How does gas density affect pressure?

According to the kinetic theory of gases, gas pressure is directly related to density and temperature. In an ideal gas model, pressure is defined by the frequency and force of molecular collisions against the walls of a container. Because pressure is proportional to the number of molecules per unit volume ($N/V$), increasing the density of a gas—thereby increasing the number of molecules in a given space—results in a higher rate of collisions with the container walls, which increases the pressure.12

While the ideal gas equation of state remains valid as density decreases, it eventually fails at high densities. At these higher levels, the simple assumptions of the kinetic theory no longer hold because molecules begin to exert forces on one another, which alters the rate of collisions with the container walls and causes deviations from ideal behavior.21