Question

Could you use photosynthesis bacteria in a oxygen tank to continually create oxygen as long as the person is expelling carbon dioxide in the tank?

Answer 1

That's an interesting question.

Short answer: yes but it would be unfeasible. (Although the bacteria /would/ continue to maintain high oxygen content in the tank long after the person has died).

Long answer:
While the bacteria (or algae or any other photosynthetic organism) would continually produce oxygen (given enough light and water), we run into the problem of how fast that oxygen is used up and how fast it's produced.
First, how fast is it used:
The average adult has uses about 2,000 kilocalories per day, or 8.368*10^6 kilojoules per day. 1g of glucose yields 16kJ of energy so you'd burn 5.230*10^5g of glucose a day. That's 2902mol glucose. For each mole of glucose you need 1/2mol of atmospheric O2 for aerobic respiration.
---Thus, you need about 1.451 kmol of oxygen each day, or 0.01679 mol/s

How fast it's produced:
917.8 kJ/mol H2O are required for the complete photolysis of water (the gas-evolving reaction in photosynthesis); two such reactions are needed for one O2 molecule so the need is 1835.6 kJ/mol O2. The sun provides about 1.3612 kJ/s/m^2. Let's guess that our bacteria are able to use 30% of that (a fairly generous approximation).
---Oxygen gas would be evolved at a rate of 7.416*10^-4 mol/s/m^2.

Bring it all together:
you use: 0.01679 mol/s
bacteria provide: 7.416*10^-4 mol/s/m^2
you need: 22.64 m^2 of bacteria exposed to the sun to survive
-That's a flat, square scuba tank 4.759 meters (say 15ft) on a side. And don't forget that's the minimum for full-sun exposure and a reasonably efficient bacterium.

Answer 2

I can't guarantee the numbers are perfect, I did use wikipedia.