I have a new computer, now I am having trouble using iTunes with my iPhone.

So my old PC died, now I have a MacBook Pro.  I downloaded the latest iTunes to it and when I connect my iPhone to it, it does recognize my phone.  However I purchased and app and I cannot get that app to sync to my phone.  Also is there a way to get the apps currently on my phone to sync with my new itunes library.  I would appreciate any help, Thanks!

You need to Authorise your New Mac...
Open iTunes
From the Store menu, choose Authorize This Computer. (In earlier versions of iTunes, access this option from the Advanced menu).
When prompted, enter your Apple ID and password, then click Authorize.
From Here
About authorization and deauthorization
See Here for...
Transfer Purchases  =  iTunes > File > Transfer Purchases
http://support.apple.com/kb/HT1848
Download Past Purchases
http://support.apple.com/kb/HT2519
Log into iTunes using the account the Purchase was made with... Click on Buy... and a notice will come up saying you already have it... do you wish to download it again... Click Yes...
All None Purchased music needs to be Copied from your Old Computer or its Backup to your New Mac...

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