Calculate the ratio of pyridine (C3H,N) to it's conjugate acid, the Pyridinium ion (C3H,NH"), CHN in a buffer made of pyridine CH,NH and the pridinium ion when the pH of that buffer solution is 4.94. K for the pyridinium ion is 5.60 x 106

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**Buffer Solution Ratio Calculation**

**Problem Statement:**
Calculate the ratio of pyridine (C₅H₅N) to its conjugate acid, the pyridinium ion (C₅H₅NH⁺), in a buffer made of pyridine and the pyridinium ion when the pH of that buffer solution is 4.94. The acid dissociation constant (Kₐ) for the pyridinium ion is 5.60 x 10⁻⁶.

**Detailed Explanation:**
To solve this problem, one needs to employ the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKₐ and the ratio of the concentrations of the conjugate base and the conjugate acid.

The Henderson-Hasselbalch equation is given by:

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

Where:
- \( \text{Conjugate Base} \) is pyridine (C₅H₅N),
- \( \text{Conjugate Acid} \) is pyridinium ion (C₅H₅NH⁺).

First, calculate the pKₐ from the Kₐ:
\[ \text{p}K_a = -\log(K_a) \]
\[ K_a = 5.60 \times 10^{-6} \]
\[ \text{p}K_a = -\log(5.60 \times 10^{-6}) \]

Then, use the Henderson-Hasselbalch equation to find the ratio of pyridine to the pyridinium ion. This will involve substituting the known values of pH and pKₐ into the equation.

Lastly, solve for the ratio:
\[ \frac{[\text{C₅H₅N}]}{[\text{C₅H₅NH⁺}]} = 10^{(\text{pH} - \text{p}K_a)} \]

Thus, through substitution and calculation, the ratio can be determined.
Transcribed Image Text:**Buffer Solution Ratio Calculation** **Problem Statement:** Calculate the ratio of pyridine (C₅H₅N) to its conjugate acid, the pyridinium ion (C₅H₅NH⁺), in a buffer made of pyridine and the pyridinium ion when the pH of that buffer solution is 4.94. The acid dissociation constant (Kₐ) for the pyridinium ion is 5.60 x 10⁻⁶. **Detailed Explanation:** To solve this problem, one needs to employ the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKₐ and the ratio of the concentrations of the conjugate base and the conjugate acid. The Henderson-Hasselbalch equation is given by: \[ \text{pH} = \text{p}K_a + \log \left( \frac{[\text{Conjugate Base}]}{[\text{Conjugate Acid}]} \right) \] Where: - \( \text{Conjugate Base} \) is pyridine (C₅H₅N), - \( \text{Conjugate Acid} \) is pyridinium ion (C₅H₅NH⁺). First, calculate the pKₐ from the Kₐ: \[ \text{p}K_a = -\log(K_a) \] \[ K_a = 5.60 \times 10^{-6} \] \[ \text{p}K_a = -\log(5.60 \times 10^{-6}) \] Then, use the Henderson-Hasselbalch equation to find the ratio of pyridine to the pyridinium ion. This will involve substituting the known values of pH and pKₐ into the equation. Lastly, solve for the ratio: \[ \frac{[\text{C₅H₅N}]}{[\text{C₅H₅NH⁺}]} = 10^{(\text{pH} - \text{p}K_a)} \] Thus, through substitution and calculation, the ratio can be determined.
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