Boiling Point Elevation Calculator (ΔTb = i · Kb · b)

Background.

Ten grams of salt stirred into a litre of pasta water raises its boiling point by less than a fifth of a degree. That surprises anyone who was taught that salted water boils hotter and cooks faster, but it follows from one of the most dependable rules in solution chemistry: a dissolved substance that does not itself evaporate raises a liquid's boiling point in proportion to how many particles it adds, whatever those particles are. For dilute solutions the rule is ΔTb = i · Kb · b, where b is the molality (moles of solute per kilogram of solvent), i is the number of particles each formula unit breaks into, and Kb is a constant belonging to the solvent alone — 0.512 K·kg/mol for water.

The relation can be used three ways here. You can work out the boiling point of a solution you have made; turn it round to find how much solute a target rise would take; or derive Kb itself from a solvent's boiling point, molar mass and enthalpy of vaporisation, which is worth doing because published constants for some solvents disagree with their own thermodynamic data by several percent.

Two warnings come before any arithmetic. The rule needs a solute that stays in the liquid. Salt, sugar and urea qualify; ethanol, acetone and ammonia do not, and for them the equation predicts a rise where the real mixture boils lower. And pressure moves boiling points far more than solutes do. Water boils about 1 °C lower for every 300 m of altitude, so a kitchen at 500 m sees a drop nearly ten times larger than the rise from that 10 g of salt. Set the pure solvent's boiling point for where you are before reading anything else.

What is boiling point elevation calculator?

Boiling-point elevation is the rise in boiling temperature that follows when a non-volatile solute is dissolved in a liquid. It is one of the four colligative properties, with freezing-point depression, vapour-pressure lowering and osmotic pressure: effects that count dissolved particles without regard to their identity, so a mole of sucrose and a mole of urea in a kilogram of water raise its boiling point by the same amount.

The cause is vapour pressure. A liquid boils when its vapour pressure equals the pressure above it. Solute particles dilute the solvent, fewer solvent molecules escape at any given temperature, and the solution has to be heated further before its vapour pressure catches up with the atmosphere. The same dilution lowers the freezing point. Dissolved solute stabilises the liquid relative to both the pure solid and the vapour, so the liquid range widens at both ends; elevation and depression are one effect seen from two sides.

How to use this calculator.

1. 01Choose the question under 'What do you want to work out?': the boiling point of a solution you have made, the solute needed for a target rise, or the ebullioscopic constant of a solvent from its thermodynamic data.
2. 02Enter Mass of SOLVENT in grams: the liquid alone, not the finished solution and not a volume. Weighing beats measuring, since 1,000 g of water occupies about 1,002 mL at 20 °C.
3. 03Enter the solute's mass and molar mass (58.44 g/mol for sodium chloride, 342.30 for sucrose, 180.16 for glucose), then the van 't Hoff factor: 1 for anything that dissolves as whole molecules, the ion count for a salt.
4. 04Set Boiling point of the pure solvent for your actual pressure. 100 °C is water at sea level; at 1,500 m it is close to 95 °C.
5. 05Leave Ebullioscopic constant at 0.512 for water. For another solvent, use the derivation mode with its boiling point, Molar mass of the SOLVENT and Enthalpy of vaporisation taken at the boiling point, for instance from the NIST Chemistry WebBook.
6. 06In the 'solute needed' mode, type the rise you want as a positive Target elevation in kelvin; a non-volatile solute can only raise a boiling point.

The formula.

Three relations sit behind the result. Molality comes first: b = (solute mass ÷ solute molar mass) ÷ kilograms of solvent. The rise is ΔTb = i · Kb · b, and the solution's boiling point is the pure solvent's boiling point plus ΔTb. Run backwards, the same line gives the solute needed for a target rise: b = ΔTb ÷ (i · Kb), then mass = b × kilograms of solvent × molar mass. Because ΔTb is a temperature difference it carries the same number in kelvin and in degrees Celsius.

The linear form is an approximation. Boiling happens where the solvent's chemical potential is equal in liquid and vapour; writing that condition out gives a relation in the logarithm of the solvent's mole fraction, and the textbook equation comes from expanding ln(1 − x) as −x for a small solute fraction x, assuming an ideal solution, and holding the enthalpy of vaporisation constant over the narrow temperature interval. Each assumption weakens as the solution gets stronger.

The same derivation yields the constant: Kb = R · Tb² · M_A ÷ ΔvapH, with R = 8.314462618 J/(mol·K), the boiling point Tb in kelvin, the solvent's molar mass M_A in kg/mol and its molar enthalpy of vaporisation in J/mol. A heavy solvent, a hot-boiling one or one that vaporises easily has a large Kb; water, light and with an unusually large enthalpy of vaporisation, has a small one. From the NIST/IAPWS-95 saturation data, water's ΔvapH at the normal boiling point is 40.65 kJ/mol (2,256.4 kJ/kg, the classical latent heat), so Kb = 8.314462618 × 373.15² × 0.018015 ÷ 40,650 = 0.5131 K·kg/mol. Handbooks print 0.512, which is 0.21% lower. The identical calculation for freezing, using the melting enthalpy of 333.427 kJ/kg from the 2006 IAPWS equation of state for ice, reproduces the tabulated cryoscopic constant of 1.86 to within 0.03%, so the method itself holds up. For benzene the gap widens: NIST's boiling point of 353.3 K and enthalpy of 30.72 kJ/mol give 2.639 against a commonly tabulated 2.53, a 4.3% difference.

A possible explanation, offered only as a hypothesis: the tabulated constants correspond to enthalpies of about 40.73 kJ/mol for water and 32.04 kJ/mol for benzene, both between each solvent's enthalpy at its boiling point and its larger value at 25 °C — the pattern an older compilation would leave if it used an enthalpy taken at the wrong temperature. Whatever the history, the enthalpy to use is the one at the boiling point. In derivation mode the computed constant goes straight into the elevation, unrounded.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST Chemistry WebBook, SRD 69 — Thermophysical Properties of Fluid Systems, implementing the IAPWS-95 formulation of Wagner & Pruß (2002). Saturation table queried 2026-07-29; the rows bracketing the normal boiling point are T = 364.60738 K (H_liquid 6.9029491, H_vapour 47.954822 kJ/mol) and T = 375.68144 K (7.7438400, 48.272745). Interpolating to T_b = 373.1243 K gives Δ_vap H = 40.6497 kJ/mol, equivalently 2256.4 kJ/kg — the classical IAPWS latent heat of vaporisation, which confirms the interpolation. This is the value from which this page derives Kb(water) = 0.5131 K·kg/mol.
2. [2]Feistel, R. & Wagner, W. (2006). 'A New Equation of State for H2O Ice Ih', Journal of Physical and Chemical Reference Data 35(2), 1021–1047 — the equation of state adopted by IAPWS in 2006, giving Δh_melt = 333.427 kJ/kg at the normal-pressure melting point. Used here as the CONTROL: the identical derivation method applied to the freezing branch reproduces the tabulated cryoscopic constant 1.86 to 0.03 %, which is what establishes that the 0.21 % gap on the boiling branch is a source conflict rather than a method error. Retrieved 2026-07-29.
3. [3]NIST Chemistry WebBook, SRD 69 — phase-change data for benzene: T_boil = 353.3 ± 0.1 K (average of 147 of 183 values) and Δ_vap H = 30.72 kJ/mol at 353.3 K (Majer & Svoboda, 1985). Deriving Kb from these gives 2.639 K·kg/mol against a commonly tabulated 2.53 — a 4.3 % disagreement, and the stated reason this page ships no table of ebullioscopic constants for organic solvents. Retrieved 2026-07-29.
4. [4]NIST Special Publication 811, 2008 edition, section 8.6.8 'Molality of solute B' — b_B = n_B/m_A, SI unit mol/kg, per mass of SOLVENT, which is why the colligative equations are written in molality rather than molarity. Section 8.5 establishes that a temperature interval or difference has the same numerical value in K and °C, so the elevation needs no unit conversion. Retrieved 2026-07-29.
5. [5]IUPAC, 'Quantities, Units and Symbols in Physical Chemistry' (Green Book), 3rd edition, 2nd printing 2012, section 2.10 composition table: molality m_B, b_B = n_B/m_A with SI unit mol kg⁻¹, note 14 on the symbol collision between molality and mass. Confirms the molality definition independently of NIST. Retrieved 2026-07-29.
6. [6]Hamer, W. J. & Wu, Y.-C. (1972). 'Osmotic Coefficients and Mean Activity Coefficients of Uni-univalent Electrolytes in Water at 25 °C', Journal of Physical and Chemical Reference Data 1(4), 1047–1100. Tabulates practical osmotic coefficients φ for 79 uni-univalent electrolytes; the effective van 't Hoff factor is i = ν·φ with φ below 1 in the dilute range, which is why the ideal factor of 2 used in this page's salt example is an upper bound. Cited for the direction of the deviation only — no numeric φ is asserted here, because the paper's data tables are scanned images and were not extracted. Free NIST reprint; retrieved 2026-07-29.
7. [7]IUPAC Commission on Isotopic Abundances and Atomic Weights (CIAAW), Standard Atomic Weights 2021, abridged values — the source of every molar mass on this page: H 1.008, C 12.011, O 15.999, Na 22.98976928, Cl 35.45, giving M(H2O) = 18.015, M(NaCl) = 58.44, M(C6H6) = 78.114 g/mol. Retrieved 2026-07-29.