Boiling Point Elevation Calculator

Article — Boiling Point Elevation Calculator

Boiling Point Elevation Calculator: ΔTb from Molality, Kb, and van't Hoff Factor

Boiling point elevation ΔTb equals i × Kb × m. For water, Kb is 0.512 K kg/mol, so dissolving one mole of sucrose in one kilogram of water raises the boiling point by 0.512 °C, while one mole of NaCl raises it by about 0.95 °C (i ≈ 1.86 because the salt dissociates into two ions). The effect is a colligative property — it depends only on the number of dissolved particles, not their identity. The formula is exact at infinite dilution and accurate within a few percent below 0.1 mol/kg; concentrated solutions deviate as activity coefficients drop and ions pair up.

This calculator handles non-electrolytes, strong electrolytes (NaCl, CaCl₂, MgCl₂), and weak electrolytes. Solvent presets cover water, benzene, chloroform, ethanol, cyclohexane, and acetone, each with its published Kb and pure-solvent boiling point. The output shows ΔTb in kelvin and the new boiling temperature of the solution.

What is boiling point elevation

Boiling point elevation is the rise in boiling temperature when a non-volatile solute dissolves in a solvent. Adding solute reduces the vapor pressure of the solvent (Raoult's law), so a higher temperature is needed to reach atmospheric pressure and start boiling. The shift is small for dilute solutions but real: pure water boils at 100.00 °C; one-molal sucrose water boils at 100.51 °C.

The effect is colligative — it scales with the number of solute particles, not their chemical type. One mole of sugar, one mole of urea, and one mole of glycerol all raise water's boiling point by 0.512 °C, because each contributes one particle per molecule. Ionic salts dissociate, so one mole of NaCl contributes nearly two moles of particles and the shift roughly doubles.

The boiling point elevation formula

The boiling point elevation formula is ΔTb = i × Kb × m, where m is molality (moles of solute per kg of solvent), Kb is the ebullioscopic constant of the solvent, and i is the van't Hoff factor. Use molality rather than molarity because molality does not change with temperature — mass is conserved when water expands on heating, but volume is not.

The new solution boiling point equals the pure solvent boiling point plus the elevation: Tb(solution) = Tb° + ΔTb. The elevation is always positive when the solute is non-volatile. For a volatile solute (alcohol in water), the rule changes — the lighter component evaporates preferentially and the boiling point depends on composition.

Ebullioscopic constant Kb values

Kb is a property of the solvent only and follows from thermodynamics: Kb = R · Tb² · M / ΔHvap. Solvents with high heats of vaporisation and high boiling points have large Kb values, so they show bigger boiling point elevation per unit molality. Water is on the low end of Kb because its hydrogen-bonded structure already provides a strong reference.

Camphor has the largest Kb among common solvents — 5.95 K kg/mol — which is why it was historically used in cryoscopic and ebullioscopic measurement of unknown molar masses. Benzene (2.53) and chloroform (3.63) are also good for sensitive ΔTb measurements when an organic solvent is needed.

van't Hoff factor and electrolytes

The van't Hoff factor i counts how many solute particles appear in solution per formula unit dissolved. For non-electrolytes (sugar, urea, glycerol), i = 1. For strong electrolytes that dissociate completely, i equals the number of ions: NaCl → Na⁺ + Cl⁻, so i = 2 in theory. The measured i is always somewhat less because ions interact: about 1.86 for NaCl, 2.55 for CaCl₂, and 2.7 for MgCl₂.

Weak electrolytes (acetic acid, ammonia) only partially dissociate, giving fractional i values between 1 and 2 depending on concentration. The van't Hoff factor formula i = 1 + α(ν − 1) connects i to the degree of dissociation α (0 to 1) and the maximum number of ions ν.

Boiling point elevation of salt water

Seawater (about 0.6 mol/kg of dissolved salts, mostly NaCl, MgSO₄, and CaCl₂) has a boiling point elevation of roughly 0.6 °C above pure water. That is the reason laboratory deionised water boils at exactly 100.00 °C while a beach water sample boils slightly higher, around 100.6 °C, at sea-level pressure.

Freezing point depression vs boiling point elevation

Both are colligative effects but freezing point depression is bigger. For water, Kf = 1.86 K kg/mol — about 3.6× larger than Kb = 0.512. The ratio Kf/Kb is a thermodynamic constant for each solvent that depends on the boiling point, melting point, and heats of vaporisation and fusion. Practically, this is why road salt depresses freezing more dramatically than it raises boiling.

Measuring molar mass by ebullioscopy

Before mass spectrometry, ebullioscopy was a standard way to measure molar mass. Dissolve a known mass of unknown in a known mass of high-Kb solvent (camphor or benzene), measure ΔTb precisely with a Beckmann thermometer, then solve M = (Kb × mass_solute) / (mass_solvent_kg × ΔTb). The method is still useful in undergraduate labs and for compounds that are hard to ionise for MS.

Common boiling point elevation mistakes

The biggest error is using molarity instead of molality. Molarity changes with temperature; molality does not. Always convert your concentration to mol/kg of solvent before applying the formula. The second error is forgetting i — students applying ΔTb = Kb × m to a salt will underestimate the effect by a factor of 2 or 3. The third is extrapolating to high concentrations: above 1 mol/kg the linear formula breaks down by 10 to 30%.