To query the application serial number, use the APN field code.  

Please note that a US patent's application serial number is in the form 12/012345 and is the number assigned to the application shortly after it is received by the USPTO.  In this example, 12 is the series code (containing one million applications) and the six digits following the slash are the number that identifies the application.  If you instead wanted to search for the Application Publication Number, use the DN or PN field codes.  Remember that the application publication numbers are in the form of US20100047408 A1, for example.

Note that APNs are not universally unique since a patent and its published application shares the same APN.