Why a dissolved solute makes a liquid boil hotter
A liquid boils when its vapour pressure equals the pressure pushing down on it. Dissolve a non-volatile solute and you reduce the vapour pressure at every temperature, because solvent molecules now make up less than the whole of the liquid surface — that is Raoult's law. A liquid whose vapour pressure has been pulled down has to be heated further before it can match atmospheric pressure again. The extra heating is the boiling point elevation.
The effect is colligative: it depends on how many dissolved particles are present and not on what they are. One mole of sucrose and one mole of urea per kilogram of water raise the boiling point by exactly the same 0.512 °C. One mole of sodium chloride raises it by twice as much, not because sodium chloride is special but because each formula unit becomes two ions in solution.
The elevation is small. That surprises people, because the intuition from de-icing suggests salt has a big effect on phase behaviour. Water's ebullioscopic constant Kb is 0.512 °C·kg/mol against a cryoscopic constant Kf of 1.86 — the boiling side of the same physics is about three and a half times weaker. If you want the freezing side, the freezing point depression calculator runs the mirror-image calculation.
The formula, variable by variable
ΔTb = i · Kb · b, and the solution's boiling point is the pure solvent's boiling point plus that shift. Three inputs, each with its own trap.
Kb, the ebullioscopic constant, belongs to the solvent, not the solute. It follows from the solvent's own boiling point and enthalpy of vaporisation: Kb = R·(Tb°)²·Msolvent / ΔHvap, with Tb° in kelvin and Msolvent in kg/mol. Read that expression and the pattern in the reference table below stops being arbitrary. Water's constant is small because water's enthalpy of vaporisation is enormous relative to its molar mass; carbon tetrachloride's is ten times larger because it is heavy and vaporises easily.
b, the molality, is moles of solute per kilogram of solvent. Not per litre, and not per kilogram of solution. Molality is used rather than molarity because the experiment changes temperature and volumes change with it, while masses do not. The molality calculator converts between the two if you have a density.
i, the van 't Hoff factor, is the particle count per formula unit: 1 for sugars, glycols and urea; 2 for NaCl and KNO₃; 3 for CaCl₂ and Na₂SO₄. Weak acids fall between 1 and 2. In concentrated solution the effective factor drifts from the ideal integer because ions interact, so treat whole numbers as the dilute limit.
One condition is easy to overlook: the solute must be non-volatile. Dissolve ethanol in water and the equation fails entirely, because ethanol contributes its own vapour pressure and the mixture boils below pure water. That case belongs to Raoult's law for volatile mixtures, not here.
Worked example: salt water, sugar water, and pasta
1. One mole of salt per kilogram of water. Dissolve 58.44 g of NaCl (M = 58.44 g/mol) in 1.000 kg of water.
- Moles: 58.44 ÷ 58.44 = 1.000 mol.
- Molality: 1.000 mol ÷ 1.000 kg = 1.000 mol/kg.
- Particle molality: i·b = 2 × 1.000 = 2.000 mol/kg.
- Elevation: 0.512 × 2.000 = 1.024 °C.
- Boiling point: 100.000 + 1.024 = 101.024 °C.
2. The same effect with sugar. Dissolve 342.30 g of sucrose — one mole — in 500 g of water. The molality is 1.000 ÷ 0.500 = 2.000 mol/kg, sucrose does not dissociate so i = 1, and the elevation is 0.512 × 2.000 = 1.024 °C again. Six times the mass of chemical, identical result: the particle count is what matters.
3. Now salt your pasta water. A generous 10 g of salt in 4.0 L of water gives 10 ÷ 58.44 = 0.1711 mol in 4.0 kg, a molality of 0.0428 mol/kg. With i = 2 the elevation is 0.512 × 2 × 0.0428 = 0.044 °C. Four hundredths of a degree. Salt your pasta water for flavour; it does nothing measurable to the cooking temperature.
To reach a full degree of elevation you would need about 114 g of salt per litre — roughly a third of the way to saturation, and completely inedible.
How to read the result, and what dominates it in practice
Compare the elevation you get against the two effects that usually swamp it: pressure and impurity of the solvent.
Pressure wins, almost always. Water's boiling point falls by roughly 1 °C for every 285 m of altitude near sea level, so Denver at 1,600 m boils water near 95 °C. A colligative elevation of a tenth of a degree is invisible next to that. This calculator gives you the shift relative to the normal boiling point at 1 atm; if you are working anywhere other than at sea level, first correct the base boiling point for pressure with the Clausius-Clapeyron calculator, then add the elevation this calculator returns.
The concentration limit. The linear law is a limiting law, exact only as the solution becomes infinitely dilute. Below roughly 0.1 mol/kg it is very good; by 1 mol/kg expect a few percent of error; above that treat it as an order-of-magnitude estimate. Saturated brine — about 6.1 mol/kg NaCl — would give an ideal prediction of 0.512 × 2 × 6.1 = 6.2 °C, while the measured boiling point of saturated sodium chloride solution is close to 108 °C. The ideal law understates it substantially at that concentration.
Where the effect actually earns its keep. Not in cooking, but in industry and analysis. Sugar boiling is governed by it: confectioners read the boiling point of a syrup as a proxy for concentration, and the 114–116 °C of firm-ball stage corresponds to a specific sucrose molality. Evaporator design in sugar refining and paper pulping budgets for boiling-point rise stage by stage, because a rise reduces the temperature difference driving heat transfer. And ebullioscopy, like cryoscopy, can determine a molar mass — though its lower sensitivity means cryoscopy is nearly always preferred.
Ebullioscopic constants for common solvents
| Solvent | Normal boiling point (°C) | Kb (°C·kg/mol) | ΔTb at 0.100 m (°C) |
|---|---|---|---|
| Water | 100.0 | 0.512 | 0.0512 |
| Ethanol | 78.4 | 1.22 | 0.122 |
| Benzene | 80.1 | 2.53 | 0.253 |
| Cyclohexane | 80.7 | 2.79 | 0.279 |
| Acetic acid | 118.1 | 3.07 | 0.307 |
| Chloroform | 61.2 | 3.63 | 0.363 |
| Carbon tetrachloride | 76.8 | 5.03 | 0.503 |
Constants as tabulated in the CRC Handbook of Chemistry and Physics; sources differ slightly in the final digit.
This only works for a non-volatile solute
The derivation assumes the solute contributes no vapour of its own. Salts, sugars, glycols and polymers qualify. Alcohols, acetone, ammonia and dissolved gases do not — a volatile solute adds its own vapour pressure to the mixture, and the boiling point of the blend can fall well below that of the pure solvent. A 20% ethanol-water mixture boils near 87 °C, not above 100 °C.
If both components are volatile you need a vapour-liquid equilibrium treatment. Start with the Raoult's law calculator, which gives the total vapour pressure and the vapour composition above an ideal mixture.
Mistakes that make a boiling point prediction wrong
- Dividing by the mass of solution. Molality uses the mass of solvent only. For a 20% solution this error shrinks your answer by a fifth.
- Leaving out the van 't Hoff factor. An electrolyte modelled with i = 1 gives half or a third of the real elevation.
- Applying it to a volatile solute. Ethanol, acetone and ammonia lower the boiling point of water rather than raising it.
- Ignoring pressure. A tenth of a degree of colligative elevation is meaningless if you have not corrected the base boiling point for altitude or for a vacuum.
- Extending the linear law to concentrated solution. Above about 1 mol/kg the constant Kb assumption breaks down and the error can run to several degrees.
- Confusing the elevation with the new boiling point. ΔTb is the shift; the boiling point is the solvent's value plus that shift.
- Assuming salted water cooks food faster. The elevation from culinary quantities of salt is a few hundredths of a degree, which changes nothing about cooking time.
Where this sits among the colligative properties
Boiling point elevation is one of four properties that respond only to particle concentration. The others are freezing point depression, osmotic pressure, and vapour-pressure lowering. All four follow from the same statement — a solute lowers the chemical potential of the solvent in the liquid phase — and they differ only in which equilibrium you disturb.
They differ enormously in sensitivity, and that decides which one you use. For a 0.010 molal aqueous solution the boiling point rises 0.0051 °C, the freezing point falls 0.019 °C, and the osmotic pressure reaches about 0.24 atm at 25 °C, which is roughly 180 mm of mercury. The first is barely measurable, the second needs a good thermometer, the third is trivially readable on a manometer. That is the whole reason osmometry dominates polymer and protein work while ebullioscopy is now mostly a teaching exercise.
Boiling point elevation still matters where evaporation is the process, not the measurement. Multi-effect evaporators concentrating sugar juice, black liquor or brine lose available temperature difference at every stage to boiling-point rise, and that loss goes straight into the heat-transfer area you have to buy. In those calculations engineers use measured boiling-point-rise curves rather than the ideal law, for the same reason this page keeps warning you about: at the concentrations that matter industrially, the linear law has long since stopped being accurate.
Key terms
- Ebullioscopic constant (K<sub>b</sub>)
- The boiling point elevation produced by a 1 molal ideal solution of a non-dissociating, non-volatile solute, in °C·kg/mol. A property of the solvent alone.
- Normal boiling point
- The temperature at which a liquid's vapour pressure equals exactly 1 atm (101.325 kPa). Distinct from the standard boiling point, defined at 1 bar.
- Molality (b)
- Moles of solute per kilogram of solvent. Temperature-independent, which is why colligative equations use it instead of molarity.
- Non-volatile solute
- A solute with negligible vapour pressure at the temperature of interest — salts, sugars, polymers. Required for this equation to apply.
- Boiling-point rise
- The engineering name for the same quantity, used in evaporator design, where it is read from measured curves rather than the ideal law.