The applications running on my web server need the ability to send internal and external email.  The following steps for creating an email relay receive connector will allow email to be sent from the specified IP address without any type of authentication.

1. Create a new receive connector called "Email Relay".  Server Configuration -> Hub Transport -> New Receive Connector...
    
   
    
2. Leave the default receive settings and specify your FQDN for this connector:
    
   
    
3. Specify the IP addresses of any servers which will be allowed to send mail:
    
   
    
4. Edit the properties of the newly created Email Relay to configure its Permission Groups and Authentication:
    
   
    
5. Allow Exchange Servers to use the Email Relay send connector.  Permission Groups Tab -> Check Exchange Servers.
    
   
    
6. Specify that connections have already been authenticated, allowing anonymous access.  Authentication Tab -> Externally Secured (for example, with IPSec).
    
   
    
7. That's It!  Now you can specify an SMTP server for your applications to send internal and external mail.
    
   

References:

• http://msexchangeteam.com/archive/2006/12/28/432013.aspx
• http://social.technet.microsoft.com/Forums/en-US/exchange2010/thread/68fee0e8-9e3d-4f7d-ab1a-cb5675daf6ff