Answers to Questions

1. Do the values for the pK_a you found in the two methods agree? Which value is better for this mathematical model? Which would be more useful experimentally? Why?
   1. They should be close, but not exact (unless by chance).
   2. The spreadsheet answer would be better for the mathematical model, since the mathematical model represents an exactly known system with defined values etc.
   3. The graphical method is better for experimental data since no data point is known with certainty and the best fit line represents an average of many points. Hopefully in this situation the best fit line will provide a value in which the errors have canceled to give a more accurate and precise estimate of reality. Remember, in the real world, we don't know the exact function followed by the data. Our models may be close without being "real." (For example, Newtonian physics gives marvelously accurate and precise predictions for everyday phenomena, but is known to be a "false" picture of the world.)
2. Do the values for the equivalence point you found in the two methods agree? Which value is better for this mathematical model? Which would be more useful experimentally? Why?
   1. Again, they should be close, but not exact (unless by chance).
   2. As above, the spreadsheet answer would be better for the mathematical model, since the mathematical model represents an exactly known system with defined values etc.
   3. See 1.3 above, the graphical method is better for experimental data since no data point is known with certainty and the best fit line represents an average of many points.
3. Does the buffer region you found graphically correspond to the range found on the sheet (pK_a±1)?
   1. Here the correspondence depends on how you perceive the "linear" region. If one looks for a very close fit to a straight line, then a narrower region than ±1 pH unit will be seen, as shown in the figure below, where I would guess the "buffer region" goes from about pH 4 to about pH 5.5 which is a range more like ± 0.75 pH units:

Any definition of the buffer region will be somewhat arbitrary, we are really trying to make a pragmatic judgment on the behavior of the system in maintaining pH within a range needed for a particular experimental, biological, etc. situation.

4. What is a buffer? For pH, a substance which when added to a solution resists changes in pH (hydrogen ion concentration). A pH buffer is a mixture of an acid and its conjugate base (or vice-versa), with significant fractions of each present.

5. Why does the pH level off at high pH values? Is this another titration and buffer region? (Hint: What's the pH of 0.1 molar base? 1.0 molar?) The highest pH achievable in a titration with a base will be the pH of the pure base (e.g. for 0.1M NaOH the pH = 13, for 1.0M pH = 14 in aqueous solutions). Thus as base is added a limiting value will be approached, causing the curve to level off. This is thus not another buffer region.