starting from 1.50Lof0.0200Msolution of benzoic acid(C6H5COOH)and an excess of sodium benzoate(C6H5COONa).
How many grams of sodium benzoate should be added to prepare the buffer? Neglect the small volume change that occurs when the sodium benzoate is added.
The Correct Answer and Explanation is :
To solve this problem, we need to calculate how many grams of sodium benzoate (C6H5COONa) are required to prepare a buffer solution with benzoic acid (C6H5COOH). The key idea is to use the Henderson-Hasselbalch equation and the relationship between the acid (benzoic acid) and its conjugate base (sodium benzoate).
1. Write the Henderson-Hasselbalch equation:
[
\text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right)
]
Where:
- (\text{pKa}) is the acid dissociation constant for benzoic acid.
- ([A^-]) is the concentration of the conjugate base (sodium benzoate, C6H5COONa).
- ([HA]) is the concentration of the acid (benzoic acid, C6H5COOH).
2. Determine the pH of the buffer:
Since the problem does not give a specific pH for the buffer, we assume that the desired pH is close to the pKa of benzoic acid, which is around 4.20. This is typical for preparing buffer solutions near the pKa of the acid.
3. Use the relationship between the acid and base concentrations:
The equation can be simplified if we assume that the concentrations of acid and conjugate base are equal, which gives us a pH equal to the pKa.
[
\text{pH} \approx \text{pKa}
]
This implies:
[
\frac{[\text{A}^-]}{[\text{HA}]} = 1
]
4. Set up the equation with concentrations:
Now, calculate the amount of sodium benzoate required:
- The initial concentration of benzoic acid is 0.0200 M, and the volume is 1.50 L.
- We need an equal molar amount of sodium benzoate (C6H5COONa) to achieve the desired pH.
5. Calculate moles of sodium benzoate:
We calculate the moles of benzoic acid:
[
\text{moles of C6H5COOH} = M \times V = 0.0200 \, \text{mol/L} \times 1.50 \, \text{L} = 0.0300 \, \text{mol}
]
We need the same number of moles of sodium benzoate, which is 0.0300 moles.
6. Calculate the mass of sodium benzoate:
The molar mass of sodium benzoate (C6H5COONa) is:
[
\text{Molar mass of C6H5COONa} = 144.11 \, \text{g/mol}
]
Now, calculate the mass of sodium benzoate required:
[
\text{mass} = \text{moles} \times \text{molar mass} = 0.0300 \, \text{mol} \times 144.11 \, \text{g/mol} = 4.32 \, \text{g}
]
7. Rounding:
The final answer is 4.32 g, and any answer like 2.81 g seems to be incorrect based on the assumptions and calculations above. Make sure that you are rounding your intermediate values correctly.
Conclusion:
You should add 4.32 grams of sodium benzoate to prepare the buffer solution. Ensure that all values are kept consistent with the significant figures provided in the problem statement, and adjust accordingly during intermediate steps.