Boiling Point Elevation Calculator
Calculate the boiling point elevation of a solution from molality, the ebullioscopic constant Kb, and the van 't Hoff factor. Enter the pure solvent's boiling point to get the new boiling point in °C and °F.
Find the Boiling Point of a Solution
Boiling Point Elevation Formula
Where:
- \(\Delta T_b\) — boiling point elevation (°C)
- \(i\) — van 't Hoff factor (number of particles the solute forms in solution)
- \(K_b\) — molal boiling point elevation constant, or ebullioscopic constant, of the solvent (°C·kg/mol)
- \(m\) — molality of the solution (mol solute per kg solvent)
- \(T_b^\circ\) — boiling point of the pure solvent (°C)
- \(T_b\) — boiling point of the solution (°C)
The elevation is proportional to the concentration of dissolved particles, not their chemical identity. Adding the elevation to the pure solvent's boiling point gives the temperature at which the solution boils.
Boiling Point Elevation – Calculation Example
Example: 1.5 mol of sucrose is dissolved in 1 kg of water (molality 1.5 mol/kg). Sucrose does not dissociate, so \(i = 1\), and water has \(K_b = 0.512\) °C·kg/mol with a normal boiling point of 100 °C.
\[ \Delta T_b = i \cdot K_b \cdot m = 1 \times 0.512 \times 1.5 = 0.768 \text{ °C} \]
\[ T_b = 100 + 0.768 = 100.768 \text{ °C} \]
Result: the boiling point rises by 0.768 °C (1.382 °F), so the solution boils at 100.768 °C, or about 213.38 °F.
How to Use the Calculator
- Enter the Molality (m) in mol/kg — the moles of solute per kilogram of solvent, not per litre of solution. If you only know masses, use a molality calculator first.
- Enter the Boiling Point Elevation Constant (Kb) of the solvent in °C·kg/mol (water: 0.512, ethanol: 1.22, benzene: 2.53, chloroform: 3.63).
- Enter the van 't Hoff Factor (i): 1 for non-electrolytes like sucrose, about 2 for NaCl, about 3 for CaCl₂.
- Enter the Pure Solvent Boiling Point (Tb°) and choose °C or °F from the unit dropdown.
- Read the results: the elevation \(\Delta T_b\) in °C and °F, and the boiling point of the solution in both units.
What Is Boiling Point Elevation?
Boiling point elevation is a colligative property: when a non-volatile solute is dissolved in a solvent, the solution boils at a higher temperature than the pure solvent. The effect depends only on the number of dissolved particles, not on what they are. A spoon of salt and a spoon of sugar raise the boiling point of water by the same amount if they produce the same number of particles.
The physical reason is vapour pressure lowering. A solute dilutes the solvent at the surface, reducing how many solvent molecules escape into the vapour phase, so the solution reaches atmospheric pressure — the boiling condition — only at a higher temperature. The same principle drives freezing point depression, and both effects can be described through the temperature dependence of vapour pressure, which is the basis of the Clausius–Clapeyron equation.
The van 't Hoff factor accounts for dissociation. Sodium chloride splits into Na⁺ and Cl⁻ ions, so one formula unit gives roughly two particles and \(i \approx 2\). In practice, ion pairing in real solutions makes the effective value slightly smaller: \(i\) for NaCl is closer to 1.9, and for CaCl₂ closer to 2.6 than the ideal 3. For sugar, ethanol, and other molecular solutes that do not dissociate, \(i = 1\) exactly.
The result tells you the new boiling temperature, useful for cooking (salted water boils slightly hotter), for laboratory reflux and distillation set-ups, and for checking solution concentrations: since \(\Delta T_b\) is proportional to molality, a measured elevation can be used backwards to determine the molar mass of an unknown solute.
Ebullioscopic Constants of Common Solvents
| Solvent | \(K_b\) (°C·kg/mol) | Normal boiling point (°C) |
|---|---|---|
| Water | 0.512 | 100.0 |
| Ethanol | 1.22 | 78.4 |
| Benzene | 2.53 | 80.1 |
| Chloroform | 3.63 | 61.2 |
| Carbon tetrachloride | 5.03 | 76.8 |
Assumptions and Limitations
- The solute must be non-volatile. Volatile solutes (e.g. ethanol in water) change the vapour pressure in both directions, and the simple formula no longer applies.
- The formula is for dilute solutions. At high molality, deviations from ideality grow and \(K_b\) is no longer constant; treat results above a few mol/kg as estimates.
- Molality is used, not molarity. Molality does not change with temperature, which is why colligative properties use it. Do not enter a molarity value; if needed, convert via a molarity calculator and the solution's density.
- Use a realistic van 't Hoff factor. Ideal values (2 for NaCl, 3 for CaCl₂) overestimate the effect slightly in concentrated solutions. Experimental values are available for common salts.
- Pressure matters. The entered pure-solvent boiling point should match your actual pressure. At high altitude, water boils well below 100 °C, so enter the local value rather than the standard one.
Related Colligative Properties
Boiling point elevation is one of four colligative properties, together with freezing point depression, vapour pressure lowering, and osmotic pressure. All four scale with the concentration of dissolved particles, so measuring one lets you predict the others.
Frequently Asked Questions
How do I calculate boiling point elevation by hand if I only know the masses of solute and solvent?
First convert the mass of solute to moles by dividing by its molar mass, then divide by the mass of solvent in kilograms to get molality. Multiply molality by the solvent's Kb and by the van 't Hoff factor to get \(\Delta T_b\). For example, 58.5 g of NaCl (1 mol) in 1 kg of water gives \(\Delta T_b \approx 2 \times 0.512 \times 1 = 1.02\) °C, so the water boils at about 101 °C.
How much does salt actually raise the boiling point of cooking water?
Far less than most people expect. A typical tablespoon of salt (about 15 g, or 0.26 mol) in a litre of water gives a molality near 0.26, so the boiling point rises by only about \(0.26 \times 2 \times 0.512 \approx 0.27\) °C — barely half a degree Fahrenheit. Salt is added to water mainly for flavour, not to cook food faster.
Why are degrees Celsius and Kelvin interchangeable for Kb and the elevation?
Because \(\Delta T_b\) is a temperature difference, not an absolute temperature. One degree Celsius and one kelvin are exactly the same size interval, so a Kb quoted in K·kg/mol has the same numerical value as one in °C·kg/mol. Only when converting an absolute boiling point to Fahrenheit do you need the full formula \(T_F = T_C \times 9/5 + 32\); for the elevation alone, multiply by 9/5 only.
Can boiling point elevation ever be negative?
No — with a non-volatile solute the solution always boils higher than the pure solvent, so \(\Delta T_b\) is always positive. If adding something seems to lower the boiling point, that solute is volatile: it contributes its own vapour pressure, and the simple colligative formula does not apply. Ethanol poured into water is the classic example — the mixture actually boils below 100 °C.
Can I use this calculator to find the molar mass of an unknown solute?
Yes, by working backwards. Dissolve a weighed mass of solute in a weighed mass of solvent, measure the solution's boiling point precisely, and compute \(\Delta T_b\) as the difference from the pure solvent's boiling point. Rearranging gives \(m = \Delta T_b / (i K_b)\). Since molality equals moles of solute per kg of solvent, dividing the dissolved mass by the calculated moles yields the molar mass — a classic laboratory technique.
What are the most common mistakes when calculating boiling point elevation?
The top errors are: using molarity (moles per litre of solution) instead of molality (moles per kilogram of solvent); forgetting that dissociating solutes need an van 't Hoff factor greater than 1; using 100 °C for water at high altitude where it actually boils several degrees lower; and applying the formula to concentrated solutions where it loses accuracy. Double-check each input against these points if your result looks surprising.
How is boiling point elevation related to freezing point depression?
Both are colligative properties driven by the same vapour pressure lowering, and both use the same math structure: \(\Delta T = i \cdot K \cdot m\). For water the freezing point constant Kf is 1.86 °C·kg/mol, much larger than Kb = 0.512, so the same solution depresses freezing far more than it elevates boiling — that's why salt melts ice effectively while barely changing boiling water.