CO2 movement

[Soper]

Hello. I'm newbie. And English isn't my native language.
Please help me to settle my problem.
The matter I'm gonna build vent system and i a little confused.
Look at the picture.
Lets take a living room.
Fresh air comes trough windows and mixes with hot air. Most of hot air stays up right under a ceiling. Then cold air right above floor goes through crack between a floor and a door to a kitchen (for example). Then hot air goes to vent on a ceiling.

But lets back to a living room. If in this room is a human he exhale CO2. CO2 is heavier than air so CO2 go down to floor and then with cold air goes to a kitchen as I said above.

So my question is: Why in a kitchen vent in a ceiling ? Why we should lost hot air if CO2 is down right above floor ? Why vent don't placed right above floor ? Can I place vent like that to discard CO2 not a hot air under ceiling without CO2 ?

Thanks.

P.S. Or hot air need to make air move out of house ?