[Win,odd Dhamnekar]

Are the following two definitions of buffer solution same, correct, valid  and equal in meaning.

[Babcock_Hall]

What are your thoughts?

[Win,odd Dhamnekar]

 In my opinion, both definitions of buffer solution are same, correct, valid and equal in meaning.

[Babcock_Hall]

I don't see anything the matter with either definition.

[Meter]

Why not let the definition be "a system in solution that resists change to pH" and allow for different mechanisms?

[Win,odd Dhamnekar]

 Both of these definitions of buffer solution are given by the authors of chemistry textbook.

In the first definition, Authors says " You can treat buffer solutions quantitatively if you use the appropriate K_a or K_b and recognize the role of common ion".

What does it mean? What message authors want to give to the readers? Would anyone elaborate on this topic?

[Meter]

Both of these definitions of buffer solution are given by the authors of chemistry textbook.

In the first definition, Authors says " You can treat buffer solutions quantitatively if you use the appropriate K_a or K_b and recognize the role of common ion".

What does it mean? What message authors want to give to the readers? Would anyone elaborate on this topic?

He is probably referring to the Henderson-Hasselbalch equation which is pH = pKa + log([A^-]/[HA]).

Another version exists where you use pKb instead, and as you know, pKa and pKb depend on Ka and Kb. You also derive the HH equation from Ka or Kb.

If it's not that, I don't know what he's talking about.

As for the common ion effect, recall that the concentration ratio uses equilibrium concentrations. When calculating such concentrations (like with ICE tables), one must take into account the common ion effect.

[Babcock_Hall]

Using the H-H equation allows one to estimate how much base must be added to a weak acid, in order to prepare a buffer, among other things.  If I had written the passage, I might have mentioned that ionic strength affects the practical pK_a values.