Question

Calculate the ph of a buffered solution prepared by dissolving 21. 5 g benzoic acid and 37. 7 g sodium benzoate

Answer 1

The pH of the buffered solution is approximately 4.39.

Here's how to calculate the pH of the buffered solution:

**1. Determine the concentrations of the acid and its conjugate base:**

* Calculate the moles of benzoic acid (BA) and sodium benzoate (NaBA):

- Molar mass of BA = 122.12 g/mol

- Molar mass of NaBA = 144.11 g/mol

- Moles of BA = 21.5 g / 122.12 g/mol ≈ 0.176 mol

- Moles of NaBA = 37.7 g / 144.11 g/mol ≈ 0.262 mol

* Calculate the concentrations of BA and NaBA in the solution:

- Volume of solution is not provided, so assume 1.00 L for calculation.

- [BA] = 0.176 mol / 1.00 L = 0.176 M

- [NaBA] = 0.262 mol / 1.00 L = 0.262 M

**2. Use the Henderson-Hasselbach equation:**

The pH of a buffer can be calculated using the Henderson-Hasselbach equation:

pH = pKa + log([Conjugate base] / [Acid])

where:

* pKa is the acid dissociation constant of the weak acid (benzoic acid)

* [Conjugate base] is the concentration of the conjugate base (sodium benzoate)

* [Acid] is the concentration of the weak acid (benzoic acid)

* The pKa of benzoic acid is approximately 4.20.

**3. Substitute and solve:**

pH = 4.20 + log(0.262 / 0.176)

pH ≈ 4.39

Therefore, the pH of the buffered solution is approximately 4.39.

The probable question may be:

Calculate the pH of a buffered solution prepared by dissolving 21. 5 g benzoic acid and 37. 7 g sodium benzoate?

Answer 2

4.19

Step-by-step explanation:

The pH of a buffer solution can be calculated using the Henderson-Hasselbalch equation:

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

where pKa is the acidic dissociation constant of the weak acid (in this case, benzoic acid), [A-] is the concentration of the conjugate base (sodium benzoate), and [HA] is the concentration of the weak acid (benzoic acid).

To find [A-] and [HA], we need to convert the masses of benzoic acid and sodium benzoate to moles.

First, let's convert the mass of benzoic acid to moles:

21.5 g ÷ 122.12 g/mol = 0.176 moles

Next, let's convert the mass of sodium benzoate to moles:

37.7 g ÷ 144.11 g/mol = 0.262 moles

Now we can use the mole ratios to find [A-] and [HA]. Since sodium benzoate is the salt of benzoic acid, the ratio of sodium benzoate to benzoic acid is 1:1, so [A-] = [HA] = 0.176 moles.

Finally, we can use the Henderson-Hasselbalch equation to calculate the pH of the buffer solution:

pH = pKa + log([A-]/[HA]) = 4.19 + log(0.176/0.176) = 4.19

So the pH of the buffer solution is 4.19.