1. Understand the Chemistry

* Benzoic acid (C₆H₅COOH) is a weak acid.

* Sodium benzoate (C₆H₅COONa) is the salt of its conjugate base.

* When you mix a weak acid and its conjugate base, you create a buffer solution.

2. The Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer to the pKa of the weak acid and the ratio of the concentrations of the conjugate base and weak acid:

pH = pKa + log ([conjugate base] / [weak acid])

3. Information Given

* pH: 4.30

* Volume of benzoic acid solution: 160.0 mL

* Concentration of benzoic acid solution: 0.15 M

* pKa of benzoic acid: 4.20 (you'll likely need to look this up or be given it)

4. Calculate the Ratio of Conjugate Base to Weak Acid

* Rearrange the Henderson-Hasselbalch equation to solve for the ratio:

[conjugate base] / [weak acid] = 10^(pH - pKa)

* Plug in the values:

[conjugate base] / [weak acid] = 10^(4.30 - 4.20) = 1.0

5. Calculate the Moles of Benzoic Acid

* Moles = Concentration × Volume (in Liters)

* Moles of benzoic acid = 0.15 M × 0.160 L = 0.024 moles

6. Calculate the Moles of Sodium Benzoate Needed

* Since the ratio of [conjugate base] / [weak acid] is 1.0, we need an equal number of moles of sodium benzoate as benzoic acid:

* Moles of sodium benzoate = 0.024 moles

7. Calculate the Mass of Sodium Benzoate

* Mass = Moles × Molar Mass

* Molar mass of sodium benzoate (C₆H₅COONa) = 144.11 g/mol

* Mass of sodium benzoate = 0.024 moles × 144.11 g/mol = 3.46 g

Therefore, you need to add approximately 3.46 grams of sodium benzoate to the benzoic acid solution to create a buffer with a pH of 4.30.