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.