Boiling-point elevation: why solutions boil hotter

What boiling-point elevation is

Pure water boils at 100 °C at sea level. Stir in a mole of salt per kilogram of water and it boils at about 101 °C instead. The dissolved particles did not change the water molecules — they changed the conditions under which those molecules can escape as vapor.

Boiling-point elevation is the increase in boiling point caused by a dissolved nonvolatile solute. Like all colligative properties, it counts particles: more dissolved particles, higher boiling point, regardless of what the particles are.

From vapor-pressure lowering to a higher boiling point

The mechanism starts one step earlier, at vapor pressure. Dissolved solute particles occupy positions at the liquid surface and hinder solvent molecules from escaping, so the solution's vapor pressure sits below the pure solvent's at every temperature.

A liquid boils when its vapor pressure equals the surrounding atmospheric pressure (1 atm at sea level). With the whole vapor-pressure curve pushed downward, the solution must be heated to a higher temperature before its vapor pressure climbs back up to 1 atm. That extra heating is exactly $\Delta T_b$.

The formula: ΔTb = i·Kb·m

The quantitative relationship is:

$$\Delta T_b = i \cdot K_b \cdot m$$

• $\Delta T_b$: the boiling-point rise in °C.
• $i$: the van't Hoff factor — particles per formula unit (2 for NaCl, 1 for glucose).
• $K_b$: the solvent's boiling-point elevation constant (0.512 °C·kg/mol for water).
• $m$: the molality in mol/kg of solvent.

Molality appears rather than molarity because the measurement spans temperatures at which the solution's volume changes. $K_b$ belongs to the solvent alone; tables list it for common solvents (ethanol 1.22, benzene 2.53 °C·kg/mol).

Worked example: 1.00 m NaCl in water

Calculate the boiling point of a 1.00 m aqueous NaCl solution at 1 atm, using $i = 2$ and $K_b = 0.512$ °C·kg/mol for water.

1. Substitute into the formula: $\Delta T_b = 2 \times 0.512 \times 1.00$.
2. Multiply: $2 \times 0.512 = 1.024$, so $\Delta T_b \approx 1.02$ °C.
3. Add to water's normal boiling point: $100.00 + 1.02 = 101.02$ °C.

For contrast, 1.00 m glucose ($i = 1$) gives $\Delta T_b = 0.512$ °C and boils at 100.51 °C — half the rise, because each glucose molecule contributes one particle instead of two. Real NaCl solutions show a touch less than the ideal 1.02 °C due to ion pairing.

Antifreeze, candy, and concentration gauges

Antifreeze earns its name in winter, but ethylene glycol protects engines in summer too: a 50/50 glycol-water coolant boils well above 100 °C, preventing boilover under load. The same particle count that depresses the freezing point elevates the boiling point — one additive, two colligative benefits.

Candy makers read the effect in reverse. As sugar syrup boils, water evaporates, the sugar concentration climbs, and the boiling point rises steadily. A thermometer in the pot therefore reports the syrup's concentration: 112 °C means thread stage, 150 °C means hard crack. The boiling point is a concentration gauge.

Measuring molar mass by ebullioscopy

Analytical chemists run the formula backward to weigh molecules. Dissolve a known mass of an unknown nonvolatile compound in a known mass of solvent, measure the boiling-point rise precisely, and solve for molality:

$$m = \frac{\Delta T_b}{i \cdot K_b}$$

Moles of unknown = $m \times$ (kg of solvent); molar mass = grams / moles. This technique, ebullioscopy, complements freezing-point (cryoscopic) measurements. It demands careful thermometry — a 0.01 °C error in $\Delta T_b$ translates directly into a proportional error in the molar mass.

Errors to avoid

The usual suspects: forgetting the van't Hoff factor (NaCl needs $i = 2$), using molarity instead of molality, and mixing up $K_b$ with $K_f$. Water's two constants — 0.512 for boiling, 1.86 for freezing — are worth memorizing as a pair.

Also watch the solute requirements: it must be nonvolatile and must not react with the solvent. A volatile solute like ethanol contributes its own vapor pressure and the simple formula fails. And remember the direction: solute raises boiling points but lowers freezing points — elevation for boiling, depression for freezing.

Variables and units

Common mistakes

Real-world applications

• Antifreeze also raises the coolant's boiling point, protecting engines in summer

• Candy making: sugar concentration tracked through boiling-point rise

• Desalination and distillation: accounting for boiling-point shifts in brines

• Determining molar masses of unknown compounds from measured ΔTb

• Chemical engineering: designing evaporators and reboilers for solutions

• Food processing: concentrating juices and syrups by controlled boiling