Lesson 2 · 25 min

Vapour pressure and boiling

Molecules leave and return across every liquid surface. Vapour pressure depends only on temperature; when it catches up with the outside pressure, the liquid boils — which is why water boils at 88 °C in Lhasa.

In this lesson

Understand vapour pressure as a dynamic balance of evaporation and condensation that depends only on temperature
Explain boiling as vapour pressure reaching the outside pressure, and predict the effect of altitude and pressure cookers
Compare the volatility of liquids through their intermolecular forces
Use the Clausius–Clapeyron equation to estimate a boiling point at another pressure, and name its approximations

In Lhasa, 3650 m up on the Tibetan plateau, a pot of water rolls into a boil below 88 °C; noodles refuse to cook and every kitchen owns a pressure cooker. At sea level, a glass of water left on the table disappears “by itself” within days without ever reaching 100 °C. Both stories are about one quantity: the vapour pressure of the liquid.

Predict first

Some water at 25 °C is put into a sealed, evacuated flask and kept at 25 °C. What happens to the pressure inside?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

Stays at zero — the water is not boiling Rises to about 3.2 kPa and then stays there, as evaporation and condensation balance Keeps rising until all the water has evaporated Rises to 101 kPa (1 atm)

Vapour pressure depends on temperature alone

Raise the temperature and the fraction of molecules energetic enough to escape grows exponentially, so vapour pressure climbs steeply: water is at 3.17 kPa at 25 °C, 19.9 kPa at 60 °C and about 101 kPa at 100 °C.

Different liquids differ even more. At 25 °C diethyl ether has a vapour pressure of about 71 kPa, acetone about 31 kPa, ethanol 7.9 kPa and water only 3.2 kPa. The stronger the intermolecular forces, the harder it is to escape and the lower the vapour pressure — ethanol and water hydrogen-bond, ether and acetone do not. Liquids with high vapour pressures are volatile: you smell them as soon as the bottle is opened.

Boiling: vapour pressure catches up with the outside

Evaporation happens only at the surface; boiling is when bubbles form inside the liquid. A bubble can exist and grow only if the vapour pressure inside it can hold back the pressure outside. So a liquid boils when its vapour pressure equals the external pressure. The boiling point at 1 atm (101.325 kPa) is the normal boiling point.

Change the outside pressure and the boiling point moves: the air pressure in Lhasa is about 64.5 kPa, so water boils near 88 °C; at the summit of Everest, about 31 kPa, it boils at 70 °C. Conversely, a pressure cooker raises the pressure inside to about 2 atm and water does not boil until about 120 °C — the pot is hotter and food cooks faster.

\ln\frac{p_2}{p_1} = -\frac{\Delta_\mathrm{vap}H}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)

The Clausius–Clapeyron equation: ln p against 1/T is a straight line of slope −ΔvapH/R.

$p_1, T_1$: a known point, e.g. the normal boiling point (101.325 kPa)
$p_2, T_2$: the point you want (T in kelvin)
$\Delta_\mathrm{vap}H$: molar enthalpy of vaporization, 40.7 kJ/mol for water
$R$: gas constant 8.314 J mol⁻¹ K⁻¹

Measured vapour-pressure curves · outside pressure

Vapour pressure and boiling point

Liquid to analyse Probe temperature · 25 °C

$\ln p = -\frac{\Delta_\text{vap}H}{R}\cdot\frac{1}{T} + \text{const}$

Measured · Water
Clausius–Clapeyron line (ΔH at the boiling point)

Measured · 25 °C: 3.17 kPa
Straight-line prediction: 3.76 kPa (+19 %)
ΔvapH from the local slope: 44.1 kJ/mol
Calorimetric ΔvapH (normal bp): 40.65 kJ/mol

Switch to the Clausius–Clapeyron plot: each liquid is almost a straight line. The dashed line is drawn from the normal boiling point and ΔvapH — near 25 °C it overshoots the data by about 18 %, because water’s enthalpy of vaporization is larger at low temperature (about 44 kJ/mol at 25 °C).

Worked example

The boiling point on Everest

In the standard atmosphere the pressure at the top of Everest (8849 m) is about 31.4 kPa. Estimate the boiling point of water there with the Clausius–Clapeyron equation ( $\Delta_\mathrm{vap}H = 40.7$ kJ/mol).

Concept check

Which of these liquids has the highest vapour pressure at 25 °C?

Water Ethanol Acetone Toluene

Try the calculation

Ethanol boils at 78.3 °C under 1 atm, with $\Delta_\mathrm{vap}H = 38.6$ kJ/mol. Use the Clausius–Clapeyron equation to estimate its boiling point (°C) at 50.0 kPa.

Key takeaways

Vapour pressure is the pressure of the vapour when evaporation and condensation balance; it depends only on the liquid and the temperature.
The stronger the intermolecular forces, the lower the vapour pressure; hydrogen-bonded liquids are markedly less volatile.
A liquid boils when its vapour pressure equals the outside pressure: lower on mountains, higher in a pressure cooker.
The Clausius–Clapeyron equation, ln p ∝ −ΔvapH/(RT), turns the vapour-pressure curve into a line and lets one boiling point predict another.

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Data and references

W. Wagner et al., “The IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam”, J. Eng. Gas Turbines Power 122, 150 (2000).
NIST Chemistry WebBook, SRD 69: Antoine parameters for ethanol (Kretschmer & Wiebe 1949; Ambrose & Sprake 1970), acetone (Ambrose et al. 1974), diethyl ether (Taylor & Smith 1922) and toluene (Williamham et al. 1945).
W. M. Haynes (ed.), CRC Handbook of Chemistry and Physics, 97th ed. (2016): enthalpies of vaporization; vapour pressure of water.
ISO 2533:1975, Standard Atmosphere (pressure–altitude relation).