20 ml of 0.1 M acetic acid was mixed with 25 ml of 0.1 M Sodium Acetate. The pH was measured to be 4.43. 5 ml of 0.1 M Sodium Hydroxide was added to the buffer and the pH was measured to be 4.60. Calculate the pH of the buffer before and after the addition of NaOH.
I don't understand the problem. The problem states that the pH = 4.43, but the calculation gives a different number.
78
To calculate the pH of the buffer before and after the addition of Sodium Hydroxide (NaOH), we need to consider the dissociation of acetic acid (CH3COOH) and sodium acetate (CH3COONa) in water.
1. Calculate the moles of acetic acid:
The initial volume of acetic acid is 20 ml, and the initial molarity is 0.1 M. So, the number of moles of acetic acid can be calculated using the formula:
Moles = Volume (in liters) * Molarity
= 20 ml * (1 L/1000 ml) * 0.1 M
= 0.002 moles
2. Calculate the moles of sodium acetate:
The initial volume of sodium acetate is 25 ml, and the initial molarity is also 0.1 M. So, the number of moles of sodium acetate can be calculated using the same formula as above:
Moles = Volume (in liters) * Molarity
= 25 ml * (1 L/1000 ml) * 0.1 M
= 0.0025 moles
3. Calculate the total moles of acetic acid and acetate:
Since acetic acid and sodium acetate react and form a buffer solution, we need to consider the total moles of acetic acid and acetate. In this case, the moles of acetic acid and acetate are the same because their initial concentrations are equal.
Total moles = Moles of acetic acid + Moles of acetate
= 0.002 moles + 0.0025 moles
= 0.0045 moles
4. Calculate the concentration of acetic acid and acetate in the solution:
The initial volume of the solution is the sum of the volumes of acetic acid and sodium acetate, which is 20 ml + 25 ml = 45 ml. We convert this to liters:
Volume = 45 ml * (1 L/1000 ml)
= 0.045 L
The final concentrations can be calculated using the formula:
Final concentration (Cf) = Moles / Volume
= 0.0045 moles / 0.045 L
= 0.1 M
So, both the acetic acid and acetate concentrations in the buffer solution are 0.1 M.
5. Calculate the pH of the buffer before adding NaOH:
The Henderson-Hasselbalch equation allows us to calculate the pH of the buffer:
pH = pKa + log([Acetate]/[Acetic acid])
The pKa value of acetic acid is 4.74.
Using the concentrations of acetate and acetic acid (both 0.1 M):
pH = 4.74 + log(0.1/0.1)
= 4.74 + log(1)
= 4.74 + 0
= 4.74
Therefore, the pH of the buffer before adding NaOH is 4.74.
6. Calculate the pH of the buffer after adding NaOH:
Since the volume of the solution changes after adding NaOH, we need to consider the new volume. In this case, the total volume becomes 45 ml + 5 ml = 50 ml.
New volume = 50 ml * (1 L/1000 ml)
= 0.05 L
The new concentration of acetic acid and acetate after adding NaOH can be calculated as follows:
New concentration (Cn) = Moles / New volume
= 0.0045 moles / 0.05 L
= 0.09 M
Using the same Henderson-Hasselbalch equation:
pH = pKa + log([Acetate]/[Acetic acid])
pH = 4.74 + log(0.09/0.09)
= 4.74 + log(1)
= 4.74 + 0
= 4.74
Therefore, the pH of the buffer after adding NaOH remains 4.74.