Do acids and bases neautralize over time?

Fresh, reagent grade NaOH pellets typically contain about 1% sodium carbonate by weight.

No, there’s no reason why solid NaOH can’t react directly with gaseous CO[sub]2[/sub], which is why you’d want to keep a container of solid sodium hydroxide sealed. It would be a fairly slow reaction, though.

The fact that solid NaOH does not have a pH is irrelevant.

Well, if you’re paying attention to significant figures, half of 13.9965 is not lower than 7.0, actually. Nor is it lower than 7.00 (though it is lower than 7.000).

I haven’t paid attention to sig figs since I was in high school. When I wrote papers for publication, I just calculated the error and chopped off the number at the right spot.

I’m no chemist either, but the pH of deionized water exists (and should be 7) but it is not easy to measure. There are very few ions in the water for a pH meter to use to get a reading.

If you get the chance, put a pH meter into deionized water and you’ll see what I mean - it will give you numbers all over the place - 5, 8, 10, 6, and even if it does settle down at a particular value, that value will almost certainly not be 7. This has to do with how pH is measured, not with any actual reflection of the concentration of ions in deionized water.

To simplify, would it be accurate to say that if the storage medium is inert the acid/alkali will remain stable?

Assuming it’s not reacting with anything present in the airspace of the container - yes.

Depends on the acid/base.
Acids such as nitric, sulfuric, hydrochloric, perchloric, phosphoric, and acetic are pretty stable as are inorganic bases and triethanolamine and ammonia. Alpha hydroxy acids, keto acids, deoxyribonucleic acids, and many organic bases will react or break down over time. Usually, you can slow the process by keeping such things in the refrigerator.