# How to find the resist in pH change when both are same buffers of same concentration? [closed]

We are given two buffers [a) 0.1 M phosphate buffer of pH 7.7 and (b) 0.1 M phosphate buffer at pH 6.71 . If acid is to be added to the buffers, which of them, will resist the pH changes better

I used Henderson Hesselbach equation in both cases but the log part and pka is same, so how to solve it? Please provide a detailed solution

• I am not getting, can you please explain – Sayantan Bhanja Aug 6 '19 at 16:31
• Also no information has been given about its alpha fractions, neither of PO43-, nor of HP042- , nor of H2PO4- nor of H3PO4 – Sayantan Bhanja Aug 6 '19 at 16:36
• Why is the log part the same? I think that highlights the root of your problem. – Zhe Aug 6 '19 at 16:50
• Because both are 0.1M and we do not know individual conc of P043-, neither of H3PO4, neither of H2PO4 nor of HPO4 and there is no way to find – Sayantan Bhanja Aug 6 '19 at 16:57
• The pH defines the ratios of the various phosphate species. see en.wikipedia.org/wiki/Phosphoric_acid#Acidic_properties – MaxW Aug 6 '19 at 17:37

This particular question is testing basic knowledge of buffers. In the most simplest explanation possible, a buffer will resist changes in pH the best when the pH is at the pKa. In the case of phosphoric acid, there are three acidic protons thus making three pKa values. Pulling the following table from Wikipedia

$$\hspace{3.25cm}$$ We can see $$pK_{a2}$$ is closest to the values of interest. Buffer solution a) is $$|7.20-7.7| = 0.5$$ pH units above $$pK_{a2}$$ while buffer solution b) is $$|7.20 - 6.71| = 0.49$$ pH units below $$pK_{a2}$$. Almost equivalent distances from $$pK_{a2}$$ though in different directions.

Now we must consider what is being added. Since acid is being added to the solution, the solution will decrease in pH. Thus we want to choose the buffer that is more basic as it will be more capable of neutralizing the acid. Therefore buffer a) should be the answer.

As a visual answer, consider the following titration curve for phosphoric acid.

$$\hspace{1cm}$$ The green smudge is the pH of buffer solution $$\color{green}{a)}$$ while the red smudge is the pH of buffer solution $$\color{red}{b)}$$. If acid is added, we clearly stay within the buffer region of the $$H_2PO_4^-/HPO_4^{2-}$$ equilibrium for $$\color{green}{a)}$$ while for $$\color{red}{b)}$$ the pH has the possibility of dropping off to become a very acidic solution. Therefore $$\color{green}{a)}$$ has the better properties of a buffer.

• How is it that buffers of different compositions can have the same pH?for example it is possible to prepare 0.01M phosphate buffer of pH 7.0 and 0.1M phosphate buffer of pH 7.0 How? – Sayantan Bhanja Aug 6 '19 at 23:21