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To make a phosphate buffer at pH 12.38 starting with one liter of 10 mM phosphoric acid (H₃PO₄; pKs are of 2.15, 6.82, and 12.38), you could add

a) 0.01 M NaOH
b) 0.1 M NaOH
c) 1 M NaOH
d) 10 M NaOH

1 Answer

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Final answer:

To create a phosphate buffer at pH 12.38 using 10 mM phosphoric acid, one should add 0.1 M NaOH. This allows for the appropriate balance between the phosphate species in equilibrium near the buffer's pKa to maintain the desired pH. Therefore, correct option is b.

Step-by-step explanation:

To make a phosphate buffer at pH 12.38 starting with one liter of 10 mM phosphoric acid (H₃PO₄; pKs are of 2.15, 6.82, and 12.38), you should add 0.1 M NaOH. This is due to the fact that at pH 12.38, the dominating species in equilibrium is HPO₄²-, which is the conjugate base formed after two protons (H+) have been dissociated from H₃PO₄.

The addition of NaOH to the solution provides OH- ions that will react with the H₃PO₄ to form H₂PO₄⁻ and further deprotonate to create more HPO₄²-.

Since the pH is closest to the third pKa value, we must be near the point where HPO₄²- is in equilibrium with PO₄³-, and the amount of NaOH needed should be equivalent to the amount needed to deprotonate nearly all of the H₂PO₄⁻ present.

Example calculations that support understanding in this context include the description of how pH changes when different quantities of NaOH are added to a buffer or an unbuffered solution, emphasizing the role of the buffer in moderating pH changes.

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