How do I calculate the amount of grams of Na2HPO4 and NaH2PO4 to prepare 200 mL of a buffer with an 8.25 pH so the sum of the concentrations of HPO4 and H2PO4 ions is 0.5 M? Does this involve writing a Ka expression and equilibrium? I am confused and Thanks for your help!
Sorry I don't know how it posted twice! Oops! :-)
See your other post. The HH equation is the secret weapon.
To calculate the amount of grams of Na2HPO4 and NaH2PO4 required to prepare the buffer, we need to consider the Henderson-Hasselbalch equation and the dissociation equilibrium of the phosphate buffer system.
First, let's write the dissociation equilibrium equation for Na2HPO4 and NaH2PO4 in water:
Na2HPO4 ⇌ 2Na+ + HPO4^2-
NaH2PO4 ⇌ Na+ + H2PO4^-
Next, we can write the equilibrium expressions for these dissociation reactions:
K1 = [Na+][HPO4^2-]/[Na2HPO4]
K2 = [Na+][H2PO4^-]/[NaH2PO4]
The pH of the buffer solution is given as 8.25, which corresponds to the pOH of 14 - pH = 14 - 8.25 = 5.75. To calculate the concentration of HPO4^2- and H2PO4^- ions, we need to know the pKa values for HPO4^2-/H2PO4^-.
The pKa1 value for HPO4^2-/H2PO4^- is typically around 7.21, so we can use this value to estimate the concentration ratio of HPO4^2- to H2PO4^- in the buffer solution.
pKa1 = -log10(Ka1), so Ka1 = 10^(-pKa1)
Using the Henderson-Hasselbalch equation:
pH = pKa + log10([HPO4^2-]/[H2PO4^-])
Rearranging this equation:
[HPO4^2-]/[H2PO4^-] = 10^(pH - pKa)
Now, let's assume that the sum of the concentrations of HPO4^2- and H2PO4^- ions in the buffer solution is 0.5 M. We can assign x as the molar concentration of H2PO4^-.
[HPO4^2-] = 0.5 - x
[H2PO4^-] = x
Substituting these expressions into the above equation:
(0.5 - x)/x = 10^(pH - pKa)
Solving this equation to find x will give you the concentration of H2PO4^- in the buffer solution. Then, you can substitute this value into [HPO4^2-] = 0.5 - x to find the concentration of HPO4^2- in the buffer solution.
Once you have determined the molar concentrations of H2PO4^- and HPO4^2-, you can use their molar masses to calculate the amount of grams of Na2HPO4 and NaH2PO4 needed to prepare the 200 mL buffer solution using the formula:
mass (g) = molar concentration (M) × molar mass (g/mol) × volume (L)
Remember to convert the volume from mL to L before calculations.
In summary, calculating the amount of grams of Na2HPO4 and NaH2PO4 to prepare the buffer solution involves writing the Ka expression, determining the pH of the buffer solution, using the Henderson-Hasselbalch equation, and solving the equations to find the molar concentrations of H2PO4^- and HPO4^2-. Finally, you can calculate the mass of Na2HPO4 and NaH2PO4 using their molar concentrations, molar masses, and volume of the buffer solution.