Newton’s Second Law
Let’s consider first just one molecule of mass, m, and speed vx in the x direction colliding with a wall in the y-z direction:
Newton’s 2nd law: ?Fx = ?px/?t
since P = F/A, F = P*A, and using Newton’s 3rd law: force on molecule = -force on wall, so Fwall = P*A = -?px/?t .