Boiling Point Formula & How to Calculate It

This calculator finds the boiling point of a liquid at a given atmospheric pressure using the Clausius–Clapeyron equation. You enter the normal boiling point, the enthalpy of vaporization, and the pressure of interest, and you get the new boiling point in degrees Celsius. The same formula also works in reverse to find the pressure at a known temperature.

Formula

The Clausius–Clapeyron equation relates the vapor pressure of a liquid to its temperature. In its two-point form, it lets you calculate the boiling point at a new pressure when you know the boiling point at one reference pressure and the enthalpy of vaporization:

ln(P₂ / P�) = −(ΔH_vap / R) × (1/T₂ − 1/T�)

Where:

• Pâ‚� = reference pressure (usually 1 atm), in atm
• Pâ‚‚ = new pressure, in atm
• Tâ‚� = boiling point at Pâ‚�, in kelvin (K)
• Tâ‚‚ = boiling point at Pâ‚‚, in kelvin (K)
• ΔH_vap = molar enthalpy of vaporization, in J/mol (the calculator takes kJ/mol and converts internally)
• R = universal gas constant = 8.314 J/(mol·K)

To solve for Tâ‚‚, rearrange:

T₂ = 1 / [ 1/T� − (R × ln(P₂/P�)) / ΔH_vap ]

The calculator above uses this exact form, with P� set to 1 atm and T� as the normal boiling point you enter. The result is converted back to Celsius for display.

Worked Example

Using the default values from the calculator (water):

• Normal boiling point Tâ‚� = 100 °C = 373.15 K
• ΔH_vap = 40.65 kJ/mol = 40,650 J/mol
• New pressure Pâ‚‚ = 0.5 atm, Pâ‚� = 1 atm

1. Compute ln(P₂/P�) = ln(0.5) = −0.6931
2. Compute (R × ln(P₂/P�)) / ΔH_vap = (8.314 × −0.6931) / 40,650 = −0.0001418 K�¹
3. Add to 1/T�: 1/373.15 = 0.0026799 K�¹; 0.0026799 + (−0.0001418) = 0.0025381 K�¹
4. Take the reciprocal: Tâ‚‚ = 1 / 0.0025381 = 393.99 K
5. Convert to Celsius: 393.99 − 273.15 = 120.84 °C

So water boils at about 120.8 °C when the pressure is 0.5 atm. The calculator shows 120.84 °C, matching this result.

When to Use This Formula

Use the Clausius–Clapeyron equation whenever you need a boiling point at a pressure different from standard atmospheric pressure. Common situations include:

• High-altitude cooking, where lower pressure lowers the boiling point of water
• Laboratory distillations under reduced pressure to avoid decomposing heat-sensitive compounds
• Engineering design of pressure vessels, steam systems, and refrigeration cycles
• Estimating boiling points of solvents when vacuum is applied

The formula assumes the enthalpy of vaporization is constant over the temperature range of interest. This is a good approximation for small pressure changes (within about 0.5–2 atm) but becomes less accurate for very large deviations.

How to Read the Result

The output is the temperature at which the liquid’s vapor pressure equals the surrounding pressure. At that point, bubbles form throughout the liquid, not just at the surface. A lower pressure means a lower boiling point; a higher pressure means a higher boiling point.

For water, the normal boiling point is 100 °C at 1 atm. At the top of Mount Everest (about 0.33 atm), the formula gives roughly 71 °C. In a pressure cooker at 2 atm, water boils near 121 °C, which is why food cooks faster.

Remember that the result is a thermodynamic estimate. Real liquids with impurities, dissolved gases, or strong intermolecular forces may deviate slightly. Also, the enthalpy of vaporization changes with temperature; for precise work, use tabulated values at the actual temperature.

Common Mistakes and Pitfalls

• Unit mix-ups: The enthalpy of vaporization must be in J/mol when used with R = 8.314 J/(mol·K). If you use kJ/mol, the result will be off by a factor of 1000. The calculator handles this conversion for you.
• Forgetting to convert Celsius to kelvin: The formula requires absolute temperatures. Adding 273.15 is essential; forgetting it gives a wildly wrong answer.
• Using the wrong pressure units: The equation uses the ratio Pâ‚‚/Pâ‚�, so any consistent pressure unit works, but the reference pressure must match the normal boiling point you entered. If you enter a normal boiling point at 1 atm, Pâ‚� must be 1 atm, not 1 bar (1 bar ≈ 0.987 atm).
• Assuming linearity: Boiling point vs. pressure is not linear. Doubling the pressure does not halve the boiling point; the relationship is logarithmic.
• Ignoring the sign: The natural log of a number less than 1 is negative, which raises the boiling point when pressure increases. Keep track of signs carefully in manual calculations.

Limitations of the Formula

The Clausius–Clapeyron equation is an approximation. It assumes the vapor behaves as an ideal gas and that the liquid’s molar volume is negligible compared to the vapor’s. These assumptions hold well at pressures well below the critical point and for non-polar or slightly polar liquids.

For highly accurate results over wide pressure ranges, use the Antoine equation, which is an empirical correlation with three constants specific to each substance. The Antoine equation is more accurate because it accounts for the temperature dependence of ΔH_vap implicitly.

Another limitation: the formula requires the enthalpy of vaporization at the reference temperature. For many substances, this value is tabulated at the normal boiling point, which is exactly what you need. If you only have ΔH_vap at 25 °C, the result will be less accurate.

Finally, the formula only applies to pure substances. Mixtures, azeotropes, and solutions with non-volatile solutes behave differently. For example, salt water boils slightly higher than pure water at the same pressure because the solute lowers the vapor pressure.

Frequently Asked Questions

What is the normal boiling point?

The normal boiling point is the temperature at which a liquid boils at exactly 1 atmosphere of pressure (101.325 kPa). For water, it is 100 °C. The term “normal� distinguishes it from boiling points at other pressures.

Why does water boil at a lower temperature on a mountain?

At higher altitudes, atmospheric pressure is lower. A liquid boils when its vapor pressure equals the surrounding pressure. Lower surrounding pressure means the liquid reaches that equality at a lower temperature. At 2,000 meters elevation, water boils at about 93 °C.

Can I use this formula for any liquid?

Yes, as long as you know the normal boiling point and the enthalpy of vaporization. The formula is general. For example, ethanol has a normal boiling point of 78.37 °C and ΔH_vap of 38.6 kJ/mol. Enter those values to find its boiling point at any pressure.

What is the difference between boiling point and vapor pressure?

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. Boiling point is the temperature at which that vapor pressure equals the external pressure. They are two sides of the same relationship: higher vapor pressure at a fixed temperature means a lower boiling point at a fixed pressure.

How accurate is the Clausius–Clapeyron equation?

For pressure changes within a factor of about 2–3 from the reference, the error is typically less than 1–2 °C for many common liquids. For larger pressure swings, the error grows. The Antoine equation, which uses three empirical constants, is more accurate over a wider range but requires those constants for each substance.

Does adding salt change the boiling point?

Yes. Dissolving a non-volatile solute like salt raises the boiling point of a solution compared to the pure solvent. This is called boiling point elevation. The effect is small for typical cooking amounts—about 0.5 °C for a 2% salt solution—and depends on the number of dissolved particles, not their identity.

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in t | Normal boiling point | °C | 100 | 0
in h | Enthalpy of vaporization | kJ/mol | 40.65 | 0
in p | Pressure | atm | 0.5 | 0
out bp | Boiling point | °C | (1 / (1 / (t + 273.15) - (8.314 * ln(p) / (h * 1000)))) - 273.15 | 2