You prepare a buffer solution by dissolving 2.00 g each of benzoic acid, C6H5COOH, and
sodium benzoate, NaC6H5COO, in 750.0 mL water. (2 pts each)
a) What is the pH of this buffer? Assume that the solution’s volume is 750.0 mL.
b) If 0.55 mL of 12 M HCl is added to 0.750 L of this buffer solution, what will be the pH
of the resulting solution?
c) If 0.35 mL of 15 M NH3 is added to 0.750 L of this buffer solution, what will be the pH
of the resulting solution?
My calculations are estimates. You should recalculate everything that follows.
a. Let's call benzoic acid, C6H5COOH, HBz and sodium benzoate, NaBz.
HBz molar mass = 122, NaBz molar mass = 144
mols HBz = 2/122 = about 0.016
(HBz) = 0.016/0.750 = ? M
mols NaBz = 2/144 = about 0.014
(NaBz) = 0.014/0.750 = ? M
pH = pKa + log (NaBz)/(HBz) = ?
b. I prefer to wor in millimoles for this. You can convert to M if you wish.
millimoles HBz initially = about 16. Remember that's just an estimate.
millimoles NaBz = 14
HCl added = 0.55 mL x 12 M HCl = 6.6 millimoles
.....................Bz^- + H^+ ==> HBz
Initial............14........0..............16
add.........................6.6.................
change........-6.6....-6.6.............+6.6
equilibrium..7.4.........0...............6.6
The equilibrium line is millimoles you have in the final solution. (Bz^-) = millimoles/mL = 7.4/750 =? M
M HBz = 6.6/750 = ? M
Plug these into the Henderson-Hasselbalch equation and solve for pH.
c. Same thing as b except it's base being added and not acid.
You want to start with HBz + NH3 ==> NH4Bz
Post your work if you get stuck.
To find the pH of the buffer solution, we need to determine the concentration of the acid and its conjugate base. We can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log([salt]/[acid])
where pKa is the dissociation constant of the acid, [salt] is the concentration of the conjugate base, and [acid] is the concentration of the acid.
a) Calculate the concentration of the acid (benzoic acid):
molar mass of benzoic acid = 122.12 g/mol
moles of benzoic acid = mass / molar mass = 2.00 g / 122.12 g/mol = 0.01637 mol
concentration of benzoic acid = moles / volume = 0.01637 mol / 0.750 L = 0.0218 M
b) Calculate the concentration of the conjugate base (sodium benzoate):
molar mass of sodium benzoate = 144.11 g/mol (1 sodium atom + 1 benzoate ion)
moles of sodium benzoate = mass / molar mass = 2.00 g / 144.11 g/mol = 0.01387 mol
concentration of sodium benzoate = moles / volume = 0.01387 mol / 0.750 L = 0.0185 M
The pKa of benzoic acid is 4.20.
a) Substitute the values into the Henderson-Hasselbalch equation:
pH = 4.20 + log(0.0185 / 0.0218) = 4.20 + log(0.8466) ≈ 4.20 + (-0.0714) = 4.13
Therefore, the pH of the buffer solution is approximately 4.13.
b) When 0.55 mL of 12 M HCl is added to the buffer solution, we need to calculate the resulting concentration of the acid and use the Henderson-Hasselbalch equation again.
moles of HCl = concentration x volume = 12 M x 0.00055 L = 0.0066 mol
moles of benzoic acid after addition = initial moles - moles of HCl = 0.01637 mol - 0.0066 mol = 0.00977 mol
concentration of benzoic acid after addition = moles / volume = 0.00977 mol / 0.750 L = 0.013 L
Substitute the new values into the Henderson-Hasselbalch equation:
pH = 4.20 + log(0.0185 / 0.013) = 4.20 + log(1.423) ≈ 4.20 + 0.1529 = 4.35
Therefore, the pH of the resulting solution after adding HCl is approximately 4.35.
c) When 0.35 mL of 15 M NH3 (ammonia) is added to the buffer solution, we need to calculate the resulting concentration of the conjugate base (sodium benzoate) and use the Henderson-Hasselbalch equation again.
moles of NH3 = concentration x volume = 15 M x 0.00035 L = 0.00525 mol
moles of sodium benzoate after addition = initial moles + moles of NH3 = 0.01387 mol + 0.00525 mol = 0.01912 mol
concentration of sodium benzoate after addition = moles / volume = 0.01912 mol / 0.750 L = 0.0255 M
Substitute the new values into the Henderson-Hasselbalch equation:
pH = 4.20 + log(0.0255 / 0.0218) = 4.20 + log(1.169) ≈ 4.20 + 0.0670 = 4.27
Therefore, the pH of the resulting solution after adding NH3 is approximately 4.27.
To determine the pH of a buffer solution, we can use the Henderson-Hasselbalch equation:
pH = pKa + log ([A-] / [HA])
Where:
- pH is the measure of the solution's acidity or basicity
- pKa is the logarithmic acid dissociation constant of the acid in the buffer
- [A-] is the concentration of the conjugate base
- [HA] is the concentration of the weak acid
Let's calculate the pH for each part of the question:
a) First, we need to find the pKa value for the benzoic acid (HA). A pKa table or a reliable reference source can provide this information. In this case, the pKa of benzoic acid is 4.20.
Next, we need to calculate the concentration of the benzoic acid (HA) and sodium benzoate (A-).
Given:
- mass of benzoic acid (HA) = 2.00 g
- mass of sodium benzoate (A-) = 2.00 g
- volume of water = 750.0 mL
First, convert the volumes to liters:
- volume of water = 750.0 mL = 0.750 L
Next, calculate the molar mass of benzoic acid (HA) and sodium benzoate (A-):
- molar mass of benzoic acid (HA) = 122.12 g/mol
- molar mass of sodium benzoate (A-) = 144.11 g/mol
Now, calculate the moles of each compound:
- moles of benzoic acid (HA) = (mass of benzoic acid (HA)) / (molar mass of benzoic acid (HA))
- moles of sodium benzoate (A-) = (mass of sodium benzoate (A-)) / (molar mass of sodium benzoate (A-))
Finally, calculate the concentrations of each compound:
- concentration of benzoic acid (HA) = (moles of benzoic acid (HA)) / (volume of water)
- concentration of sodium benzoate (A-) = (moles of sodium benzoate (A-)) / (volume of water)
Now we can substitute these values into the Henderson-Hasselbalch equation to calculate the pH:
- pH = 4.20 + log ([A-] / [HA])
b) To determine the pH of the resulting solution after adding HCl, we need to use the Henderson-Hasselbalch equation again. However, this time we will be working with a new concentration of [A-] and [HA]. We can follow the same steps as before to calculate the new concentrations and, subsequently, the pH.
c) Similarly, to determine the pH after adding NH3, we need to recalculate the new concentrations of [A-] and [HA] using the given values. Then we can use the Henderson-Hasselbalch equation to calculate the new pH.
Remember to adjust the volumes and concentrations accordingly when adding new substances to the buffer solution.