I don't understand how to work out the volumes of weak acid and strong base to mix to make 1L of buffer when given the concentrations of weak acid and strong base (in my case 0.160M NaOH and 0.200M H3PO4) and the pH required (7.00).

Specifically the textbook is Fundamentals of Analytical chem by skoog. west, holler, and crouch, and the question is 15-21.
Thanks

To determine the volumes of weak acid and strong base needed to make 1L of a buffer at a desired pH, you can use the Henderson-Hasselbalch equation. The Henderson-Hasselbalch equation is given by:

pH = pKa + log([A-]/[HA])

Where pH is the desired pH, pKa is the pKa of the weak acid, [A-] is the concentration of the conjugate base, and [HA] is the concentration of the weak acid.

In this case, you are given the concentrations of the weak acid (0.200M H3PO4) and the strong base (0.160M NaOH), and the desired pH (7.00). However, you haven't provided the pKa of H3PO4.

To solve this problem, you first need to determine the pKa of H3PO4. The pKa can be found in the acid-base table provided in your textbook (Fundamentals of Analytical Chem by Skoog, West, Holler, and Crouch).

Once you know the pKa value, you can rearrange the Henderson-Hasselbalch equation to solve for the ratio of [A-]/[HA]:

[A-]/[HA] = 10^(pH - pKa)

Next, you can calculate the volume of weak acid (H3PO4) to use. Assuming you have started with 1L of solution, the volume of weak acid will be:

Volume of weak acid = (concentration of weak acid) * (total volume) * ([HA]/([A-] + [HA]))

Similarly, you can calculate the volume of strong base (NaOH) to use:

Volume of strong base = (concentration of strong base) * (total volume) * ([A-]/([A-] + [HA]))

In this case, since you are given the concentrations of NaOH and H3PO4 (0.160M and 0.200M, respectively), and the desired pH (7.00), you just need to find the pKa of H3PO4 and then apply the equations above to calculate the volumes of weak acid and strong base.

Please refer to the textbook (Fundamentals of Analytical Chem by Skoog, West, Holler, and Crouch) for the pKa value of H3PO4 and detailed worked examples for buffer calculations.