Why is the address 172.31.255.255 with a sub net mask of 255.255.255.0 invalid as a host ID?

because that is the last number of the subnet. the last number in a subnet is used as the broadcast domain. the first number is also not usable. an example would be:

id 192.168.20.XX

subnet 0f 255.255.255.128

192.168.20.0 and 192.168.20.127 may not be used and 192.168.20.128 starts the next subnet making 192.168.20.128 and 192.168.20.255 not usable