You want to prepare a pH=4.50 buffer using sodium acetate and glacial acetic acid. You have on hand 300 mL of 0.100 M sodium acetate. How many grams of glacial (water free) acetic acid should you add to prepare the buffer? (Ka of acetic acid is 1.8e-5 at: 25 degrees Celsius)
To prepare a pH=4.50 buffer, we need to calculate the amount of glacial acetic acid (CH3COOH) needed to be added to the solution containing sodium acetate (CH3COONa).
The Henderson-Hasselbalch equation can be used to find the ratio of the concentration of the weak acid and its conjugate base in the buffer solution:
pH = pKa + log([A-]/[HA])
Given:
pH = 4.50
Ka = 1.8e-5
Rearranging the equation:
log([A-]/[HA]) = pH - pKa
Taking the antilog (raised to the power of 10) of both sides:
[A-]/[HA] = 10^(pH - pKa)
Substituting the values:
[A-]/[HA] = 10^(4.50 - (-5))
Simplifying the equation:
[A-]/[HA] = 10^9.5
Next, we can calculate the molar concentration of sodium acetate using the given information:
0.100 M = [A-]
We can assume that the concentration of glacial acetic acid will be equal to [HA]. Therefore, to calculate the amount of glacial acetic acid required, we need to find its molar concentration.
Now, we know that:
[A-]/[HA] = 10^9.5
Substituting the known values:
0.100 M/[HA] = 10^9.5
Rearranging the equation to solve for [HA]:
[HA] = 0.100 M / (10^9.5)
Calculating the value:
[HA] = 3.16228e-12 M
To convert the molar concentration of glacial acetic acid to grams, we need to use its molar mass.
The molar mass of acetic acid (CH3COOH) is:
Molar mass = 12.01 g/mol (C) + 1.01 g/mol (H) + 12.01 g/mol (C) + 16.00 g/mol(O) + 1.01 g/mol (H)
Molar mass = 60.05 g/mol
To find the mass of acetic acid needed, we can use the following formula:
Mass = Molar concentration (mol/L) * Volume (L) * Molar mass (g/mol)
Substituting the known values:
Mass = 3.16228e-12 M * 0.300 L * 60.05 g/mol
Calculating the value:
Mass ≈ 5.67e-11 g
Therefore, you should add approximately 5.67e-11 grams of glacial acetic acid (CH3COOH) to prepare the pH=4.50 buffer solution.