This project would take 2-3 days to filter the volume of air in a 1,000 sq foot apartment... which is to say it would do nothing of significance. To be effective, you want to change the air something closer to once every 30 minutes.
With a few adaptations, however, it might be good as a soldering station fume extractor. These already exist and are little more than a tube, a fan, and a filter (usually with activated charcoal).
The nice thing about this one is that it's circular and could easily adapt to a flexible tube and you could perhaps stack fans for greater sucking power.