The `HF_(2)^(Θ)` ion solid state and in liquid `HF` but not in the dilute aqueous solution
At `300 K` and `1.00 ` atm, the density of `HF` is `3.17 gL^(-1)` We conclude that there is a .

Options

A. dimer formation by H-bonding
B. trimer formation by H-bonding
C. tetramer formation by H-bonding
D. ionisation formation `HF_(2)^(Θ)` and `H^(o+)`

Explanation

To solve the problem regarding the `HF2^(-)` ion in solid state and liquid HF, we will follow these steps:

### Step 1: Understand the Given Data
We are given:
- Temperature (T) = 300 K
- Pressure (P) = 1.00 atm
- Density of HF = 3.17 g/L

### Step 2: Use the Ideal Gas Law
We will use the ideal gas equation \( PV = nRT \) to find the number of moles (n) of HF present in 1 liter of the gas.

\[ n = \frac{PV}{RT} \]

Where:
- \( R = 0.0821 \, \text{L atm/(K mol)} \)
- \( V = 1 \, \text{L} \)

Substituting the values:

\[ n = \frac{(1.00 \, \text{atm}) \times (1 \, \text{L})}{(0.0821 \, \text{L atm/(K mol)}) \times (300 \, \text{K})} \]

Calculating this gives:

\[ n \approx 0.0406 \, \text{moles} \]

### Step 3: Calculate the Mass of HF
Using the density to find the mass of HF in 1 liter:

\[ \text{Mass} = \text{Density} \times \text{Volume} = 3.17 \, \text{g/L} \times 1 \, \text{L} = 3.17 \, \text{g} \]

### Step 4: Calculate the Molar Mass of HF
Using the number of moles calculated earlier, we can find the molar mass (M):

\[ M = \frac{\text{Mass}}{n} = \frac{3.17 \, \text{g}}{0.0406 \, \text{moles}} \approx 78.1 \, \text{g/mol} \]

### Step 5: Compare with the Molar Mass of HF
The molar mass of HF is approximately 20 g/mol (1 g/mol for H and 19 g/mol for F).

### Step 6: Determine the Association of Molecules
To find out how many HF molecules are associated to give a molar mass of 78.1 g/mol:

\[ \text{Number of molecules associated} = \frac{78.1 \, \text{g/mol}}{20 \, \text{g/mol}} \approx 3.9 \approx 4 \]

### Step 7: Conclusion
Since approximately 4 HF molecules are associated, we conclude that there is tetramer formation by hydrogen bonding in liquid HF.

### Final Answer
The correct conclusion is that there is a **tetramer formation by hydrogen bonding**.

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