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

Background.

Dissolve a non-volatile solute in a liquid and it boils above the temperature the pure liquid would. That is boiling-point elevation, and like freezing-point depression it depends to a good approximation only on how many solute particles are present: ΔTb = i · Kb · b, where b is the molality in moles per kilogram of solvent, Kb is a constant belonging to the solvent, and i is the number of particles each formula unit releases. This calculator solves that relation, sizes the amount of solute needed to hit a target elevation, and derives Kb itself from a solvent's enthalpy of vaporisation.

The headline result is worth stating before the equations, because it contradicts something most people have been told. Add 10 g of salt — a generous tablespoon — to a litre of water, and the boiling point rises by 0.175 °C. Not two degrees. Not enough to cook pasta faster. Slightly under two tenths of one degree, and because the real van 't Hoff factor for sodium chloride is below the ideal value of 2 used in that calculation, the true figure is smaller still. To raise water's boiling point by a full kelvin you would need about 57 g of salt per litre, roughly five and a half tablespoons, which is a sixth of the way to saturation and completely inedible. Salt the pasta water for flavour. It is not doing anything thermodynamically useful.

For scale, compare that with the pressure basis. Boiling point falls about 1 °C for every 285 m of altitude, so a kitchen 500 m above sea level shifts the boiling point roughly ten times further than a heavily salted pot does, in the opposite direction. Every number on this page assumes the normal boiling point at 101.325 kPa. If you are at altitude, change the solvent boiling point field first; the solute effect is a rounding error beside it.

Now the limits, which belong here rather than in a collapsed FAQ because one of them can reverse the sign of the answer. The equation is the dilute-solution limit of an exact thermodynamic condition and assumes an ideal solution, the linearisation ln(1 − x) ≈ −x, a constant enthalpy of vaporisation over the interval, and — critically — a non-volatile solute. If the solute has its own vapour pressure, it contributes to the total and can lower the boiling point instead of raising it. An ethanol–water mixture boils below 100 °C. This equation will confidently tell you it boils above. That is not a small error; it is a reversal, and it is the single most important thing to check before using this page.

Kb is not an independent constant. It follows from the solvent's own thermodynamics as Kb = R·Tb²·M_A ÷ ΔvapH, and the third mode of this calculator will compute it from data you can look up. That mode exists because of a discrepancy this page documents rather than hides. Deriving Kb for water from the NIST/IAPWS-95 saturation enthalpy gives 0.5131 K·kg/mol, while every handbook prints 0.512 — a gap of 0.21 percent. The identical derivation on the freezing side reproduces the tabulated cryoscopic constant to 0.03 percent, so the gap is real, not a flaw in the method. For benzene it is far worse: the thermodynamics give 2.639 against a tabulated 2.53, a 4.3 percent disagreement. This page therefore ships no table of ebullioscopic constants for organic solvents. It ships the derivation, and one default — 0.512 for water, because that is what textbooks use and what a student checking homework needs to match.

Below the widget you will find the derivations in full, the hand-computed salt example the unit tests are built from, the inverse calculation that makes the pasta result unforgettable, an explanation of why the boiling point rises while the freezing point falls from the same physics, and the domain edges where the calculator refuses rather than returning a plausible-looking number.

What is boiling point elevation calculator?

Boiling-point elevation is one of the four colligative properties, alongside freezing-point depression, vapour-pressure lowering and osmotic pressure. Colligative means the effect counts particles rather than identifying them: one mole of sucrose and one mole of urea raise water's boiling point by the same amount.

The mechanism is vapour pressure. A liquid boils when its vapour pressure equals the surrounding pressure. Dissolving a non-volatile solute dilutes the solvent at the liquid surface, so fewer solvent molecules escape per unit time and the vapour pressure at any given temperature is lower. The liquid therefore has to be heated further before its vapour pressure catches up with the atmosphere. That is also why the effect reverses for a volatile solute: a solute with its own vapour pressure adds to the total rather than diluting it.

The working form is ΔTb = i · Kb · b. Kb, the ebullioscopic constant, has units of K·kg/mol and belongs to the solvent alone. Its value follows from the solvent's normal boiling point Tb, molar mass M_A and molar enthalpy of vaporisation ΔvapH: Kb = R·Tb²·M_A ÷ ΔvapH, with Tb in kelvin, M_A in kg/mol and ΔvapH in J/mol.

Comparing the two branches explains why boiling-point constants are so much smaller than freezing-point ones. The ratio Kb/Kf equals (Tb²/Tf²) × (ΔfusH/ΔvapH). For water the temperature ratio is about 1.87, which pushes Kb up, but the enthalpy ratio is 6.01/40.65 ≈ 0.148, which pushes it down much harder — because it takes almost seven times as much energy to vaporise water as to melt it. The product is 0.276, and the tabulated ratio 0.512/1.86 is 0.275. The same physics that makes water hard to boil makes its boiling point hard to shift.

The sign difference between the two branches has the same single explanation. Solute lowers the chemical potential of the liquid solvent while leaving the pure solid and the vapour untouched. That makes the liquid more stable relative to both neighbours, so it persists to lower temperatures before freezing and to higher temperatures before boiling. The liquid range widens at both ends, which is one fact rather than two rules to memorise.

How to use this calculator.

1. 01Check first that your solute is non-volatile. Salt, sugar, urea and most ionic compounds are. Ethanol, acetone and ammonia are not, and for those this equation gives the wrong sign, not just the wrong size.
2. 02Set the solvent boiling point for your actual pressure before anything else. The default 100 °C is sea level. At 1000 m water boils near 96.5 °C, and that shift is an order of magnitude larger than any solute effect you are about to compute.
3. 03Enter the mass of SOLVENT, not of the solution and not a volume. A kilogram of water is about 1003 mL at 20 °C.
4. 04Choose the van 't Hoff factor deliberately. Use 1 for sugar or any molecular solute. The default 2 is the ideal value for sodium chloride assuming complete dissociation; real values are lower, so treat the ideal answer as an upper bound.
5. 05Leave Kb at 0.512 only for water, and read the FAQ on why the derived value is 0.5131. For any other solvent, switch to the derivation mode and enter the boiling point, molar mass and enthalpy of vaporisation from the NIST Chemistry WebBook — using the enthalpy AT the boiling point, not at 25 °C.
6. 06Use the 'solute needed' mode to sanity-check intuitions. Asking how much salt is required for a full kelvin is far more instructive than asking what a tablespoon does.
7. 07Read the elevation as a difference and the boiling point as an absolute. A difference has the same number in K and °C; an absolute temperature does not.
8. 08Do not use this to decide a coolant mixture. Boiling protection in an engine comes mostly from system pressure, not from colligative elevation, and the concentration is set by the manufacturer's specification.

The formula.

Two equations, one of which is usually handed over as a constant to be looked up.

ΔTb = i · Kb · b the colligative relation b = (mass ÷ M) ÷ kg of solvent molality of the solute Kb = R · Tb² · M_A ÷ ΔvapH the constant, from solvent thermodynamics mass = b × kg of solvent × M inverse: solute needed for a target ΔTb

The first line is a linearisation. The exact condition for boiling equates the chemical potential of the solvent in the liquid and the vapour, and writing that out gives a relation in ln(x_solvent). Expanding ln(1 − x_solute) as −x_solute for small x_solute and converting mole fraction to molality produces the linear form. Everything that fails at high concentration fails in that expansion or in the assumption that activity equals mole fraction.

The third line matters because it lets you check a constant instead of trusting it — and on this page, checking finds a disagreement worth knowing about. Take water. The NIST Chemistry WebBook implements the IAPWS-95 formulation of Wagner and Pruß; its saturation table brackets the normal boiling point with rows at 364.607 K and 375.681 K, whose vaporisation enthalpies are 41.052 and 40.529 kJ/mol. Interpolating to 373.124 K gives 40.650 kJ/mol. Dividing by the molar mass gives 2256.4 kJ/kg, which is the classical IAPWS latent heat of vaporisation of water — so the interpolation is sound. Then Kb = 8.314462618 × 373.15² × 0.018015 ÷ 40650 = 0.5131 K·kg/mol.

Handbooks print 0.512. The gap is 0.21 percent. That is not obviously alarming until you run the identical derivation on the freezing branch, where the melting enthalpy from Feistel and Wagner's 2006 equation of state for ice reproduces the tabulated 1.86 to 0.03 percent. Same method, seven times the error. And benzene is worse again: NIST's boiling point of 353.3 K and vaporisation enthalpy of 30.72 kJ/mol at that temperature give Kb = 2.639, against a commonly tabulated 2.53 — a 4.3 percent gap.

A hypothesis, offered as one rather than as fact: the tabulated 0.512 for water is consistent with a vaporisation enthalpy near 40.73 kJ/mol, and the tabulated 2.53 for benzene with 32.04 kJ/mol. Both sit between the value at the boiling point and the value at 25 °C, which is what you would expect if an older compilation used an enthalpy not evaluated at Tb. This is arithmetic consistent with a plausible history; it is not a claim about any particular table's provenance. The practical consequence is firm regardless: use the enthalpy at the boiling point, and prefer a constant you derived to one you copied.

Rounding: all arithmetic is arbitrary-precision and rounding happens once, at the return boundary, to ten decimal places. A Kb derived in mode 3 is applied unrounded. Rounding it to 0.513 first would shift a 1 mol/kg answer by 0.07 mK, and rounding to the tabulated 0.512 by 1.1 mK — which is larger than the entire salt effect in the worked example below. The tests assert the unrounded path.

Invalid domain: a van 't Hoff factor of zero or less is rejected, as is an ebullioscopic constant of zero or less, a solvent mass of zero, and a solute molar mass of zero. A negative target elevation is rejected, because a non-volatile solute cannot lower a boiling point — if your mixture boils below the pure solvent, the solute is volatile and this equation does not describe it. In the derivation mode an absolute boiling point at or below 0 K is rejected, since the formula squares it, and a zero enthalpy of vaporisation is rejected because the formula divides by it.

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.