# 27: The Kinetic Theory of Gases

- Page ID
- 11823

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- 27.1: The Average Translational Kinetic Energy of a Gas
- The gas laws were derived from empirical observations. Connecting these laws to fundamental properties of gas particles is subject of great interest. The kinetic molecular theory is one such approach. In its modern form, the kinetic molecular theory of gases is based on five basic postulates. This section will describe the development of the ideal gas law using these five postulates.

- 27.2: The Gaussian Distribution of One Component of the Molecular Velocity
- The distribution function for one component of the molecular velocity is a Gaussian curve. Because the molecule can move in both a positive or negative direction along an axis, the range of the distribution function is negative infinity to positive infinity.

- 27.3: The Distribution of Molecular Speeds is Given by the Maxwell-Boltzmann Distribution
- If we were to plot the number of molecules whose velocities fall within a series of narrow ranges, we would obtain a slightly asymmetric curve known as a velocity distribution. The peak of this curve would correspond to the most probable velocity. This velocity distribution curve is known as the Maxwell-Boltzmann distribution, but is frequently referred to only by Boltzmann's name.

- 27.4: The Frequency of Collisions with a Wall
- The frequency with which a gas collides with a wall is dependent upon the number density (the number of molecules per volume) and the average molecular speed.

- 27.5: The Maxwell-Boltzmann Distribution Has Been Verified Experimentally
- The Maxwell-Boltzman distruction distribution has been verified experimentally by a device called a velocity selector, which is essentially a series of spinning wheels with a hole through which the gas is effused. This ensures that only gas particles with a certain velocity will pass through all the holes as the wheels are spun at various rates. Thus it is possible to count the number of particles with various velocities and show that, indeed they do satisfy the Maxwell-Boltzmann distribution.

- 27.6: Mean Free Path
- The mean free path is the distance a particle will travel, on average, before experiencing a collision event. This is defined as the product of the speed of a particle and the time between collisions.

- 27.7: Rates of Gas-Phase Chemical Reactions
- The rate law of a gas-phase reaction can be derived using collision theory. The rate of the reaction depends on the rate of collisions with sufficient kinetic energy that exceeds the activation energy.