The freezing point of a `1.00 m` aqueous solution of `HF` is found to be `-1.91^(@)C`. The freezing point constant of water, `K_(f)`, is `1.86 K kg mol^(-1)`. The percentage dissociation of `HF` at this concentration is:-

Options

A. `2.7%`
B. `30%`
C. `10%`
D. `5.2%`

Answer

To find the percentage dissociation of HF in a 1.00 m aqueous solution, we can follow these steps:

### Step 1: Understand the given data
- Freezing point of the solution (Tf) = -1.91 °C
- Freezing point constant of water (Kf) = 1.86 K kg mol⁻¹
- Molality (m) = 1.00 m

### Step 2: Calculate the change in freezing point (ΔTf)
The change in freezing point (ΔTf) can be calculated as follows:
\[ \Delta T_f = T_f^0 - T_f \]
Where:
- \(T_f^0\) (freezing point of pure solvent, water) = 0 °C
- \(T_f\) = -1.91 °C

Thus,
\[ \Delta T_f = 0 - (-1.91) = 1.91 \, \text{°C} \]

### Step 3: Use the formula for freezing point depression
The formula for freezing point depression is:
\[ \Delta T_f = i \cdot K_f \cdot m \]
Where:
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = freezing point constant
- \(m\) = molality

Substituting the known values:
\[ 1.91 = i \cdot 1.86 \cdot 1.00 \]

### Step 4: Solve for \(i\)
Rearranging the equation to solve for \(i\):
\[ i = \frac{1.91}{1.86} \approx 1.02688 \]

### Step 5: Relate \(i\) to the degree of dissociation (α)
For a weak acid like HF that dissociates into H⁺ and F⁻:
\[ HF \rightleftharpoons H^+ + F^- \]
The van 't Hoff factor \(i\) can be expressed as:
\[ i = 1 + (n - 1) \cdot \alpha \]
Where \(n\) is the number of ions produced (which is 2 for HF).

Substituting \(n = 2\) into the equation:
\[ 1.02688 = 1 + (2 - 1) \cdot \alpha \]
This simplifies to:
\[ 1.02688 = 1 + \alpha \]

### Step 6: Solve for α
Rearranging gives:
\[ \alpha = 1.02688 - 1 = 0.02688 \]

### Step 7: Calculate the percentage dissociation
To find the percentage dissociation, multiply α by 100:
\[ \text{Percentage dissociation} = \alpha \cdot 100 = 0.02688 \cdot 100 \approx 2.688\% \]

### Final Answer
The percentage dissociation of HF at this concentration is approximately **2.7%**.

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