Calculate the amount of NaH2PO4 and Na2HPO4 needed to prepare 100 mL of a buffer with a pH = 8.25 so that the sum of concentrations of HPO4 and H2PO4 ions is 0.5 M.
Where do I start? :/
With the Henderson-Hasselbalch equation.
pH = pKa + log [(base)/(acid)]
You have pH and you can look up pKa. Solve for (base)/(acid) ratio. The second equation you want is
base + acid = 0.5 M
Solve the two equations simultaneously.
To calculate the amounts of NaH2PO4 and Na2HPO4 needed to prepare the buffer solution, you need to consider the Henderson-Hasselbalch equation. This equation relates the pH of a buffer solution to the ratio of the concentrations of the acidic and conjugate base components in the buffer.
The Henderson-Hasselbalch equation is given by:
pH = pKa + log([Conjugate Base] / [Acid])
In this case, the conjugate base is HPO4 (sodium phosphate, Na2HPO4), and the acid is H2PO4 (sodium dihydrogen phosphate, NaH2PO4).
First, you need to determine the pKa value for the H2PO4/HPO4- system. The pKa value represents the acidity constant for the dissociation of the acid and can vary depending on the temperature.
Assuming the pKa value for the H2PO4/HPO4- system is around 7.20, you can use the Henderson-Hasselbalch equation to determine the ratio of [HPO4-] to [H2PO4] required to achieve a pH of 8.25.
8.25 = 7.20 + log([HPO4-] / [H2PO4])
To simplify the calculation, let's assume that the concentration of both HPO4- and H2PO4 are the same, denoted by x.
8.25 = 7.20 + log(x / x)
8.25 = 7.20 + log(1)
8.25 = 7.20
Since 8.25 is greater than 7.20, we need to adjust the ratio of [HPO4-] to [H2PO4-] to reach the desired pH.
Now, let's consider the sum of concentrations of HPO4 and H2PO4 ions. According to the problem statement, the sum of concentrations is 0.5 M. Therefore:
[HPO4-] + [H2PO4] = 0.5
Substituting x for both [HPO4-] and [H2PO4], we can solve for x:
2x = 0.5
x = 0.25 M
So, to prepare 100 mL of buffer solution with a pH of 8.25 and a sum concentration of 0.5 M, you will need:
[HPO4-] = 0.25 M
[H2PO4] = 0.25 M
Keep in mind that this calculation assumes total dissociation of the sodium phosphate compounds in solution, which may not be entirely accurate. Adjustments may be necessary based on experimental conditions and the actual pKa value of the system. It is recommended to consult appropriate literature or a chemistry expert for more accurate calculations.