Hey Cory,
When you add unbaked baking soda, ie sodium bicarbonate, the long and the short of it is that you introduce more CO2 per unit of alk than if you add carbonate. Normal tank bicarb/carbonate mix is partly bicarbonate (ie at equilibrium with air, or roughly so, there is a mix of bicarbonate and carbonate in the tank). If you add bicarb as you say, the tank has excess CO2 now, compared to what will end up at if its well aerated with outdoor air, and it will release some of this extra CO2 as you aerate it. If you add carbonate (baked baking soda) instead, the tank will have depleted CO2 compared to outdoor air, and it will suck CO2 from outside air as you aerate the tank with such air. When you bake baking soda, you drive the extra CO2 off into your oven (ie before it goes into the tank) and convert the bicarb into carbonate.
So as per your question above, you add bicarbonate (pure bicarb, not a balanced mix of bicarb and carbonate), and the tank now has excess CO2, which means the pH drops (thats a simplification of the chemistry I believe but Randys page 2002/05 has the full details). As you aerate the tank, the CO2 is released, and the pH rises again, higher than the original pH because you now have more alk in the water. The pH that the tank will stabilise at is complicated to explain but essentially to simplify, if you imagine that you have no CO2 being produced in the tank, and no CO2 being consumed, and you aerate the tank with outside air at 400 ppm CO2, then the tank partial pressure of CO2 will be 0.0004 atmospheres. There was a graph I linked to in a previous question to Randy about this subject, I cant remember the title of the thread, but look through my recent posts if you want to find it. It provided the numerical comparison between pCO2 (partial pressure of CO2) and pH at natural seawater alk and other conditions of natural seawater. The page the graph is on also had the maths to calculate for other alk and salinity factors but the maths was a bit too much for me to mess with!
A tank at equilibrium with outdoor air has a balanced mix of bicarb and carbonate, lets just say its 20% bicarb and 80% carbonate (I cant remember the real values but Randy has a graph in one of his articles which shows the real ones). If you add a mix of 20% bicarb and 80% carbonate to this tank, the tank will still be at equilibrium with the air, and the pH will rise by the amount shown on Randys pH vs alkalinity graph. No aeration will be required for this tank to bring it back in balance with the air.
Its really complicated for most of us to understand IMO and its taken me years just to get to this point, and I still dont understand it 100%. But a few simple rules seem to be all thats needed. Bicarb temporarily lowers pH and effectively adds CO2 which will then be released. Carbonate raises pH and sucks CO2 from the tank for a short while. Hydroxide sucks even more CO2 and raises pH even more, once again until its had its fill of CO2. All 3 end up at the same place after a few hours, with one unit of alk added causing pH to rise by the same amount (ie the same eventual pH rise per meq of alk). If you are OK with your tank pH spiking down for a bit you can use bicarb, if you are ok with an upwards pH spike you can use carbonate, if you want your tank pH to not spike then you need to mix bicarbonate and carbonate in a balanced mix (weighed out parts of bicarb and carbonate in the right proportions).
Re putting a tank outside, my understanding is that the process of equilibrating a tank with air is not 100% efficient. Say outside air is 400ppm and you are producing a few grams of CO2 a day in your tank from fish, you have to drive an awful lot of air through the tank water to bring the tank CO2 partial pressure close to 400 ppm. I calculated roughly that 500 litres per hour air in a tank thats producing 15 grams of CO2 a day would result in something like 1500 ppm CO2 in the tank, even if the process of mixing air and water to exchange the CO2 from the water to the air was 100% efficient. Its probably much lower than 100%. Thankfully a smallish tank like yours or mine is not producing 15g a day CO2, in fact mine must be producing milligrams a day it looks like, from my pH readings (unless my probe is broke). But your aim is the same as mine was and I am happy with it now with the outside skimmer air intake + skimmer cranked to max air. The simplest answer to really stable pH would be shed loads of air exchange, like for a 100 gallon tank 1000 kg of air a day (a million litres a day or about 10 litres per second), because air is the best CO2 buffer. If the tank CO2 is low (daytime, plenty of nutrients and algae growth) then air brings CO2 up, if the tank CO2 is high (night time) then air brings CO2 down. Air tries to pull your tank CO2 back towards normal, ie 400 ppm (about pH 8.4 in a raised alk tank). But you need a real lot of air to make this effective in a high CO2 tank. If your tank is not that high a CO2 producer like mine, you get away with less air. 500 litres per hour of outside air, or about 12 kg per day, has brought my pH to daytime 8.4, night time 8.3 (from day time 7.9, night time unknown previously). Good enough for now! However if a 50 gram fish dies and is eaten / rots in 24 hours, my pH will spike to around 7.6 for that 24 hour period (calculated value), which is not great and thats why more air would be good. But in normal operation this works fine. Try running a bit of 10mm silicone tubing to a window kept open a crack, and try it for a day and watch your pH. If it gives you what you need, try to think of a way to engineer it without drilling, you can probably snake a clean tube around the room to a vent or crack somewhere without bothering the landlord I imagine.