If you're going direct from Salzburg to Vienna Airport, without stopping off in Vienna itself, then don't stay on the train all the way to Wien Westbahnhof. Instead, get off at Wien Hütteldorf, then take a local train (S3) to Wien Rennweg, then another local train (S7) to the airport.

Alternatively if you want to spend time in Vienna before heading out to the airport then the quickest way to get to the airport is the dedicated airport train (CAT) - it takes all of 15 minutes but is quite expensive. I took a normal local train to the airport when I was there earlier this year - from memory it took about half an hour. Most of the cost of the journey was included in the day pass I had bought that day, I just had to pay a small supplement (1 Euro or thereabouts) to cover the last few stops.