Work is done or received by several entities here:
- The expanding gas
- The external gas at 0.2 atm
- And something else!
It needs something else, like an alternator, a machine-tool... to balance the forces. Imagine that the expansion operates against a piston (after all, thermodynamics was invented for that purpose):
- pressure from 1 atm down to unknown at the inner face
- pressure 0.2 atm at the outer face
- some additional force on the piston must balance the other two! Have a connecting rod and a crankshaft a the piston, and a use at the shaft.
Now, the initial question isn't perfectly clear, but I'd rather understand that the "work" is the one available at the shaft, that is, the work provided by the gas minus the work absorbed by the atmosphere.
Both are accessible through formulas written as function of the proper variable (is it P V, T, U, H, Q, W...?). Write the difference, solve (probably not an algebraic solution) for this variable to get 200J, and convert this solution to a pressure.
In case you get two solutions, choose the best. I'd stop the expansion as soon as the desired work is obtained.