Calculate the molality of a sulphuric acid solution of specific gravity `1.2` containing `27% H_(2)SO_(4)` by weight.

Explanation

To calculate the molality of a sulfuric acid solution with a specific gravity of 1.2 and containing 27% H₂SO₄ by weight, follow these steps:

### Step 1: Understand the given data
- Specific gravity of the solution = 1.2
- Percentage of H₂SO₄ by weight = 27%

### Step 2: Calculate the mass of the solution
Assume we have 1000 grams of the solution (this simplifies calculations since percentages are based on 100 grams).

### Step 3: Calculate the mass of H₂SO₄ in the solution
Since the solution is 27% H₂SO₄ by weight:
\[ \text{Mass of H₂SO₄} = 27\% \text{ of } 1000 \text{ g} = 270 \text{ g} \]

### Step 4: Calculate the mass of the solvent (water)
The mass of the solvent (water) can be calculated as:
\[ \text{Mass of solvent} = \text{Total mass of solution} - \text{Mass of H₂SO₄} = 1000 \text{ g} - 270 \text{ g} = 730 \text{ g} \]

### Step 5: Calculate the number of moles of H₂SO₄
To find the number of moles of H₂SO₄, use its molar mass. The molar mass of H₂SO₄ is approximately 98 g/mol.
\[ \text{Number of moles of H₂SO₄} = \frac{\text{Mass of H₂SO₄}}{\text{Molar mass of H₂SO₄}} = \frac{270 \text{ g}}{98 \text{ g/mol}} \approx 2.75 \text{ moles} \]

### Step 6: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent. Since we have the mass of the solvent in grams, we need to convert it to kilograms:
\[ \text{Mass of solvent in kg} = \frac{730 \text{ g}}{1000} = 0.730 \text{ kg} \]
Now, we can calculate the molality:
\[ \text{Molality} = \frac{\text{Number of moles of H₂SO₄}}{\text{Mass of solvent in kg}} = \frac{2.75 \text{ moles}}{0.730 \text{ kg}} \approx 3.77 \text{ molal} \]

### Step 7: Round the answer
Rounding to two decimal places, we can say the molality is approximately:
\[ \text{Molality} \approx 3.77 \text{ molal} \approx 4 \text{ molal} \]

### Final Answer
The molality of the sulfuric acid solution is approximately **4 molal**.

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