Using a 0.20 M phosphate buffer with a pH of 6.5, you add 0.72 mL of 0.46 M NaOH to 58 mL of the buffer. What is the new pH of the solution? (Enter your answer to three significant figures.)

I don't even know where to begin!! I just need a set up of the problem - without answers

You have two/three problems in one here. First I would determine the base and acid concentrations in the initial buffer. To do that use

pH = pKa + log (base)/(acid)
and solve for base/acid ratio.
Then you know acid + base = 0.2

Solve those two equation simultaneously to determine (H2PO4^-), the acid, and (HPO4^=), the base. I would then convert that to mols (or millimols) for the 58 mL sample. Let a = millimoles acid and b millimols base

............H2PO4^- + OH^- ==> HPO4^=
I.............a........0........b
add................mL x M = c........
C............ a-c.....-c........+c
E.............a-c......0........b+c

Then plug the E line back into a new HH equation and solve for the new pH.

No problem! Let's break down the problem and lay out a plan to solve it step by step:

1. Firstly, we have a phosphate buffer solution with a concentration of 0.20 M and a pH of 6.5. This means that the buffer solution contains both a weak acid and its conjugate base that can resist changes in pH when small amounts of acid or base are added.

2. Next, we are adding 0.72 mL of 0.46 M NaOH to the buffer solution. NaOH is a strong base, and when added to a buffer solution, it will react with the weak acid component of the buffer.

3. To determine the new pH of the solution, we need to find out how the concentration of the weak acid component changes after the addition of NaOH and how that affects the pH of the buffer solution.

4. To find this, we can use the principles of acid-base reactions and the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the concentration of its weak acid and conjugate base components.

5. We can start by calculating the initial amounts (in moles) of the weak acid and its conjugate base in the buffer solution by multiplying the initial concentration (0.20 M) by the volume (58 mL).

6. Next, using stoichiometry, we can determine the amount (in moles) of the weak acid that reacts with the added NaOH by multiplying the volume of NaOH (0.72 mL) by its concentration (0.46 M).

7. After the reaction, the remaining amount (in moles) of the weak acid in the buffer solution can be found by subtracting the moles of the weak acid that reacted with NaOH from the initial moles of the weak acid in the buffer solution.

8. Then, we can use the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]), to calculate the new pH of the buffer solution, where pKa is the logarithmic acidity constant of the weak acid and [A-] and [HA] represent the concentrations (in moles per liter) of the conjugate base and weak acid, respectively.

9. Finally, we can substitute the calculated values into the Henderson-Hasselbalch equation and solve for the new pH.

By following these steps, you'll be able to determine the new pH of the solution accurately.