In typical scenarios, especially when discussing gases in everyday sized containers, the effect of gravity on the distribution of pressure within the gas is negligible. This is because gases have low density and high molecular motion which causes the gas molecules to distribute themselves relatively evenly in the available volume. Thus, any influence of gravity is generally not apparent, making the pressure essentially uniform throughout the gas in the container. The main factor influencing the pressure exerted by a gas is described by the ideal gas law, $$PV = nRT$$, where P is the pressure, V is the volume, n is the number of moles of gas, R is the universal gas constant, and T is the temperature in Kelvin.

This law implies that the pressure is dependent on the temperature, volume, and number of gas molecules but does not include gravity as a factor. Only in very tall containers, or in cases dealing with significantly dense gases under strong gravitational fields (such as on massive planets), does the effect of gravity on the distribution of a gas in a container become significant enough to create a gradient in pressure from top to bottom. For most practical purposes and common situations, gravity's effect on gas pressure in a container can be ignored.

Therefore, the statement is FALSE under typical conditions involving everyday applications and container sizes.