Liquid-vapor density profiles from equilibrium limit of diffusion equation for interacting particles

Y Chen1, G L Aranovich, M D Donohue

  • 1Department of Chemical and Biomolecular Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA.

Related Concept Videos

Distillation: Vapor–Liquid Equilibria01:01

Distillation: Vapor–Liquid Equilibria

Distillation is a separation technique that takes advantage of the boiling point properties of disparate elements in a mixture. To perform distillation, we begin by heating a miscible mixture of two liquids with a significant difference in boiling points (at least 20°C). As the solution heats up and reaches the bubble point of the more volatile component, some molecules of the more volatile component transition into the gas phase and travel upward into the condenser, which is a glass tube with...
Vapor Pressure Lowering03:28

Vapor Pressure Lowering

The equilibrium vapor pressure of a liquid is the pressure exerted by its gaseous phase when vaporization and condensation are occurring at equal rates: Dissolving a nonvolatile substance in volatile liquid results in a lowering of the liquid’s vapor pressure. This phenomenon can be explained by considering the effect of added solute molecules on the liquid's vaporization and condensation processes. To vaporize, solvent molecules must be present at the surface of the solution. The presence of...
Vapor Pressure02:34

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally collide with the surface of the condensed phase, and in some cases, these collisions will result in the molecules re-entering the condensed phase. The change from the gas phase to the liquid is called condensation. When the rate of condensation becomes equal to the rate of vaporization, neither the amount of the liquid nor the amount of the vapor...
Distribution of Molecular Speeds01:27

Distribution of Molecular Speeds

The motion of molecules in a gas is random in magnitude and direction for individual molecules, but a gas of many molecules has a predictable distribution of molecular speeds. This predictable distribution of molecular speeds is known as the Maxwell-Boltzmann distribution. The distribution of molecular speeds in liquids is comparable to that of gases but not identical and can help to understand the phenomenon of the boiling and vapor pressure of a liquid. Consider that a molecule requires a...
Clausius-Clapeyron Equation02:35

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...