When installing a separate 32 bit web application in a SharePoint 2013 Farm the new application might fail to load and give a general 503 Service Unavailable error message. When looking in IIS manager, the Application Pool for the new app would be in the stopped state.
The following error messages might be visible in the Event log…
For the new 32 bit web application

Event ID 5002 – Error <date and time> WAS 5002 None
Application pool ‘<App Pool Name>’ is being automatically disabled due to a series of failures in the process(es) serving that application pool.
And
Event ID 5139 – Warning <date and time> WAS 5139 None
A listener channel for protocol ‘http’ in worker process ‘<process number>’ serving application pool ‘<App Pool Name>’ reported a listener channel failure. The data field contains the error number.
For SharePoint 2013
Event ID 2282 – Error <date and time> IIS-W3SVC-WP 2282 None
The Module DLL ‘C:Program FilesCommon FilesMicrosoft SharedWeb Server Extensions15isapispnativerequestmodule.dll’ could not be loaded due to a configuration problem. The current configuration only supports loading images built for a x86 processor architecture. The data field contains the error number. To learn more about this issue, including how to troubleshooting this kind of processor architecture mismatch error, see http://go.microsoft.com/fwlink/?LinkId=29349.
The Microsoft link for the issue will only redirect you to the www.iis.net web site.
Solution / work around
The solution to this issue is to enable 32 bit applications to be loaded together with SharePoint and ask the SharePoint Module to only load in 64 bit mode. This can be done by running the following command, located in the %WINDIR%System32inetsrv folder:
appcmd.exe set config -section:system.webServer/globalModules /[name=’SPNativeRequestModule’].preCondition:integratedMode,bitness64
More information on configuring IIS can be found here: http://technet.microsoft.com/en-us/library/cc627313.aspx
Hat Tip to my colleague Markus Lind for pointing this out.