iTunes Unable To Backup iPhone
The default location for iPhone Backups is:

$HOME/Library/Application Support/MobileSync/Backup


If the Macintosh HD doesn't have adequate free space and or adequate free space cannot easily be made available at the default location, then the following can be used as a workaround.

First, if the iPhone is showing in iTunes eject it, then close iTunes.

If you have existing backups at the default location you can first copy the existing Backup folder to a new location on a different drive/partition/volume that has adequate free space.

Once you've copied the Backup folder to a new location you can either delete the original or rename it, e.g.: Backup.old. This needs to be done to allow for the creation of a symbolic link to the new location of the MobileSync Backup folder and the symlinks name also needs to be "Backup".

To create the symbolic link, it Terminal, use the following command line example while changing the path to what's appropriate for your use.

ln -s /Volumes/&lt;Your External HDD&gt;/MobileSync/Backup ~/Library/Application\ Support/MobileSync/Backup


With the symbolic link created you can now open iTunes, connect the iPhone and perform a backup.