The ionization constant of HF is 3.2 × 10–4. Calculate the degree of dissociation of HF in its 0.02 M solution. Calculate the concentration of all species present (H3O+, F– and HF) in the solution and its pH ?

To tackle the problem of calculating the degree of dissociation of hydrofluoric acid (HF) in a 0.02 M solution, we first need to understand the concept of ionization constants and how they relate to the dissociation of weak acids. The ionization constant (Ka) for HF is given as 3.2 × 10^-4. Let's break this down step by step.

Understanding the Ionization of HF

HF is a weak acid, which means it does not completely dissociate in solution. The dissociation can be represented by the following equilibrium reaction:

HF ⇌ H₃O⁺ + F^-

The ionization constant (Ka) is defined by the expression:

Ka = [H₃O⁺][F^-]/[HF]

Setting Up the Equilibrium Expression

Let’s denote the degree of dissociation of HF as α (alpha). In a 0.02 M solution of HF, at equilibrium, the concentrations of the species can be expressed as follows:

• [HF] = 0.02 - α
• [H₃O⁺] = α
• [F^-] = α

Substituting these values into the Ka expression gives us:

3.2 × 10^-4 = (α)(α)/(0.02 - α)

Assuming α is Small

Since HF is a weak acid, we can assume that α is small compared to 0.02 M. Therefore, we can simplify the equation:

3.2 × 10^-4 ≈ (α²)/(0.02)

Solving for α

Rearranging the equation to solve for α gives:

α² = 3.2 × 10^-4 × 0.02

Calculating this, we find:

α² = 6.4 × 10^-6

Taking the square root of both sides yields:

α = √(6.4 × 10^-6) ≈ 0.00253

Calculating Concentrations of All Species

Now that we have α, we can find the concentrations of all species in the solution:

• [H₃O⁺] = α ≈ 0.00253 M
• [F^-] = α ≈ 0.00253 M
• [HF] = 0.02 - α ≈ 0.02 - 0.00253 ≈ 0.01747 M

Calculating the pH

The pH of the solution can be calculated using the concentration of H₃O⁺:

pH = -log[H₃O⁺]

Substituting the value we found:

pH = -log(0.00253) ≈ 2.59

Summary of Results

In summary, for a 0.02 M solution of HF:

• Degree of dissociation (α) ≈ 0.00253 (or 0.01265%)
• [H₃O⁺] ≈ 0.00253 M
• [F^-] ≈ 0.00253 M
• [HF] ≈ 0.01747 M
• pH ≈ 2.59

This analysis illustrates how to approach the dissociation of weak acids and calculate the concentrations of the species in equilibrium. If you have any further questions or need clarification on any part of this process, feel free to ask!