Sometimes when I download a PDF, Chrome will open a new blank tab, how do I prevent this?
The only way to stop the blank page is to use Right Click and Save Link As.
Since Chrome does not natively support an embedded PDF reader it assumes the PDF link is trying to open another page. It then let's the file system take over allowing your PDF reader to open the actual file. It doesn't have any facility to close the new tab that opened as it assumes it is being used for displaying the file.
However there is good news. You can use the Docs Preview Extension to preview all these documents in Chrome and it will stop this behaviour since the files will open in Chrome.
Newer versions of Chrome does support embedded PDF viewing so a lot of this answer is obsolete
Okay, I got it to do this finally.
(Steps 1 and 2 might be redundant, but this is what I did and it worked.)
Hope that helps.