Antoine Equation & Vapor Pressure: 50+ Industrial Compounds Reference Guide

1. Introduction: The Importance of Vapor Pressure in Process Engineering

Saturated vapor pressure ($P^{sat}$) is one of the most fundamental thermodynamic properties in chemical process design. It governs phase equilibria across all unit operations involving liquid-vapor interfaces???including continuous fractionating distillation columns, flash drums, vacuum evaporators, VOC emission scrubbers, and atmospheric storage tank breathing calculations per API 2000.

When modeling multicomponent separation in commercial process simulators (such as Aspen Plus, HYSYS, or PRO/II), ideal Vapor-Liquid Equilibrium (VLE) is evaluated via Raoult's Law:

$$y_i P = x_i P_i^{sat}(T)$$

For non-ideal systems, modified Raoult's Law introduces liquid activity coefficients ($\gamma_i$) and vapor fugacity coefficients ($\phi_i$):

$$y_i \phi_i P = x_i \gamma_i P_i^{sat}(T) \exp\left[ \frac{V_i^L (P - P_i^{sat})}{RT} \right]$$

In both rigorous and shortcut engineering workflows, an accurate, fast, and continuous mathematical function for pure component vapor pressure as a function of temperature ($P^{sat} = f(T)$) is essential. The Antoine Equation remains the global standard for engineering design across moderate pressure and temperature regimes.

2. The Antoine Equation: Theory & Mathematical Formulation

2.1 Standard 3-Parameter Form

Introduced by French engineer Louis Charles Antoine in 1888, the Antoine equation is a semi-empirical extension of the fundamental Clausius-Clapeyron equation:

$$\frac{d \ln P^{sat}}{dT} = \frac{\Delta H_{vap}}{R T^2}$$

Assuming that the latent heat of vaporization ($\Delta H_{vap}$) varies linearly with temperature, integration yields the standard 3-parameter Antoine form:

$$\log_{10}(P^{sat}) = A - \frac{B}{T + C} \quad \text{or} \quad \ln(P^{sat}) = A - \frac{B}{T + C}$$

2.2 Converting Units of Antoine Parameters

Because historical literature and software packages utilize varying base units ($\log_{10}$ vs. $\ln$, and bar vs. kPa vs. mmHg vs. Pa), process engineers must exercise extreme caution when compiling parameter sets. The table below summarizes conversion factors:

$$\log_{10}(P_{ \text{bar}}) = \log_{10}(P_{ \text{mmHg}}) - \log_{10}(750.062) = (A - 2.8751) - \frac{B}{T + C}$$ $$\ln(P_{ \text{kPa}}) = \ln(10) \cdot \left[ A - \frac{B}{T + C} \right] - \ln(7.50062)$$

2.3 Calculating the Normal Boiling Point ($T_b$)

The normal boiling point is defined as the temperature at which the saturated vapor pressure equals standard atmospheric pressure ($P^{sat} = 760 \text{ mmHg} = 1.01325 \text{ bar a}$). Rearranging the Antoine equation directly yields:

$$760 = 10^{A - \frac{B}{T_b + C}} \implies \log_{10}(760) = 2.88081 = A - \frac{B}{T_b + C}$$ $$T_b = \frac{B}{A - 2.88081} - C \quad (^\circ \text{C})$$

This closed-form analytical expression allows instantaneous flash boiling and initial bubble point checks without iterative root-finding.

3. Master Reference Table: Antoine Constants for 50+ Industrial Compounds

The table below provides verified Antoine coefficients ($A, B, C$ for $\log_{10}(P \text{ [mmHg]}) = A - B / (T \text{ [}^\circ \text{C]} + C)$), experimental validity ranges ($T_{min}$ to $T_{max}$), and normal boiling points compiled from NIST Chemistry WebBook and DIPPR evaluations.

4. Step-by-Step Worked Calculation Example

Scenario: A chemical engineer is designing an overhead condenser on an atmospheric distillation column separating a mixture of Benzene and Toluene. The condenser operates at an overhead vapor temperature of $T = 75.0^\circ \text{C}$. Determine the pure-component saturated vapor pressures of Benzene and Toluene, and calculate the ideal relative volatility ($\alpha_{B/T}$) at this operating condition.

Step 1: Retrieve Antoine Constants

• Benzene ($C_6H_6$): $A = 6.90565$, $B = 1211.033$, $C = 220.790$ (Valid: 8 to 103??C)
• Toluene ($C_7H_8$): $A = 6.95464$, $B = 1344.800$, $C = 219.482$ (Valid: 35 to 136??C)

Since $T = 75.0^\circ \text{C}$, both components reside strictly within their experimental validity windows.

Step 2: Calculate Benzene Saturated Vapor Pressure ($P_B^{sat}$)

$$\log_{10}(P_B^{sat}) = 6.90565 - \frac{1211.033}{75.0 + 220.790} = 6.90565 - \frac{1211.033}{295.790}$$ $$\log_{10}(P_B^{sat}) = 6.90565 - 4.09423 = 2.81142$$ $$P_B^{sat} = 10^{2.81142} = 647.77 \text{ mmHg} = \frac{647.77}{750.062} = 0.8636 \text{ bar a} = 86.36 \text{ kPa}$$

Step 3: Calculate Toluene Saturated Vapor Pressure ($P_T^{sat}$)

$$\log_{10}(P_T^{sat}) = 6.95464 - \frac{1344.800}{75.0 + 219.482} = 6.95464 - \frac{1344.800}{294.482}$$ $$\log_{10}(P_T^{sat}) = 6.95464 - 4.56666 = 2.38798$$ $$P_T^{sat} = 10^{2.38798} = 244.33 \text{ mmHg} = \frac{244.33}{750.062} = 0.3257 \text{ bar a} = 32.57 \text{ kPa}$$

Step 4: Calculate Relative Volatility ($\alpha_{B/T}$)

$$\alpha_{B/T} = \frac{P_B^{sat}}{P_T^{sat}} = \frac{647.77 \text{ mmHg}}{244.33 \text{ mmHg}} = 2.65$$

Conclusion: With a relative volatility of $\alpha = 2.65 > 1.2$, separation via conventional fractional distillation is highly feasible, requiring moderate stage counts and standard reflux ratios per Fenske-Underwood-Gilliland shortcut sizing.

5. Critical Limitations & Industrial Design Pitfalls