ph a mixture which is 0.1 M in ch3cooh and 0.05M in (ch3cooh)2ba is

To determine the pH of a mixture that is 0.1 M in acetic acid (CH3COOH) and 0.05 M in barium acetate ((CH3COO)2Ba), we need to consider the properties of both compounds in solution. Acetic acid is a weak acid, while barium acetate is a salt that can affect the pH by providing acetate ions (CH3COO⁻) that can interact with the acetic acid.

Understanding Acetic Acid

Acetic acid (CH3COOH) partially dissociates in water according to the following equilibrium:

• CH3COOH ⇌ CH3COO⁻ + H⁺

The equilibrium constant for this reaction is known as the acid dissociation constant (Ka). For acetic acid, Ka is approximately 1.8 x 10⁻⁵ at room temperature. This means that not all acetic acid molecules will dissociate into ions, which is characteristic of weak acids.

Role of Barium Acetate

Barium acetate ((CH3COO)2Ba) is a salt that dissociates completely in solution:

• (CH3COO)2Ba → 2 CH3COO⁻ + Ba²⁺

The acetate ions produced from barium acetate can shift the equilibrium of acetic acid to the left, reducing the concentration of H⁺ ions in the solution. This is known as the common ion effect.

Calculating pH

To find the pH of the mixture, we can use the following steps:

1. Calculate the concentration of acetate ions from both acetic acid and barium acetate.
2. Set up the equilibrium expression for acetic acid considering the common ion effect.
3. Use the Ka value to find the concentration of H⁺ ions.
4. Calculate the pH from the H⁺ concentration.

Step 1: Concentration of Acetate Ions

From acetic acid, the concentration of acetate ions is equal to the concentration of acetic acid that dissociates. However, for simplicity, we can initially assume that the concentration of acetate ions from barium acetate is significant:

• From barium acetate: 0.05 M (from 2 moles of acetate per mole of salt)
• From acetic acid: Let’s denote the dissociated amount as x, so the total acetate concentration is approximately 0.05 + x.

Step 2: Setting Up the Equilibrium Expression

The equilibrium expression for acetic acid is:

• Ka = [CH3COO⁻][H⁺] / [CH3COOH]

Substituting the concentrations, we have:

• 1.8 x 10⁻⁵ = (0.05 + x)[H⁺] / (0.1 - x)

Since x will be small compared to 0.05 and 0.1, we can simplify the equation to:

• 1.8 x 10⁻⁵ ≈ (0.05)[H⁺] / (0.1)

Step 3: Solving for [H⁺]

Rearranging gives:

• [H⁺] = 1.8 x 10⁻⁵ * (0.1) / (0.05) = 3.6 x 10⁻⁵ M

Step 4: Calculating pH

Finally, the pH can be calculated using the formula:

• pH = -log[H⁺]

Substituting the value we found:

• pH = -log(3.6 x 10⁻⁵) ≈ 4.44

Final Thoughts

The pH of the mixture, which is 0.1 M in acetic acid and 0.05 M in barium acetate, is approximately 4.44. This value reflects the weakly acidic nature of acetic acid, influenced by the presence of the acetate ions from barium acetate, which suppress the dissociation of acetic acid due to the common ion effect.