Vapor Pressure & the Antoine Equation

Use a standard Antoine correlation to compute saturation pressure P* of a pure liquid at a given temperature.

Material & Energy BalancesChemical Engineering Year 1Free preview

⏱️ About 14 min

At a fixed temperature, a pure liquid has a very specific equilibrium vapor pressure. How do you compute it quickly and safely?

💡

The big idea: For many pure liquids, saturation vapor pressure P*(T) is well represented over a temperature range by the Antoine equation.

🎯 By the end, you'll be able to

Define vapor pressure P* as an equilibrium saturation property of a pure liquid
Use the Antoine equation in the standard log10 form with consistent units
Compute P* for water at a specified temperature with verified arithmetic
Avoid common unit/range pitfalls when using tabulated Antoine constants

📎 Helpful to know first

PVT Applications in Process Calculations

What “Vapor Pressure” Means

The vapor pressure P* of a pure liquid at temperature T is the equilibrium pressure of the vapor above that liquid when liquid and vapor coexist.

It is also called the saturation pressure. If the surrounding pressure equals P*, the liquid is at its boiling point for that pressure.

\[ P = P^*(T)\quad\text{(pure liquid–vapor equilibrium)} \]

At VLE for a pure substance, the pressure is fixed by the saturation curve P*(T).

Antoine Equation (log10 form used in standard tables)

A widely used correlation for many liquids is the Antoine equation:

log₁₀(P*/mmHg) = A − B/(C + T[°C])

Antoine constants (A, B, C) are tabulated for specific unit conventions and temperature ranges (commonly in appendices of thermodynamics texts).

\[ \log_{10}\!\left(\frac{P^*}{\text{mmHg}}\right)=A-\frac{B}{C+T\,[^\circ\text{C}]} \]

Standard Antoine form (P* in mmHg, T in °C) consistent with many textbook appendix tables.

⚠️ Pitfall: Antoine constants are range- and unit-specific

Antoine constants must match the exact equation form and units. Here we use log₁₀(P*/mmHg) with T in °C. Also, each triplet is only valid over a stated temperature range (often ~1–100°C for the water constants used below).

📝 Worked example: Compute the vapor pressure of water at 50.0°C using the standard Antoine constants valid roughly over 1–100°C: A = 8.07131, B = 1730.63, C = 233.426 in the form log10(P*/mmHg) = A − B/(C + T[°C]).

Given: T = 50.0°C, A = 8.07131, B = 1730.63, C = 233.426
Compute denominator: C + T = 233.426 + 50.0 = 283.426
Compute the fraction: B/(C+T) = 1730.63 / 283.426 = 6.10611
Compute log10(P*/mmHg):
log10(P*/mmHg) = A − B/(C+T) = 8.07131 − 6.10611 = 1.96520
Raise 10 to both sides to get P*:
P*/mmHg = 10^(1.96520) = 92.30 mmHg

✓ P*(50.0°C) = 92.30 mmHg (using Antoine A=8.07131, B=1730.63, C=233.426)

✏️ Practice: Using the same Antoine constants for water (A = 8.07131, B = 1730.63, C = 233.426), compute P* at 60.0°C. Give the answer in mmHg.

mmHg

Solution

C + T = 233.426 + 60.0 = 293.426
B/(C+T) = 1730.63 / 293.426 = 5.89801
log10(P*/mmHg) = 8.07131 − 5.89801 = 2.17330
P*/mmHg = 10^(2.17330) = 149.04 mmHg

Check your understanding

1. Vapor pressure P* of a pure liquid at temperature T is best described as:

P*(T) is the saturation (equilibrium) pressure for the pure substance at temperature T.

2. In the Antoine equation log10(P*/mmHg) = A − B/(C + T[°C]), a common mistake is:

The equation uses log10; using ln (or mixing bases) gives incorrect pressures.

✅ Key takeaways

Vapor pressure P*(T) is the equilibrium saturation pressure of a pure liquid at temperature T
Antoine equation (common textbook form): log10(P*/mmHg) = A − B/(C + T[°C])
Always use consistent units and stay within the tabulated temperature range
You can compute P* by evaluating the log10 expression, then exponentiating with base 10

➡️ Antoine is a convenient correlation. Next, we connect vapor pressure to enthalpy of vaporization via the Clausius-Clapeyron equation and interpret the result on a P-T phase diagram.

Want to test yourself on this? Try the Chemical Aptitude test →