The behavior and properties of gases can be explained by the kinetic-molecular theory which is based on several postulates (assumptions):
2. The space between the gas particles is very large compared to the size of the particles.
3. Collisions of gas particles, either with other gas particles or the wall of the container, are elastic –the total kinetic energy is not changed.
4. The average kinetic energy of the gas particles increases with an increase in temperature (K).
The gas laws discussed previously were all determined based on experimental data. According to kinetic molecular theory, gas particles are presumed to be small when compared to the distance between particles. Gases can fit a smaller or a larger container, and most of the volume is due to empty space. According to Boyle’s Law at constant temperature, if the volume of a gas is increased, the pressure is decreased or if the volume is decreased, the pressure increases. If we decrease the volume at constant temperature, the collisions between gas particles and the container walls will also increase because there is less distance for the particles to travel. The force of collisions does not change, but in a decreased volume the gas particles will hit the walls of the container more frequently resulting in a higher pressure.
The average kinetic energy of the gas particles is proportional to the temperature in Kelvin. Due to an increase in kinetic energy, the gas particles will collide with the walls of the container with a greater force. The number of collisions with a greater force increases with increasing temperature. According to Charles’s law the pressure remains constant. The container volume then, must increase in order to reduce the more forceful collisions with the walls of the container.
If the number of gas particles is increased, at constant pressure and temperature, an increase in the number of collisions with the wall of the container will also increase. The volume of the container will increase according to Avogadro’s Law.
Speed of Gas Particles
From kinetic molecular theory we know the average kinetic energy of the gas particles is proportional to the Kelvin temperature. The gas particles can move at different speeds which is why we refer to the average kinetic energy.
where \(\overline{E_k}\) is the average kinetic energy, m is the mass of the particles, and μ2 is the speed squared. The horizontal lines above \(\overline{E_k}\) and \(\overline{μ_2}\) indicate average kinetic energy and average speed. The square root of \(\overline{μ^2}\) is called the root mean square (rms) speed, μrms.
The figure below is a plot of the number of gas particles with a given speed vs the speed. The three curves differ in temperature. Notice, the curves broaden and the most probable speed (the maximum of each curve) increases with increasing temperature. The root mean square speed is greater than the most probable speed. This is called a Maxwell-Boltzmann distribution. If temperature is increased, the curve broadens and the μrms increases.
We have seen the average kinetic energy of gas particles is proportional to the temperature. At constant temperature, the average kinetic energy is inversely proportional to the molar mass of the gas particles. A heavier particle will move more slowly than a lighter particle as shown in the figure below.
The root mean square speed is:
where R = 8.314\(\frac{J}{mol⋅K}\) and molar mass, Mm is in kg/mol. The equation can be used to determine the speed of a gas particle at a given temperature.
In summary, the kinetic energy of gas particles depends on both the mass and speed of the particle. At the same temperature a heavier gas particle will move more slowly than a lighter one. At a given temperature, all gas particles have the same average kinetic energy.
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