The conversation list contains the last message sent or received however it does not indicate which one it is. As is, there is no easy way to determine th is without having to open the individual conversation.

Please color code the messages in the conversation view to provide this useful information. Hangouts does this by prefixing sent messages with, 'You:' so that at a glance I know if I'm supposed to reply to the 'where are you?' or if I'm waiting for the response in my conversations list.