How would you prepare 1.000 L of a 0.200 M phosphate buffer at pH 7.02 using crystalline Na2HPO4 and a solution of 1.000 M HCl?
To prepare a phosphate buffer at a specific pH, you need to calculate the amount of Na2HPO4 and HCl required to achieve the desired concentration and pH. Here are the steps to prepare 1.000 L of a 0.200 M phosphate buffer at pH 7.02 using Na2HPO4 and HCl:
Step 1: Determine the pH range
Phosphate buffers can be effective within a pH range that depends on the pKa values of the phosphoric acid (H3PO4) and its conjugate base, dihydrogen phosphate (H2PO4-). In this case, we are targeting a pH of 7.02.
Step 2: Calculate the pKa value
The pKa value of phosphoric acid is a measure of its acidity. The pKa value of H3PO4 is approximately 2.15. To determine the pKa value of H2PO4-, you can use the Henderson-Hasselbalch equation:
pH = pKa + log([H2PO4-]/[H3PO4])
Solving for pKa:
pKa = pH - log([H2PO4-]/[H3PO4])
Using the given pH of 7.02:
pKa = 7.02 - log([H2PO4-]/[H3PO4])
Step 3: Calculate the ratio of [H2PO4-] to [H3PO4]
To create a buffer, you need a reasonable ratio of [H2PO4-] to [H3PO4]. A commonly used ratio is 1:1. To achieve this ratio, [H2PO4-] and [H3PO4] must be equal.
[H2PO4-] = [H3PO4] = 0.200 M
Step 4: Calculate the amount of Na2HPO4 needed
Na2HPO4 is a solid compound, and you need to determine the mass required to achieve the desired concentration.
Molar mass of Na2HPO4 = atomic mass of Na (22.99 g/mol) + 2 * atomic mass of H (1.01 g/mol) + atomic mass of P (30.97 g/mol) + 4 * atomic mass of O (16.00 g/mol) = 141.96 g/mol
To calculate the mass required:
Mass (g) = Volume (L) × Concentration (M) × Molar Mass (g/mol)
Substituting the values:
Mass (Na2HPO4) = 1.000 L × 0.200 M × 141.96 g/mol
Step 5: Prepare the Na2HPO4 solution
Use the calculated mass of Na2HPO4 to prepare a solution by dissolving it in water and bringing the total volume to 1.000 L.
Step 6: Calculate the amount of HCl needed
HCl is a solution with a known concentration of 1.000 M. To calculate the volume of HCl required, you can use the equation:
Concentration (C1) × Volume (V1) = Concentration (C2) × Volume (V2)
Substituting the values:
1.000 M × Volume (V1) = 0.200 M × 1.000 L
Solving for V1:
Volume (V1) = (0.200 M × 1.000 L) / 1.000 M
Step 7: Prepare the HCl solution
Measure the calculated volume of 1.000 M HCl and add it to the Na2HPO4 solution prepared in step 5. Make sure to mix them thoroughly to create the phosphate buffer.
By following these steps, you can prepare 1.000 L of a 0.200 M phosphate buffer at pH 7.02 using crystalline Na2HPO4 and a solution of 1.000 M HCl.