I don't export to jpg. I design in AI then click on the rectangle tool, click once on the artboard, enter 350 px by 280 px and once the rectangle is on the artboard I center the design within it, select the rectangle and then do OBJECT>CROP AREA>MAKE. Then use "Save for Web" rather than exporting to JPEG. That way the file is set to the correct size and you can position it within the "box" before exporting to make sure you have whitespace around it.
Depending on the version of Illustrator you're using, if you don't set a crop area, it will use the edges of the design as the boundaries. (Older versions would use the artboard specs as the boundaries.)
Probably too much info, but that's what I do. :)