I tried working this question out with the help already provided, but I couldn't ever get the right answer. If you could possibly explain how to do the problem step by step and include the right answer, I'd greatly appreciate it. Thanks!

What mass of sodium benzoate should be added to 160.0mL of a 0.17M benzoic acid solution in order to obtain a buffer with a pH of 4.30?

To answer this question, we first need to understand the concept of a buffer solution. A buffer solution is a solution that can resist changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base (or a weak base and its conjugate acid).

In this case, we have a benzoic acid solution and we want to create a buffer with a pH of 4.30. To do this, we need to add sodium benzoate, which is the conjugate base of benzoic acid. The sodium benzoate will react with any added acid to maintain the pH of the solution.

To solve this problem, we can follow these steps:

Step 1: Calculate the amount of benzoic acid (C6H5COOH) in moles present in the 160.0 mL solution.

To do this, we will use the formula:

moles = concentration (M) × volume (L)

moles of benzoic acid = 0.17 M × 0.160 L
moles of benzoic acid = 0.0272 mol

Step 2: Determine the required moles of sodium benzoate (C6H5COONa) to obtain the desired pH.

To calculate this, we need to use the Henderson-Hasselbalch equation for the pH of a buffer:

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

where:
pH is the desired pH (4.30)
pKa is the ionization constant of the acid (benzoic acid), which is 4.20
[A-]/[HA] is the ratio of the amounts of the conjugate base (sodium benzoate) to the weak acid (benzoic acid)

By rearranging the equation, we can solve for [A-]/[HA]:

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

[A-]/[HA] = 10^(4.30 - 4.20)
[A-]/[HA] = 10^0.1
[A-]/[HA] = 1.26

This means that the ratio of sodium benzoate to benzoic acid in the buffer should be approximately 1.26.

Step 3: Convert the moles of benzoic acid to moles of sodium benzoate.

Since the ratio of [A-] to [HA] is 1.26, this means that for every 1 molecule of benzoic acid, we need 1.26 molecules of sodium benzoate.

moles of sodium benzoate = moles of benzoic acid × 1.26
moles of sodium benzoate = 0.0272 mol × 1.26
moles of sodium benzoate = 0.0343 mol

Step 4: Calculate the mass of sodium benzoate required.

To do this, we need to use the molar mass of sodium benzoate (C6H5COONa) which is 144.11 g/mol.

mass of sodium benzoate = moles of sodium benzoate × molar mass
mass of sodium benzoate = 0.0343 mol × 144.11 g/mol
mass of sodium benzoate = 4.95 g (rounded to two decimal places)

Therefore, you would need to add approximately 4.95 grams of sodium benzoate to 160.0 mL of the 0.17M benzoic acid solution to obtain a buffer with a pH of 4.30.

I hope this step-by-step explanation helps you understand how to solve this problem. Let me know if you have any further questions!