Calculate the volume 0.1 M of acetic acid and 0.1 M sodium acetate required to prepare 300 mL of 0.05 M acetate buffer solution at pH 5.5.
To calculate the volume of 0.1 M acetic acid and 0.1 M sodium acetate required to prepare a 0.05 M acetate buffer solution, we need to use the Henderson-Hasselbalch equation and take into account the desired pH of the buffer solution.
The Henderson-Hasselbalch equation is:
pH = pKa + log ([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution (pH 5.5 in this case)
- pKa is the dissociation constant of the weak acid (acetic acid in this case)
- [A-] is the concentration of the conjugate base (acetate ion)
- [HA] is the concentration of the weak acid (acetic acid)
First, we need to find the pKa value of acetic acid. The pKa of acetic acid is approximately 4.76.
Next, we substitute the known values into the Henderson-Hasselbalch equation:
pH = 4.76 + log ([A-]/[HA])
5.5 = 4.76 + log ([A-]/[HA])
Rearranging the equation, we get:
log ([A-]/[HA]) = 5.5 - 4.76
log ([A-]/[HA]) = 0.74
Now, we need to convert the log term into an actual ratio of concentrations. We can do this by taking the antilog of both sides of the equation:
[A-]/[HA] = antilog(0.74)
[A-]/[HA] = 5.764
Since the ratio of [A-] to [HA] is 5.764, the concentration of acetate ion ([A-]) is 5.764 times greater than the concentration of acetic acid ([HA]).
Now we know the ratio of the two components required in the buffer solution. To calculate the actual volume of each component, we can use the following equation:
(0.05 M) = [A-] + [HA]
Where:
- (0.05 M) is the desired concentration of the buffer solution
- [A-] and [HA] are the concentrations of acetate ion and acetic acid, respectively
To simplify the calculation, let's assume the final volume of the buffer solution is 1 liter (1000 mL). We can then use the volume ratios to find the actual volumes of the components.
To find the volume of acetic acid (0.1 M), we can use the equation:
Volume(acetic acid) = ([HA] / (0.1 M)) * (total volume of buffer solution)
Volume(acetic acid) = ([HA] / 0.1) * 1000 mL
Similarly, to find the volume of sodium acetate (0.1 M), we can use the equation:
Volume(sodium acetate) = ([A-] / (0.1 M)) * (total volume of buffer solution)
Volume(sodium acetate) = ([A-] / 0.1) * 1000 mL
Now, since we know the ratio of [A-] to [HA] is 5.764, we can substitute this ratio into the volume equations:
Volume(acetic acid) = (1 / 5.764) * 1000 mL
Volume(acetic acid) ≈ 173.3 mL
Volume(sodium acetate) = (5.764 / 5.764) * 1000 mL
Volume(sodium acetate) = 826.7 mL
Therefore, to prepare a 300 mL buffer solution with a pH of 5.5, you would require approximately 173.3 mL of 0.1 M acetic acid and 826.7 mL of 0.1 M sodium acetate.