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If there is a gas in a container with pressue P, then it will exert a force on the walls of the container. By Newton's third law, there should be a reactionary force where the container exerts an equal but opposite force on the gas. Does this force exists, and if so, how does it manifest? What does a force exerted on a gas by walls of a container even look like?

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You are talking about the "normal force" ( https://en.wikipedia.org/wiki/Normal_force ). The gas pushes against the container and the contai9ner pushes against the gas because two masses cannot occupy the same space. This is similar to you standing on the floor, you do not fall into the floor because of the normal forces between your shoes and the floor.

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The force does exist, and it manifests itself by stopping the molecules, which are in rapid translational motion, from escaping out of the container. When they try to escape (that is when they hit the container wall) the wall knocks them back in. The very fact that the gas stays in the container demonstrates the existence of the force.

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