There is no way in the UI or via an out of the box PowerShell command to change the application pool used by a web application. Don't bother trying to create one manually in IIS and setting the web app to use this, it won't work because the application pool does not exist as a known object in the configuration database and you'll get 500 Internal errors when you try to open the site in the browser.

 

You'll first need to create a new application pool using the SharePoint object model (which in turn creates the app pool in IIS) using either PowerShell or compiled code.

 

Compiled code example: http://code.msdn.microsoft.com/Create-a-new-application-e951983d

 

then you can change the web app to use the new app pool...

 

PowerShell example: http://gallery.technet.microsoft.com/scriptcenter/Change-SharePoint-Web-64b872d7

Compiled code example: http://code.msdn.microsoft.com/Create-a-new-application-e951983d

 

Finally you can delete any unrequired application pools:

 

PowerShell example: http://gallery.technet.microsoft.com/scriptcenter/Delete-a-SP-WebApplication-9a7d82e4