Your key question is very clearly stated: "Does it mean that vapor pressure 1L of water is same in a 10L container and a 1000L container?(both closed)"
The answer is yes, so long as the liquid water is not completely converted to vapor. Here’s one way to understand that. The vapor pressure is maintained by an equilibrium between the vapor and the liquid- equal rates of molecules flying off the liquid surface and reentering it. The balance of those rates depends only on the temperature and the vapor pressure near the surface, not on how much liquid or vapor there may be below or above the surface.
Perhaps a more fundamental way to see the same result would be in terms of the chemical potentials of the water in the liquid and the vapor, which must be equal in equilibrium and which again are determined by local properties, not overall sizes.
Of course, in a very big, hot container the calculated vapor pressure will exceed what could be obtained from all of the water you put in. In that case just treat the water as another gas with a fixed number of molecules.
Mike W.
(published on 10/22/2007)