Re: Which solution will the buffer work in?

The definition of a buffered solution is one which resists changes in pH when small amounts of acids or bases are added or when dilution occurs. I would say that the buffer worked better in tube B not only because of the smaller pH change, but also because the HCl did not convert all of the acetate into acetic acid. Buffers work as long as the weak acid and its conjugate base are not completely consumed by the addition of a strong acid or base.

In tube B, you had 0.0005 moles of the strong acid HCl and 0.00056 moles of acetate. The HCl reacts completely with the acetate to give acetic acid, but because there is a slight excess of acetate present in solution, so 0.00006 moles of acetate remain unreacted (0.00056 moles - 0.00005 moles). Because unreacted acetate remains, the buffer can continue to work.

However, in tube D you added 0.00005 moles of the strong base NaOH, which reacts completely with the 0.0005 moles of acetic acid present, leaving no acetic acid behind. When all the acetic acid is consumed, the buffer stops working.

The Henderson-Hasselbach Equation can be used to determine what the pH of a buffer solution should be after the addition of a strong acid or base and can help rationalize the results you obtained (we won't go into the math here, though). You can read more about this in any analytical chemistry book (I highly recommend "Exploring Chemical Analysis" by Daniel C. Harris, which nicely illustrates how buffers function and also explains how to predict pH changes).