To determine the amount of sodium ethanoate (CH3COONa) needed to create a buffer solution of pH 5 with a given concentration of acetic acid, we can use the Henderson-Hasselbalch equation:
pH = pKa + log (salt/acid)
In this case, the pKa is given as 4.75, and we want the pH to be 5. We need to calculate the ratio of salt (CH3COONa) to acid (acetic acid) required to achieve this pH.
Let's denote the concentration of sodium ethanoate as [CH3COONa] and the concentration of acetic acid as [CH3COOH].
Using the Henderson-Hasselbalch equation:
5 = 4.75 + log ([CH3COONa] / [CH3COOH])
Rearranging the equation:
0.25 = log ([CH3COONa] / [CH3COOH])
Now, we can convert the equation to exponential form:
10^0.25 = [CH3COONa] / [CH3COOH]
Simplifying:
1.78 = [CH3COONa] / [CH3COOH]
Since the concentration of acetic acid is given as 0.01 dm³ (which is equivalent to 0.01 mol/dm³), we substitute this value into the equation:
1.78 = [CH3COONa] / 0.01
Cross-multiplying:
[CH3COONa] = 1.78 * 0.01
[CH3COONa] = 0.0178 mol/dm³
Therefore, you would need to dissolve 0.0178 mol/dm³ (or 0.0178 M) of sodium ethanoate (CH3COONa) in 1 dm³ of acetic acid with a concentration of 0.01 dm³ (or 0.01 M) to create a buffer solution with a pH value of 5 and a pKa value of 4.75.