A buffer containing 0.2832 M of acid, HA, and 0.1504 M of its conjugate base, A−, has a pH of 2.36. What is the pH after 0.0015 mol NaOH is added to 0.5000 L of this solution?

mols HA = 0.2832M x 0.5L = about 0.142

moles A^- = 0.1504 x 0.5L = 0.0752

.............HA + OH^- ==> A^- + H2O
initial...0.142....0....0.0752
...add..........0.0015................
change..-0.0015.-0.0015...+0.0015
equil.....0.1405...0.......0.0015
Now substitute into the HH equation and solve for pH.

I forgot to note that you need to confirm all of the numbers as I just wrote the first or second significant figures.

To solve this problem, we need to consider the reaction that occurs when NaOH is added to the buffer solution. NaOH is a strong base that dissociates completely in water, releasing hydroxide ions (OH-).

The reaction between the hydroxide ions and the acid, HA, in the buffer is as follows:
HA + OH- → A- + H2O

Given that 0.0015 mol of NaOH is added to 0.5000 L of the buffer solution, we need to determine the new concentrations of the acid (HA) and its conjugate base (A-) after the reaction.

Step 1: Calculate the initial moles of acid (HA) and conjugate base (A-) in the buffer.
moles of HA = volume of buffer (L) x concentration of HA (M)
moles of HA = 0.5000 L x 0.2832 M = 0.1416 mol

moles of A- = volume of buffer (L) x concentration of A- (M)
moles of A- = 0.5000 L x 0.1504 M = 0.0752 mol

Step 2: Calculate the moles of acid (HA) and conjugate base (A-) remaining after the reaction.
moles of HA remaining = moles of HA initial - moles of OH- reacted
moles of HA remaining = 0.1416 mol - 0.0015 mol = 0.1401 mol

moles of A- formed = moles of OH- reacted = 0.0015 mol

Step 3: Calculate the new concentrations of acid (HA) and conjugate base (A-).
concentration of HA = moles of HA remaining / volume of buffer (L)
concentration of HA = 0.1401 mol / 0.5000 L = 0.2802 M

concentration of A- = moles of A- formed / volume of buffer (L)
concentration of A- = 0.0015 mol / 0.5000 L = 0.0030 M

Step 4: Calculate the new pH of the buffer solution.
Since we are working with a buffer solution, we can use the Henderson-Hasselbalch equation to calculate the pH:
pH = pKa + log10(A-/HA)

First, we need to calculate the pKa using the initial concentrations of the acid (HA) and its conjugate base (A-).
pKa = -log10(Ka)

Now, we can calculate the new pH using the updated concentrations of the acid (HA) and conjugate base (A-) and the pKa value.
pH = pKa + log10(A-/HA)
pH = -log10(Ka) + log10(A-/HA)

Remember that log10(A-/HA) is equal to -log10(HA/A-).
pH = -log10(Ka) - log10(HA/A-)

Since we know that the pH of the initial buffer solution is 2.36, we can rearrange the equation and solve for pKa.
2.36 = -log10(Ka) - log10(HA/A-)

Step 5: Calculate the new pH after the NaOH is added.
Now that we have calculated the pKa, we can use it along with the updated concentrations of the acid (HA) and conjugate base (A-) to find the new pH.
pH = -log10(Ka) - log10(HA/A-)

Substitute the known values and calculate the new pH.

This step involves calculating logarithms and summing them, which can be done using a calculator or computer software.

By following these steps, you can determine the pH of the solution after 0.0015 mol of NaOH is added to 0.5000 L of the initial buffer solution.