Unfortunately this one will not be that straightforward. Even if you succeed with the mounting it will not move the files at all. What you can do is to
- mount the disk elsewhere (mkdir /var/lib/mongodb1, mount /dev/sda3 /var/lib/mongodb1)
- stop mongo
- copy the files from /var/lib/mongodb to /var/lib/mongodb1 (only helps if the new disk is bigger)
- reconfigure mongo to use as db dir the new directory or swap the names with mv commands
- start mongo
- if everything went fine, mongo started and so on,(check it first!!!) you can delete the old data.
If you have a disk which is the same size so with moving the data you will run into the same problem, if you need larger space then a single disk you should play around with RAID and/or LVM and more disks.