The kinetic molecular theory can be used to describe the relationship between temperature and kinetic energy. In this relationship temperature is directly proportional to kinetic energy. If we increase the temperature of a gas then the particles start to move faster. The kinetic energy increases. (See the animation below.)
The pressure of a gas is caused by collisions between the gas particles and the container walls. Every time a gas particle hits the wall, it exerts a force on the wall. An increase in the number of gas particles in the container increases the frequency of collisions with the walls and increases the pressure of the gas.
Diffusion is the mixing of gases. The rate of diffusion is the speed of which the gases mix. Diffusion results from the random movement of gas particles. Increasing temperatures increase the rate of diffusion. Small molecules will diffuse faster than larger molecules.
Watch the video about diffusion below.
Source: Kinetic Molecular Theory2, trackerchem, YouTube