To prepare a 0.5 M sodium citrate buffer at pH 8.5, you will need to mix the appropriate amounts of sodium citrate and citric acid. Here's how you can do it:

  1. Calculate the molar ratio of sodium citrate to citric acid needed to achieve the desired pH using the Henderson-Hasselbalch equation:

    pH = pKa + log([A-]/[HA])

    For sodium citrate/citric acid buffer system:

    • pKa = 3.13 (for the first dissociation of citric acid)
    • [A-]/[HA] = 10^(pH - pKa)

    Plug in the values:
    pH = 8.5
    pKa = 3.13
    [A-]/[HA] = 10^(8.5 - 3.13) = 10^5.37

    This gives you the molar ratio of sodium citrate to citric acid.

  2. Determine the total molarity of the buffer. In this case, it's 0.5 M.

  3. Calculate the amount of sodium citrate needed using the molar ratio and the total molarity:

    Molar ratio = [Na3C6H5O7] / [C6H8O7]

    Let x be the amount of citric acid (C6H8O7) needed. Then, 10^5.37 = (0.5 - x) / x

    Solve for x:

    x = 0.5 / (10^5.37 + 1)

    x ≈ 0.499 M

  4. Calculate the amount of sodium citrate needed:

    0.5 M - 0.499 M ≈ 0.001 M

    So, you need approximately 0.001 moles of sodium citrate per liter of buffer.

  5. Weigh out the appropriate amount of sodium citrate dihydrate (Na3C6H5O7·2H2O) to add to your solution. The molar mass of sodium citrate dihydrate is 294.10 g/mol.

    Mass of sodium citrate = 0.001 moles * 294.10 g/mol = 0.2941 g

  6. Dissolve the sodium citrate in a small volume of distilled water to make a stock solution.

  7. Now, calculate the amount of citric acid needed to make up the difference in molarity:

    0.5 M - 0.001 M ≈ 0.499 M

    So, you need approximately 0.499 moles of citric acid per liter of buffer.

  8. Weigh out the appropriate amount of anhydrous citric acid (C6H8O7) to add to your solution. The molar mass of citric acid is 192.13 g/mol.

    Mass of citric acid = 0.499 moles * 192.13 g/mol = 95.91 g

  9. Dissolve the citric acid in a small volume of distilled water to make a stock solution.

  10. Once you have both stock solutions, mix them together and dilute to the desired volume with distilled water, while monitoring the pH with a pH meter or pH indicator strips. Adjust the pH if necessary by adding small amounts of sodium hydroxide (NaOH) for increasing the pH or citric acid for decreasing the pH.

  11. After reaching the desired pH, the buffer is ready for use.

Note: Ensure all calculations are done carefully, and measurements are accurate. Also, wear appropriate personal protective equipment when handling chemicals.