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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion03:48

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

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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...
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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...
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Passive Diffusion: Overview and Kinetics01:17

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Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
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Maxwell-Boltzmann Distribution: Problem Solving01:20

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Individual molecules in a gas move in random directions, but a gas containing numerous molecules has a predictable distribution of molecular speeds, which is known as the Maxwell-Boltzmann distribution, f(v).
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Diffusion01:12

Diffusion

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Diffusion is the passive movement of substances down their concentration gradients—requiring no expenditure of cellular energy. Substances, such as molecules or ions, diffuse from an area of high concentration to an area of low concentration in the cytosol or across membranes. Eventually, the concentration will even out, with the substance moving randomly but causing no net change in concentration. Such a state is called dynamic equilibrium, which is essential for maintaining overall...
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Diffusion01:21

Diffusion

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Diffusion is a type of passive transport. In passive transport, a substance tends to move from an area of high concentration to an area of low concentration until the concentration is equal across the space. For example, take the diffusion of substances through the air. When someone opens a perfume bottle in a room filled with people, the perfume is at its highest concentration in the bottle and is at its lowest at the edges of the room. The perfume vapor will diffuse, or spread away, from the...
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Related Experiment Video

Updated: Dec 27, 2025

The Diffusion of Passive Tracers in Laminar Shear Flow
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The Diffusion of Passive Tracers in Laminar Shear Flow

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Packets of Diffusing Particles Exhibit Universal Exponential Tails.

Eli Barkai1, Stanislav Burov1

  • 1Physics Department, Bar-Ilan University, Ramat Gan 5290002, Israel.

Physical Review Letters
|February 29, 2020
PubMed
Summary
This summary is machine-generated.

Random walkers exhibit exponential decay in their positional probability density, deviating from standard Brownian motion. This universal behavior, observed in transport in random media, is driven by step number fluctuations.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Brownian motion, typically a Gaussian process, is explained by the central limit theorem.
  • Observed deviations from Gaussian behavior include exponential decays in the positional probability density function (P(X,t)) for random walkers in various systems like glasses, cells, and bacterial suspensions.

Purpose of the Study:

  • To demonstrate the general validity of exponential decay behavior in a wide range of transport problems within random media.
  • To uncover a universal mechanism governing the decay of P(X,t) by extending theoretical frameworks.

Main Methods:

  • Extension of the large deviations approach for continuous time random walks.
  • Analysis of the impact of step number fluctuations on walker dynamics.

Main Results:

  • A universal exponential decay (with logarithmic corrections) of P(X,t) was identified for random walkers.
  • This behavior is attributed to fluctuations in the number of steps taken within a finite time.

Conclusions:

  • The study reveals a universal mechanism for exponential decay in the probability density of random walkers, extending beyond Gaussian predictions.
  • This phenomenon is broadly applicable to transport in random media and is observable even at short timescales, facilitating experimental verification.