Question

why density of gas decreases with an increase in temperature?​

Answer 1

Because when the temperature increases the volume also increases and thus decreasing the density (density and volume are inversely proportional to each other).

When we increase the temperature the kinetic energy of the molecules also increases thus the molecules vibrate more violently, hitting the walls of the container in which the gas is contained. As the molecules are in motion they need more space to vibrate that is more volume to vibrate and thus need a bigger container or will overcome the force that is applied by the walls on them. And when the volume of the container increases the molecules have a more space to spread and this will lead to an increase in density as the molecules are further away from each other.