best way to "wipe" empty space is to use the "dd" command..
once it's finished run
sudo dd if=/dev/zero of=/home/[your username]/wipe.file
The first command basically create a file called "wipe.file" and keep filling it with zero's till the disk is full.
rm /home/[your username]/wipe.file
You could use /dev/urandom instead which will fill the file with random data.
if you don't use sudo then all but 5% of the will be used (5% is reseved for the root login)
it might take a while depending on how big your drive is...