Kinetic Theory of Gases The Kinetic Theory states that all matter is made up of particles that are in constant motion. For gases, there are a number of assumptions that we use to explain observed properties.

Kinetic Theory of Gases 1. The particles in a gas are considered to be small, hard spheres with an insignificant volume. * Particles are far apart. Compared to the volume the entire gas occupies, the volume of one particle is tiny.

Kinetic Theory of Gases 2. The motion of the particles in a gas is rapid, constant, and random. * Gas particles move in straight-lines unless they collide with other particles or their container. * Gas particles spread to fill their container regardless of the shape or volume. * Gas particles are independent. Their movement is not affected by other nearby particles.

Kinetic Theory of Gases 3. All collisions between particles in a gas are perfectly elastic. * Particles don’t lose energy when they collide with their container or each other. * The particles continue to move at the same speed as before the collision.

Kinetic Theory of Gases 4. The average kinetic energy (which is related to speed) is directly proportional to the absolute temperature. * On average, particles move faster at higher temperatures. * Not all particles will have the exact same speed. * Gases of different substances at the same temperature will have the same average kinetic energy. KE = 3/2RT KE = ½ mv2

Motion of Gases The motion of a gas can be considered diffusion or effusion. Diffusion is the natural tendency for gases to spread out to fill their container. For example, when someone in the classroom has the terrible idea to spray perfume, cologne, body spray, etc., the gas particles will diffuse throughout the room until we can all “enjoy” it. Effusion is the motion of gas through a small opening, like a gas leaking out of a puncture. Mathematically, at least for our purposes, there isn’t a significant difference.

Comparing Effusion Rates The rates of effusion of two gases are inversely proportional to the square roots of their molar masses. Graham’s Law can be written as follows for comparing the effusion rates of two gases.

Example Find which gas will effuse faster. Then use the following equation to solve how many times faster. Ex.) Helium vs. Nitrogen So, helium will move 2.7 times faster than nitrogen.

Calculating the rate of gases To calculate the rate (speed) you will use the following equation. Rate = **R= 8.31 J/mol•K **molar mass (Mm): must be changed to kilograms/mole Example: 12.0 g/mol = .0120 kg/mol ** Temperature (T) : must be in Kelvin By doing this, the units for our answer end up as m/s.

Example What is the speed of Neon atoms when the temperature is 35°C? rNe = rNe = 617 m/s