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So my friend and I are stumped. This is in the context of achieving the sodium hydrogen phosphate/sodium dihydrogen phosphate buffer by titrating the acid with a strong base.

My friend says the answer would be H3PO4 + Na3PO4. In my case, I'd think that sodium hydrogen phosphate would be the acid (but I genuinely am not sure) that we'd titrate in that scenario and all we'd need then is a strong base (although I honestly don't know how to figure out what strong base in particular you must use.)

What's correct? Or what would be the correct way?

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    $\begingroup$ Start with writing the 3 equilibrium chemical reactions between 4 forms of phosphate. You will see what is an acid and when. $\endgroup$
    – Poutnik
    Aug 14 '20 at 14:35
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    $\begingroup$ Any process treating any mixture of $\ce{Na_{n}H_{3-n}PO4}$ ( n=0..3) by any of $\ce{Na_{n}H_{3-n}PO4}$ or $\ce{NaOH}$ to produce solution of $\ce{NaH2PO4 + Na2HPO4}$ with the desired $\mathrm{pH}$ or the molar ratio/concentration is a correct way. But most handy may be titration of $\ce{H3PO4}$ or $\ce{NaH2PO4}$ by $\ce{NaOH}$. $\endgroup$
    – Poutnik
    Aug 14 '20 at 14:55
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    $\begingroup$ Both methods are correct. You may mix equal amounts of $\ce{H3PO4}$ and $\ce{Na3PO4}$. Or you may mix n moles of $\ce{NaH2PO4}$ and n / $2$ moles of NaOH. $\endgroup$
    – Maurice
    Aug 14 '20 at 14:58
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    $\begingroup$ What is your target ph? $\endgroup$
    – Andrew
    Aug 14 '20 at 16:32
  • $\begingroup$ Also you have to consider ionic strength of your buffer in addition to pH. $\endgroup$ Aug 14 '20 at 17:17
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This picture says more than a thousand words:

enter image description here

You want a mixture of $\ce{HPO4^2-}$ and $\ce{H2PO4^-}$. You can start with any species (in a solution with a certain pH) and add another species whose pH is "on the other side" of the desired pH. If the pH of your starting solution is lower than the desired pH, you can also titrate with NaOH.

What you actually do (of the six options) is determined by solubility of the solution and by availability. If you titrate two phosphate solutions of the same concentration, there will be no dilution effect. If you titrate with NaOH, you would used fairly concentrated NaOH to avoid dilution, but would have to add water to a defined volume (or measure the volume after reaching your desired pH) to figure out the concentration of your buffer.

You should not titrate with HCl because then you end up with extra sodium choride in your buffer.

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