Final answer:
To make a phosphate buffer at pH 9.6 from 10 mM phosphoric acid, a calculated amount of 0.1 M NaOH would likely be required to titrate the solution to the desired pH without overshooting the target.
Step-by-step explanation:
When creating a phosphate buffer at pH 9.6 starting with one liter of 10 mM phosphoric acid (H₃PO₄), it is essential to consider that at pH 9.6 the dominant species will be hydrogenphosphate (HPO₄²⁻), which corresponds to the second dissociation with a pKa of 6.82. To achieve the desired buffer pH, the acid must be partially neutralized to form the conjugate base. Since H₃PO₄ is a weak acid and we want to make a buffer at a pH well above its second pKa value, we would need to add a strong base to convert some of the H₃PO₄ into HPO₄²⁻. To determine the amount of NaOH, we would use the henderson-Hasselbalch equation, but in this case, as the solution is starting at pH far below 9.6, using a concentration of NaOH that matches the concentration of H₃PO₄ (0.01 M NaOH) would not be sufficient to achieve the desired pH. Instead, a higher concentration of NaOH will be necessary. Choices b, c, and d describe concentrations of NaOH that exceed the 10 mM concentration of the phosphoric acid, and could potentially push the pH too high if added in excess. Therefore, a calculated amount of 0.1 M NaOH (b) would likely be the appropriate concentration to allow fine control over the buffer pH without risk of drastically overshooting the target pH of 9.6 when it is added dropwise. It is important to remember that the actual volume to be added should be determined experimentally to achieve the correct pH.