What volume (in liters) of 0.96 M KOH solution should be added to a 0.090 L solution containing 9.9 g of glutamic acid hydrochloride (Glu, FW=183.59; pKa1=2.23, pKa2 =4.42, pKa3=9.95) to get to pH 10.20?
mols glutamic acid = 9.9/183.59 = estimated 0.05.
mols KOH needed = estimated 0.05
MKOH = mols KOH/L KOH or
L KOH = mols KOH/M KOH = estimated 0.05/0.96 = estimated 0.056 L or about 56 mL and that is one of the pKa values. Multiply that by 3 for total volume KOH required.
To find the volume of 0.96 M KOH solution needed to reach a pH of 10.20, we first need to understand the chemistry involved.
Glutamic acid hydrochloride (GluHCl) is an amino acid that can act as both an acid and a base. In water, it can release a proton (H+) to become the conjugate base, Glu-, or it can accept a proton to become the conjugate acid, H3O+.
The pKa values given (pKa1=2.23, pKa2=4.42, pKa3=9.95) represent the acidity constants for the three ionization steps. Since we want to reach a pH of 10.20, which is above the pKa3 value, only the third ionization step is relevant for this calculation.
At pH values greater than the pKa3, the Glu- form predominates. Therefore, we need to calculate the concentration of Glu- necessary to achieve the desired pH.
The Henderson-Hasselbalch equation can be used to relate the pH, pKa, and concentration of an acidic or basic solution:
pH = pKa + log([A-]/[HA])
In this case, [A-] represents the concentration of Glu- and [HA] represents the concentration of GluHCl. We are given the concentration of GluHCl, but we don't know the concentration of Glu-. However, we can assume that the initial concentration of Glu- is negligibly small compared to the concentration of GluHCl.
Therefore, we can simplify the Henderson-Hasselbalch equation as follows:
pH ≈ pKa + log([A-]/[HA])
pH ≈ pKa + log(0/[HA])
pH ≈ pKa + log(0)
Since the logarithm of zero is undefined, we can conclude that the pH value of 10.20 is not achievable by simply adding the GluHCl solution. We would need a stronger base or adjust the experimental conditions.
Hence, in this case, the volume of 0.96 M KOH solution required to reach a pH of 10.20 cannot be determined as specified.