Find the molality of` H_(2)SO_(4) `solution whose specific gravity is ` 1.98 g ml^(-1) `and ` 95% `by volume ` H_(2)SO_(4) `

Options

A. ` 7.412 `
B. ` 8.412 `
C. ` 9.412 `
D. ` 10.412 `

Explanation

To find the molality of the H₂SO₄ solution, we can follow these steps:

### Step 1: Understand the given data
- Specific gravity of H₂SO₄ solution = 1.98 g/mL
- Volume percentage of H₂SO₄ = 95%

### Step 2: Calculate the mass of the solution
Since the specific gravity is given as 1.98 g/mL, this means that 1 mL of the solution weighs 1.98 grams.

For 100 mL of the solution:
\[ \text{Mass of solution} = 100 \, \text{mL} \times 1.98 \, \text{g/mL} = 198 \, \text{g} \]

### Step 3: Calculate the mass of H₂SO₄ in the solution
Since the solution is 95% H₂SO₄ by volume, the mass of H₂SO₄ in 100 mL of solution is:
\[ \text{Mass of H₂SO₄} = 95 \, \text{g} \]

### Step 4: Calculate the mass of the solvent (water)
To find the mass of the solvent (water), we subtract the mass of H₂SO₄ from the total mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of H₂SO₄} = 198 \, \text{g} - 95 \, \text{g} = 103 \, \text{g} \]

### Step 5: Convert the mass of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{103 \, \text{g}}{1000} = 0.103 \, \text{kg} \]

### Step 6: Calculate the number of moles of H₂SO₄
The molar mass of H₂SO₄ (sulfuric acid) is:
\[ \text{Molar mass of H₂SO₄} = 2 \times 1 + 32 + 4 \times 16 = 98 \, \text{g/mol} \]
Now, we can calculate the number of moles of H₂SO₄:
\[ \text{Moles of H₂SO₄} = \frac{\text{Mass of H₂SO₄}}{\text{Molar mass of H₂SO₄}} = \frac{95 \, \text{g}}{98 \, \text{g/mol}} \approx 0.969 \, \text{mol} \]

### Step 7: Calculate the molality of the solution
Finally, we can calculate the molality (m) using the formula:
\[ \text{Molality} (m) = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} = \frac{0.969 \, \text{mol}}{0.103 \, \text{kg}} \approx 9.42 \, \text{mol/kg} \]

### Final Answer
The molality of the H₂SO₄ solution is approximately **9.42 mol/kg**.

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