How many millimoles of NaOH or HCl must be added to 500.0 mL of 0.250 M NaO₂CCO₂H to prepare a pH 3.90 buffer? Assume no change in volume.pK₁ = 1.250 and pK₂ = 4.266.

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To prepare a buffer with a specific pH, the Henderson-Hasselbalch equation is used: pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the base form and [HA] is the concentration of the acid form. Given the desired pH of 3.90 and the pKa closest to this pH is 4.266 (for the dissociation of HO₂- to O₂^2-), we can calculate the ratio of [A-]/[HA]. Rearranging the equation gives log([A-]/[HA]) = pH - pKa = 3.90 - 4.266 = -0.366. Therefore, [A-]/[HA] = 10^-0.366 ≈ 0.432. Since the initial solution is 0.250 M NaO₂, which acts as [HA], to adjust the ratio to 0.432, we need to convert some of the HA to A- by adding NaOH. The amount of NaOH needed can be calculated by setting up the equation 0.432 = ([A-] + x)/(0.250 - x), where x is the moles of NaOH added. Solving for x gives the amount of NaOH needed to achieve the desired buffer ratio and pH.

How Many Millimoles of NaOH or HCl Must Be Added