the mass of the solvent (g).

π = i c R T

Van ’t Hoff law: osmotic pressure (kPa, $c$ in mol/L). For polymers $π / c = R T (1 / M_{n} + A_{2} c)$ .

Theory

Thermodynamics of solutions: chemical potential

A solution is a homogeneous mixture of two or more substances; the solvent may be aqueous or non-aqueous (liquid ammonia, benzene, alcohols). Dissolving is a physico-chemical process: ions and molecules are solvated by the solvent (hydrated in water), so dissolving takes in or gives out heat (measured in the “Thermochemistry and Gibbs energy” experiment). The property of each component is expressed by its partial molar quantity: for example, 50 mL of ethanol + 50 mL of water ≈ 96–97 mL — hydrogen bonds between the molecules reduce the volume. The most important partial quantity is the chemical potential $μ_{i} = μ_{i}^{\circ} + R T \ln a_{i}$ ( $a_{i}$ is the activity; in an ideal solution $a_{i} = x_{i}$ ). The components are interdependent: the Gibbs–Duhem equation $x_{1} d \ln γ_{1} + x_{2} d \ln γ_{2} = 0$ (seen in the $\ln γ$ graph on the panel). Solutions are ideal (benzene–toluene), infinitely dilute (the solvent obeys Raoult's law, the solute obeys Henry's law) and real (activity coefficients $γ \neq 1$ ).

Raoult's and Henry's laws

Raoult's law: the partial vapour pressure of a component above a solution is $p_{i} = x_{i} p_{i}^{\circ}$ ; the relative lowering of the solvent's vapour pressure equals the mole fraction of the solute: $Δ p / p^{\circ} = x_{2}$ . In a real solution $p_{i} = γ_{i} x_{i} p_{i}^{\circ}$ : positive deviation ( $γ > 1$ , ethanol–water: unlike molecules attract each other more weakly) and negative deviation ( $γ < 1$ , acetone–chloroform: C–H…O hydrogen bond). A sparingly dissolved substance such as a gas obeys Henry's law: $p_{i} = k_{H} x_{i}$ or $c = k_{H} p$ ; for CO₂ at 25 °C $k_{H}$ ≈ 0.034 mol/(L·atm) = 3.4·10⁻⁴ mol/(L·kPa), and as the temperature falls the solubility rises — cold fizzy water foams less when opened. For real gases fugacity is used instead of pressure. The Duhem–Margules equation $x_{1} d \ln p_{1} / d x_{1} = x_{2} d \ln p_{2} / d x_{2}$ : if one component deviates positively, the other deviates in the same way.

Distillation: the laws of Konovalov and Vrevsky

The vapour above a boiling mixture is richer in the more volatile component (Konovalov's first law) — the basis of distillation. In a T–x–y diagram the lower line is the liquid (boiling) and the upper one is the vapour (condensation). If the vapour pressure (boiling point) curve has an extremum, the liquid and vapour have the same composition at that point — an azeotrope (Konovalov's second law): ethanol–water 95.6 % (by mass) ethanol, 78.2 °C (minimum boiling point) — simple distillation cannot give purer alcohol than that; acetone–chloroform — a maximum boiling point (64.5 °C). Vrevsky's laws: if the pressure (temperature) changes, the azeotrope composition shifts — in ethanol–water, if the pressure falls, the azeotrope becomes richer in ethanol and disappears below ≈ 9 kPa. Rectification is evaporation–condensation repeated many times; each theoretical plate is one “stair” in the diagram. Vacuum distillation lowers the boiling point (aniline: 184 °C → ≈ 76 °C at 2 kPa), and steam distillation is for a substance insoluble in water: at $p_{A} + p_{water}$ = 101.3 kPa (aniline + water: 98.4 °C). At oil refineries, crude oil is separated in atmospheric and vacuum columns into petrol, kerosene, diesel and fuel-oil fractions — see the “Natural gas, oil and coal” experiment.

Cryoscopy and ebullioscopy (laboratory)

Because the activity of the solvent falls, a solution freezes at a lower temperature and boils at a higher temperature than the pure solvent: $Δ T = K i m$ , $K = R T_{0}^{2} M / Δ H$ . For electrolytes $i$ is the van ’t Hoff factor (ideally 2 for NaCl; in reality $i = 2 φ$ with an osmotic coefficient $φ$ ≈ 0.92–0.98). The Beckmann thermometer has a scale of 5–6 °C (division 0.01 °C) and is adjusted: by changing the amount of mercury in the upper reservoir, the freezing point of the pure solvent is brought to the upper part of the scale (divisions 3–5). Experiment: 25 g of solvent in a test tube is cooled, with stirring, in an ice–salt mixture; after supercooling (0.3–1 °C) crystals appear and the temperature jumps — the highest reading is the freezing point. Measure for the solvent and for the solution, then $M = K g \cdot 1000 / (Δ T G)$ . Ebullioscopy is the same at the boiling point; the boiling point of NaCl solutions is almost linear in $m$ . Polymers (high-molecular-weight compounds): if $M \sim 10^{5}$ g/mol, then for 1 g of polymer in 25 g of benzene $Δ T$ ≈ 0.002 K — a Beckmann thermometer cannot detect it, and osmometry is needed. In everyday life: road salt melts ice down to −21.1 °C (the eutectic, 23.3 % NaCl); a 50 % (by volume) ethylene glycol antifreeze freezes at ≈ −37 °C (the ideal model estimates −30 °C — a negative deviation). Safety: benzene is toxic and flammable — work in a fume cupboard, with no naked flames; if a mercury thermometer breaks, tell the teacher.

Osmosis and osmotic pressure

As a result of diffusion, a substance moves towards the side of lower concentration (“Transport phenomena”). Through a semipermeable membrane that lets only the solvent pass, the solvent moves into the solution — osmosis; the pressure that stops it is the osmotic pressure: $π = i c R T$ (van ’t Hoff, 1886; Pfeffer osmometer). 0.1 M sucrose at 25 °C gives 248 kPa — equal to a 25 m column of water. Blood plasma is ≈ 290 mOsm/kg: at 37 °C π ≈ 0.74–0.78 MPa (7.3–7.7 atm); an isotonic solution is 0.9 % NaCl. A red blood cell swells in a hypotonic solution (haemolysis begins at 0.45 % NaCl and is complete at 0.3–0.35 %) and shrivels in a hypertonic one. Reverse osmosis: if a pressure greater than π is applied on the solution side, pure water passes out through the membrane — drinking water is obtained from sea water (π ≈ 2.7 MPa) or from salty groundwater. Polymer osmometry: $π / c = R T (1 / M_{n} + A_{2} c)$ — extrapolating to $c \to 0$ gives the number-average $M_{n}$ . Extraction is the distribution of a substance between two immiscible solvents (Nernst: $K = c_{1} / c_{2}$ = const) — in the experiment on separation methods.

Safety and the model

Benzene, toluene and chloroform are toxic, acetone and alcohols catch fire easily: work in a fume cupboard and heat in a heating mantle rather than over a naked flame; an ice–salt mixture cools to −20 °C — wear gloves. A reverse-osmosis unit works at high pressure. Model: vapour pressures — NIST Antoine equations; activity coefficients — constant Van Laar parameters (the model azeotrope for ethanol–water is at x = 0.91, i.e. ≈ 96 %; in experiments 95.6 %); for NaCl solutions the osmotic coefficients at 25 °C (Robinson–Stokes) are applied at all temperatures, and the freezing and boiling points are calculated from the water activity; glycol and other non-electrolytes are ideal ( $φ$ = 1); red blood cell — Boyle–van ’t Hoff model (the osmotically inactive fraction is 40 %); polymer $A_{2}$ — a typical value; membrane permeability ≈ 1 L/(m²·h·bar); time is sped up 10 times.

Did you know?

The first Nobel Prize in Chemistry (1901) was awarded to Jacobus van ’t Hoff for discovering the laws of chemical dynamics and of osmotic pressure in solutions.
In the 1880s François Raoult systematically measured the freezing points and vapour pressures of solutions and showed that they depend on the number of solute particles — cryoscopy began with this work.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Water purification and softening — Grade 7
Electrolytic dissociation — Grade 9
Hydrolysis of salts and the medium — Grade 9
Solutions and solubility — Grade 11
Concentration of a solution — Grade 11