MaxwellBoltzmann distribution from "summary" of Physical Chemistry by Robert G. Mortimer
The Maxwell-Boltzmann distribution describes the distribution of speeds of gas molecules at a given temperature. This distribution is essential for understanding the behavior of gases and is based on the kinetic theory of gases. According to this theory, gas molecules are in constant motion, colliding with each other and the walls of the container. The distribution of speeds of gas molecules is not uniform, but rather follows a specific pattern. At any given temperature, most molecules have speeds near the average speed, with fewer molecules having speeds significantly higher or lower than the average. The distribution is described by a curve that peaks at the most probable speed and decreases as speeds deviate from this value. The shape of the Maxwell-Boltzmann distribution curve depends on the temperature of the gas. At higher temperatures, the curve is broader, indicating a wider range of speeds among the gas molecules. Conversely, at lower temperatures, the curve is narrower, indicating a more narrow range of speeds. The area under the Maxwell-Boltzmann distribution curve represents the total number of gas molecules in the sample. The curve can be used to calculate the fraction of molecules with speeds within a certain range, providing valuable information about the behavior of the gas. The Maxwell-Boltzmann distribution is a fundamental concept in physical chemistry and is used in various applications, such as calculating reaction rates and predicting the behavior of gases under different conditions. By understanding this distribution, scientists can make accurate predictions about the behavior of gases and develop more efficient processes in various fields.
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