To prepare 500.00 mL of 0.300 M buffer with a pH of 7.4. NaH2PO4/Na2HPO4 How many grams of each should be added to the 500.00mL flask to create this buffer?
pH = pK2 + log(base)/(acid)
7.4 = pK2 + log (base)/(acid)
Solve for (base)/(acid) = ?. That is equation 1.
Then
base + acid = 500 x 0.3 is equation 2.
Solve those two equations simultaneously for base and acid (in millimoles since 500 x 0.3 gives millimols).
That gives you millimols base and millimols acid. I would convert to mols, then grams = mols x molar mass.
To calculate the amount of NaH2PO4 and Na2HPO4 needed to create a buffer with a specific pH, we need to consider the Henderson-Hasselbalch equation for a buffer:
pH = pKa + log ([A-]/[HA]),
where pH is the desired pH, pKa is the acid dissociation constant of the buffer, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.
In this case, NaH2PO4 is the weak acid (HA) and Na2HPO4 is its conjugate base (A-). The pKa for the phosphate buffer system is 7.21 at 25°C.
We can start by rearranging the Henderson-Hasselbalch equation to solve for the ratio of [A-] to [HA]:
[A-]/[HA] = 10^(pH - pKa).
Next, we need to determine the total concentration of the buffer solution (0.300 M) and the volume (500.00 mL).
Concentration (C) = moles (n) / volume (V).
Rearranging this equation gives us:
moles (n) = Concentration (C) * volume (V).
To find the mass (m) of each compound, we can use the molar mass (M) of NaH2PO4 and Na2HPO4.
Mass (m) = moles (n) * molar mass (M).
Let's plug in the given values and calculate the amount of NaH2PO4 and Na2HPO4 needed:
1. Calculate the ratio of [A-] to [HA]:
[A-]/[HA] = 10^(7.4 - 7.21) = 1.831
2. Calculate the concentration of NaH2PO4 and Na2HPO4:
Total concentration of the buffer = 0.300 M.
Since NaH2PO4 and Na2HPO4 will contribute equally to the total concentration of the buffer, each component will have a concentration of 0.300 M / 2 = 0.150 M.
3. Calculate the moles of NaH2PO4 and Na2HPO4:
Moles (n) = Concentration (C) * Volume (V).
Moles of NaH2PO4 = 0.150 M * 0.500 L = 0.075 moles.
Moles of Na2HPO4 = 0.150 M * 0.500 L = 0.075 moles.
4. Calculate the mass of NaH2PO4 and Na2HPO4:
Mass (m) = Moles (n) * Molar mass (M).
The molar mass of NaH2PO4 is 119.98 g/mol, and the molar mass of Na2HPO4 is 141.96 g/mol.
Mass of NaH2PO4 = 0.075 moles * 119.98 g/mol = 8.9995 g ≈ 9.00 g.
Mass of Na2HPO4 = 0.075 moles * 141.96 g/mol = 10.697 g ≈ 10.70 g.
Therefore, to prepare a 500.00 mL buffer solution with a pH of 7.4 and a concentration of 0.300 M using NaH2PO4 and Na2HPO4, you will need approximately 9.00 grams of NaH2PO4 and 10.70 grams of Na2HPO4.