# Pressure exerted by a gas and the ideal gas equation

While determining the pressure exerted by any gas at a temperature why do we not consider the surface area of the container in which it is kept? Pressure depends on the force exerted by the gas on the container divided by the total surface area of the container.
We say that :
P=nRT/V,
where, n is the no. of moles,
R the universal gas constant,
T the temperature and
V the volume
Why doesn't pressure also depend on the surface area of the container taken?

• Why (and how) do you think we should "include the surface area"? – ACuriousMind May 28 '16 at 15:47
• pressure = force/area – Osheen Sachdev May 28 '16 at 15:49
• A better definition of pressure is rate of momentum flow across an oriented surface. The surface here is a mathematical surface, a 2d bounded area. With this the walls of the container play no role. For example, we talk about atmospheric pressure without reference to walls. – garyp May 28 '16 at 16:13
• Something to think about: the units of pressure are also the same as energy per unit volume... – user10851 May 30 '16 at 3:16
• +its a valid question and does not deserve downvotes – Lapmid Aug 5 '18 at 8:33

Why do we not include the surface area of the container in the formula?

Because it is not needed.

Pressure $p$ is force $F$ per unit of surface area $A$:

$$p=\frac{F}{A}$$

The pressure a gas exerts on the walls of a container is the collective force collisions of the gas molecules exert on the container walls, per unit of surface area.

If we look at one side with surface area $A$ of a container (containing the gas):

If the pressure inside the container is $p$, then the gas will exert a force $F$ on that side of the container acc.:

$$F=pA$$

• okay...Do you mean to say that the pressure is fixed but the force depends on the container taken? – Osheen Sachdev May 28 '16 at 16:27

Pressure is a measurement of force/unit area. It doesn't measure the total force exerted over the entirety of the surface, but the force exerted on one "unit area" of the surface. One unit of area depends on the measurement system you're using, but by doing that surface area can be disregarded.

The ideal gas law you mention is valid for any control volume.

This means for any (stationary) control volume the pressure inside it, its volume, the temperature inside it and the number of particles (or moles or density) are related through the ideal gas law.

• This doesn't actually address the question about why the surface area of the container is not a factor in the ideal gas law. – Jon Custer Oct 5 '16 at 13:16
• @Jon Custer: I suppose you're right. My intention was to clear up the OP's understanding of the ideal gas law. It appears the OP considers the gas law for a gas in a container whereas I tried to indicate that, using the control volume term, the law applies for 'any quantity of gas', whether it is in a container or not. The temperature and pressure are intrinsic to the gas irrespective of an imaginary bounding surface. I see why the original question was down-voted :) – TheCat Oct 6 '16 at 18:25

The pressure exerted by a gas is result of the continuous bombarding of collision of a gas molecules against the wall of container or it is equal to the total momentum imparted per second per unit area to the walls of the container by the bombarding molecules

I was taking force exerted by the gas molecules on the walls of the container to be constant. After studying thermodynamics this got cleared. The total force exerted by the gas on the container changes with change in surface area but the pressure of the gas remains constant.