How would I set up a home lab at home. I want to study chemicals and I have been given a medium-sized(6ft by 3ft) space in the garage.
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You will be better off if you join a real lab. Researchers can help you get started in a safe manner. Chemistry experiments killed many professionals. Here is a list of things you would need.
A chemistry lab needs at least this:
Hood with 650 cubic feet per minute air flow. You CANNOT make it with a small pump.
Chemistry waste disposal. Flushing it down the drain is not a good approach.
Freezer and fridge for chemicals only.
Rotovap. Basic one costs 5000 dollars.
Source of vacuum.
Analytical instruments. NMR costs 100 000 dollars to buy, plus you will need to refill liquid helium once in a while. You can also ask chemistry department to run you samples for 10-20 dollars per piece.
Lab rules strictly prohibit working alone. In case of emergency someone should be around to save you.
Bottom line: you will poison yourself without a hood and set garage on fire. Find a university professor and ask to join their lab. If you show decent knowledge of chemistry they might agree to help you.