The molarity of `H_(2)SO_(4)` is `18 M`. Its density is `1.8 g mL^(-1)`. Hence, molality is :

Options

A. 36
B. 200
C. 500
D. 18

Explanation

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

### Step 1: Understand the given information
- Molarity (M) of `H₂SO₄` = 18 M
- Density (d) of `H₂SO₄` = 1.8 g/mL

### Step 2: Calculate the mass of `H₂SO₄` in 1 liter of solution
Since molarity is defined as moles of solute per liter of solution, we can find the number of moles in 1 liter:
- Moles of `H₂SO₄` in 1 L = 18 moles

Next, we need to calculate the mass of `H₂SO₄` using its molar mass:
- Molar mass of `H₂SO₄` = 98 g/mol
- Mass of `H₂SO₄` = Moles × Molar mass = 18 moles × 98 g/mol = 1764 g

### Step 3: Calculate the total mass of the solution
Using the density, we can find the total mass of 1 liter of the solution:
- Density = Mass/Volume
- Therefore, Mass = Density × Volume = 1.8 g/mL × 1000 mL = 1800 g

### Step 4: Calculate the mass of the solvent (water)
Now, we can find the mass of the solvent (water) by subtracting the mass of `H₂SO₄` from the total mass of the solution:
- Mass of water = Total mass of solution - Mass of `H₂SO₄`
- Mass of water = 1800 g - 1764 g = 36 g

### Step 5: Convert the mass of water to kilograms
To find molality, we need the mass of the solvent in kilograms:
- Mass of water in kg = 36 g × (1 kg / 1000 g) = 0.036 kg

### Step 6: Calculate molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
- Molality = Moles of solute / Mass of solvent in kg
- Molality = 18 moles / 0.036 kg = 500 mol/kg

### Final Answer
The molality of the `H₂SO₄` solution is **500 mol/kg**.

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