Question

A 0.15 mole of pyridinium chloride has been added to 500 cm\(^3\) of 0.2M pyridine solution (a base). Assuming there is no change in volume upon mixing, the pH of the resulting solution is
(Note: K\(_b\) for pyridine is 1.5 \(\times\) 10\(^{-9}\))

• A. 5
• B. 6
• C. 7
• D. 8

Hint:

For any buffer solution problem, first identify if it's an acidic buffer (weak acid + its salt) or a basic buffer (weak base + its salt). Then, apply the appropriate Henderson-Hasselbalch equation:

• \textbf{Acidic Buffer:} pH = pK\(_a\) + log([Salt]/[Acid])
• \textbf{Basic Buffer:} pOH = pK\(_b\) + log([Salt]/[Base])

Always remember to convert pOH to pH if the question asks for pH of a basic buffer.

Answer 1

The Correct Option is A

Step 1: Understanding the System.
We are mixing pyridine (C\(_5\)H\(_5\)N, a weak base) with its conjugate acid, pyridinium chloride (C\(_5\)H\(_5\)NH\(^+\)Cl\(^-\)). This combination forms a basic buffer solution.
Step 2: Calculate the concentrations of the base and its conjugate acid.
Volume of solution = 500 cm\(^3\) = 0.5 L.
Concentration of pyridine (Base): [Base] = [C\(_5\)H\(_5\)N] = 0.2 M (given).
Concentration of pyridinium chloride (Salt/Conjugate Acid): Moles of salt = 0.15 mol. \[ \text{[Salt]} = [\text{C}_5\text{H}_5\text{NH}^+] = \frac{\text{moles}}{\text{volume}} = \frac{0.15 \text{ mol}}{0.5 \text{ L}} = 0.3 \text{ M} \] Step 3: Key Formula for Buffer pH (Henderson-Hasselbalch Equation).
For a basic buffer, we can calculate the pOH using the Henderson-Hasselbalch equation: \[ \text{pOH} = \text{pK}_b + \log\left(\frac{[\text{Salt}]}{[\text{Base}]}\right) \] And then find pH using pH + pOH = 14.
Step 4: Calculate pK\(_b\).
K\(_b\) = 1.5 \(\times\) 10\(^{-9}\). \[ \text{pK}_b = -\log(\text{K}_b) = -\log(1.5 \times 10^{-9}) \] \[ \text{pK}_b = -(\log(1.5) + \log(10^{-9})) = -(\log(1.5) - 9) = 9 - \log(1.5) \] Given log(1.5) \(\approx\) 0.18. \[ \text{pK}_b \approx 9 - 0.18 = 8.82 \] Step 5: Calculate pOH.
\[ \text{pOH} = 8.82 + \log\left(\frac{0.3}{0.2}\right) = 8.82 + \log(1.5) \] \[ \text{pOH} = 8.82 + 0.18 = 9.0 \] Step 6: Calculate pH.
\[ \text{pH} = 14 - \text{pOH} = 14 - 9.0 = 5.0 \] Step 7: Final Answer.
The pH of the resulting buffer solution is 5.