What is the percent dissociation in a solution that is 0.50 M in acetic acid (CH3CO2H) and 0.10 M in sodium acetate (NaCH3CO2)? (Ka = 1.8 x 10^-5) (a) 0.018% (b) 0.090% (c) 7.2 x 10^-3% (d) 2.3%

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Identify the components of the solution: acetic acid (CH3CO2H) is a weak acid, and sodium acetate (NaCH3CO2) is its conjugate base. This is a buffer solution.

Use the Henderson-Hasselbalch equation to find the pH of the buffer solution: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \), where \([\text{A}^-]\) is the concentration of the acetate ion and \([\text{HA}]\) is the concentration of acetic acid.

Calculate the pKa from the given Ka: \( \text{pKa} = -\log(1.8 \times 10^{-5}) \).

Substitute the concentrations of acetic acid and acetate ion into the Henderson-Hasselbalch equation to find the pH.

Use the pH to determine the percent dissociation of acetic acid: \( \% \text{dissociation} = \left( \frac{[\text{H}^+]}{[\text{HA}]} \right) \times 100 \), where \([\text{H}^+]\) is the concentration of hydrogen ions calculated from the pH.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Dissociation and Equilibrium

Dissociation refers to the process where a compound breaks down into its constituent ions in solution. In the context of weak acids like acetic acid, this process is reversible and reaches an equilibrium state. The equilibrium constant (Ka) quantifies the extent of dissociation, indicating how much of the acid ionizes in solution. Understanding this concept is crucial for calculating percent dissociation.

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a buffer solution to the concentration of its acid and conjugate base. It is expressed as pH = pKa + log([A-]/[HA]), where [A-] is the concentration of the conjugate base (sodium acetate) and [HA] is the concentration of the weak acid (acetic acid). This equation helps in determining the pH of the solution, which is essential for calculating the percent dissociation of the weak acid.

Percent Dissociation

Percent dissociation is a measure of the extent to which a weak acid ionizes in solution, expressed as a percentage of the initial concentration. It is calculated using the formula: (amount dissociated / initial concentration) x 100%. This concept is important for understanding the strength of weak acids and their behavior in buffer solutions, particularly in the context of the given concentrations of acetic acid and sodium acetate.

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Percent Dissociation Example

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Textbook Question

Which of the following mixtures has the highest pH?(a) Equal volumes of 1.0 M HCl and 1.0 M NaOH (b) Equal volumes of 0.1 M HNO3 and 0.1 M KOH (c) Equal volumes of 0.1 M HCN and 0.1 M NaOH (d) Equal volumes of 0.1 M NaF and 0.1 M HCl

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Textbook Question

A 1.00 L buffer solution is 0.250 M in HF and 0.250 M in NaF. Calculate the pH of the solution after the addition of 100.0 mL of 1.00 M HCl. (Ka = 3.5 x 10^-4) (a) 4.11(b) 3.82(c) 3.46(d) 3.09

Textbook Question

What is the pH of a buffer solution prepared by dissolving 0.250 mol of NaH2PO4 and 0.075 mol of NaOH in enough water to make 1.00 L of solution? (Ka (H2PO4-) = 6.2 X 10^-8) (a) 6.32(b) 6.83(c) 7.21(d) 7.71