Question

Write a chemical reaction and a few words to explain why the pH of the formic acid buffer above goes up only tenths of a pH unit (from about 3.6 to about 3.7 pH units) when a few drops of 0.10 M NaOH solution are added to it, instead of going up much more to about pH=10. {Note that if the same amount of NaOH were added to 20 mL of 0.00025 M HCl (which also has pH=3.6), the pH would go up to about pH=10. Explain qualitatively – no calculation is needed.}

Answer 1

I think that it has to do with the 5%rule, which is the following:

The measurement and calculation of pH is not as accurate as some other of the chemical measures due to differences in temperature, other ions present, purity of solutes, concentration changes due to evaporation, etc. Measurement of pH in medicine, for instance must be at 37 degrees Celsius. There may be machines that claim to measure pH to hundredths or thousandths of a pH unit, but the standard that calibrates the machine may be off a little. A change of five percent in the hydrogen ion concentration will not change the pH more than a few hundredths of a pH unit. You try it on the calculator. Enter a number, say 0.001 and punch log. Now punch a number 95% or 105% of the first number (in this case, 0.00105 or 0.00095) and punch log. How different is the pH? Our answers in pH are going to be to the nearest tenth of a pH unit, so the hydrogen ion concentration needs to be only within 5% of an accurate number. This idea is the 'five percent rule.'

You may remember we mentioned that the concentration of a strong acid is equal to the hydrogen ion concentration. That is not exactly so. In any water solution of an acid there is another source of hydrogen ions, the water. Water alone has a hydrogen ion concentration of E-7 Molar. Let's say you have a a E-5 M HCl solution, the contribution of the water is only a hundredth of the amount of hydrogen ion from the acid at the first approximation. You could approximate the real hydrogen ion concentration better by finding the hydroxide ion concentration of a solution with E-5 hydrogen ion concentration and then finding the added hydrogen ion concentration due to the dissociation of water from that. The total hydrogen ion concentration will be even further from having any significant contribution of hydrogen ion from the ionization of water. Does the ionization of water have an significance in this case? Of course not. There is much less than five percent difference between the two numbers. Here is an obvious situation where you can use the simpler approximation of the hydrogen ion concentration to find the pH. There are some times when the simpler approximation is not accurate enough. There are some times when you may be in doubt and would need to work it BOTH ways to show whether you can use a simplified method.

Hope this helps