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To calculate the pH of a solution containing 0.090 M pyridine (pK_b = 5.25) and 0.215 M pyridinium chloride, we can use the Henderson-Hasselbalch equation. This equation is suitable for buffer solutions and relates the pH, the pK_a, and the ratio of the concentrations of the conjugate base and the acid.

The Henderson-Hasselbalch equation is:

\[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{Base}]}{[\text{Acid}]} \right) \]

First, we need to find pK_a from pK_b using the relationship:

\[ \text{p}K_a + \text{p}K_b = 14 \]

Given \(\text{p}K_b = 5.25\):

\[ \text{p}K_a = 14 - 5.25 = 8.75 \]

Now we can use the Henderson-Hasselbalch equation. The base here is pyridine (C_5H_5N), and the acid is pyridinium chloride (C_5H_5NH^+).

\[ \text{pH} = 8.75 + \log \left( \frac{0.090}{0.215} \right) \]

Calculate the ratio inside the logarithm:

\[ \frac{0.090}{0.215} = 0.4186 \]

Now find the logarithm:

\[ \log (0.4186) \approx -0.378 \]

Finally, calculate the pH:

\[ \text{pH} = 8.75 - 0.378 = 8.372 \]

So, the pH of the solution is approximately 8.37.

Would you like further details or have any questions?

Here are 5 questions you might be interested in:

1. How do you determine the pH of a buffer solution?
2. What is the relationship between pK_a and pK_b?
3. How does the Henderson-Hasselbalch equation apply to weak acid and weak base systems?
4. What factors can affect the pH of a buffer solution?
5. How can you prepare a buffer solution with a specific pH?

**Tip:** Remember that the Henderson-Hasselbalch equation is most accurate for solutions where the concentrations of the acid and base are within a factor of 10 of each other.

Learn how to calculate the pH of a solution containing pyridine and pyridinium chloride using the Henderson-Hasselbalch equation. Detailed step-by-step solution provided.

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