pH of 1 L 0.1 M HCI solution when 5 g of HF is added

Options

A. 0.53
B. 1
C. 0.1
D. 0.01

Answer

To find the pH of a solution when 5 g of HF is added to 1 L of 0.1 M HCl, we can follow these steps:

### Step 1: Calculate the number of moles of HF
To find the number of moles of HF, we can use the formula:
\[ \text{Number of moles} = \frac{\text{given weight}}{\text{molecular mass}} \]
Given:
- Weight of HF = 5 g
- Molecular mass of HF = 20 g/mol

Calculating the number of moles:
\[ \text{Number of moles of HF} = \frac{5 \text{ g}}{20 \text{ g/mol}} = 0.25 \text{ moles} \]

### Step 2: Calculate the number of moles of HCl
The molarity of HCl is given as 0.1 M in 1 L of solution. Therefore, the number of moles of HCl can be calculated as:
\[ \text{Number of moles of HCl} = \text{Molarity} \times \text{Volume (L)} = 0.1 \text{ mol/L} \times 1 \text{ L} = 0.1 \text{ moles} \]

### Step 3: Calculate the total concentration of H⁺ ions
Both HCl and HF contribute to the concentration of H⁺ ions in the solution.
- HCl dissociates completely to give H⁺ ions:
- 0.1 moles of HCl gives 0.1 moles of H⁺.
- HF is a weak acid and partially dissociates, but for simplicity, we can assume it contributes approximately 0.25 moles of H⁺ (since HF is a weak acid, we will consider its contribution as complete for this calculation).

Total moles of H⁺ ions:
\[ \text{Total H⁺} = \text{H⁺ from HCl} + \text{H⁺ from HF} = 0.1 + 0.25 = 0.35 \text{ moles} \]

### Step 4: Calculate the concentration of H⁺ ions
Since the total volume of the solution is 1 L, the concentration of H⁺ ions is:
\[ [\text{H}^+] = \frac{\text{Total H⁺ moles}}{\text{Volume (L)}} = \frac{0.35 \text{ moles}}{1 \text{ L}} = 0.35 \text{ M} \]

### Step 5: Calculate the pH
The pH is calculated using the formula:
\[ \text{pH} = -\log[\text{H}^+] \]
Substituting the concentration of H⁺:
\[ \text{pH} = -\log(0.35) \]

Calculating the pH:
\[ \text{pH} \approx 0.46 \]

### Final Answer
The pH of the solution after adding 5 g of HF to 1 L of 0.1 M HCl is approximately **0.46**.

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