Find the theoretical pH of .01M and .05M benzoic acid buffer when 2ml of .1MNaOH was added to each buffer.
This problem relies on the Henderson-Hasselbalch Equation which relates the pKa of a buffer to changes in the solution such as the addition of strong acids or strong bases.
So the first thing to do in this problem is to find the pKa of benzoic acid. That can be done using a table that already exists.
The pKa of benzoic acid is 4.202.
So the next step is to figure out how the 2 mL of 0.1 M NaOH affected the acid and it's conjugate base. The equation is:
pH = pKa + log([A-]/[HA])
Where [A-] is the concentration of the conjugate base and [HA] is the concentration of the acid. For the sake of this problem we will say the NaOH is added to a liter of each of the buffer solutions.
When the base is added it will react with the buffer to increase the amount of the conjugate base and decrease the amount of the acid.
Moles of NaOH introduced to the buffer solution:
.002 L * 0.1 M = 0.0004 moles of OH-
So this is how 0.0004 moles of OH- affects the solution:
benzoic acid before NaOH: 1 L * 0.01 M = 0.01 moles H+
benzoic acid after NaOH: 0.01 moles H+ - 0.0004 moles = 0.0096 moles H+
benzoate (conjugate base) before NaOH: 1 L * 0.01 M = 0.01 moles
benzoate after NaOH: 0.01 moles + 0.0004 = 0.0104 moles
Change in pH:
pH = 4.202 - log(.0096/.0104)
pH = 4.237
You can do the one with the 0.05 M benzoic acid.
I made a couple of mistakes
1: Equation is:
pH = pKa + log([A-]/[HA]
Notice addition instead of subtraction
2: Change in pH:
pH = 4.202 + log(.0096/.0104)
pH = 4.167
To find the theoretical pH of a buffer solution after adding a strong base, you'll need to consider the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given by:
pH = pKa + log([A-]/[HA])
Where:
- pH is the desired pH of the buffer solution
- pKa is the dissociation constant of the weak acid (benzoic acid in this case)
- [A-] is the concentration of the conjugate base (benzoate ion)
- [HA] is the concentration of the weak acid (benzoic acid)
First, let's determine the pKa value of benzoic acid. The pKa value can be found using reference sources or calculated experimentally.
Assuming the pKa value of benzoic acid is known, we can calculate the concentrations of [A-] and [HA] in the buffer solution after adding NaOH.
Step 1: Calculate the initial concentrations of benzoic acid (HA) and benzoate ion (A-).
For the 0.01 M benzoic acid buffer:
- [HA] = 0.01 M
- [A-] = 0 M (since there is no initial base present)
For the 0.05 M benzoic acid buffer:
- [HA] = 0.05 M
- [A-] = 0 M (since there is no initial base present)
Step 2: Calculate the final concentrations of benzoic acid (HA) and benzoate ion (A-) after adding NaOH.
When 2 mL of 0.1 M NaOH is added to each buffer, it reacts with benzoic acid (HA) to form water and benzoate ion (A-). The reaction is as follows:
C6H5COOH (benzoic acid) + NaOH → C6H5COO- (benzoate ion) + H2O
The stoichiometry of the reaction suggests that the concentration of the benzoate ion (A-) will be equal to the concentration of NaOH (0.1 M) added, while the concentration of benzoic acid (HA) will decrease by the same amount.
For the 0.01 M benzoic acid buffer:
- [A-] = 0.1 M (since 2 mL of 0.1 M NaOH was added)
- [HA] = 0.01 M - 0.1 M = -0.09 M (0.09 M decrease)
For the 0.05 M benzoic acid buffer:
- [A-] = 0.1 M (since 2 mL of 0.1 M NaOH was added)
- [HA] = 0.05 M - 0.1 M = -0.05 M (0.05 M decrease)
Step 3: Calculate the theoretical pH using the Henderson-Hasselbalch equation.
Given that you have the pKa value of benzoic acid, you can substitute the calculated concentrations into the equation:
pH = pKa + log([A-]/[HA])
Using the values obtained, substitute into the equation and calculate the pH for both the 0.01 M and 0.05 M benzoic acid buffers after adding NaOH.