Molarity of `H_(2)SO_(4)` is `18 M`. Its density is `1.8 g//cm^(3)`, hence molaity is :

Options

A. `18`
B. `100`
C. `36`
D. `500`

Explanation

To find the molality of `H₂SO₄` given its molarity and density, we can follow these steps:

### Step 1: Understand the Definitions
- **Molarity (M)** is defined as the number of moles of solute per liter of solution.
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent.

### Step 2: Calculate the Mass of the Solution
Given:
- Molarity of `H₂SO₄` = 18 M
- Density of `H₂SO₄` = 1.8 g/cm³

Since 1 liter of solution is equivalent to 1000 mL, we can calculate the mass of the solution:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of solution} = 1.8 \, \text{g/cm}^3 \times 1000 \, \text{cm}^3 = 1800 \, \text{g} = 1.8 \, \text{kg} \]

### Step 3: Calculate the Moles of Solute
Using the molarity, we can find the number of moles of `H₂SO₄` in 1 liter of solution:
\[ \text{Moles of } H₂SO₄ = 18 \, \text{moles} \]

### Step 4: Calculate the Mass of the Solute
To find the mass of `H₂SO₄`, we need its molar mass. The molar mass of `H₂SO₄` (sulfuric acid) can be calculated as follows:
- H: 1 g/mol × 2 = 2 g/mol
- S: 32 g/mol
- O: 16 g/mol × 4 = 64 g/mol
- Total = 2 + 32 + 64 = 98 g/mol

Now, calculate the mass of `H₂SO₄`:
\[ \text{Mass of } H₂SO₄ = \text{Moles} \times \text{Molar Mass} \]
\[ \text{Mass of } H₂SO₄ = 18 \, \text{moles} \times 98 \, \text{g/mol} = 1764 \, \text{g} = 1.764 \, \text{kg} \]

### Step 5: Calculate the Mass of the Solvent (Water)
To find the mass of the solvent (water), we subtract the mass of the solute from the mass of the solution:
\[ \text{Mass of water} = \text{Mass of solution} - \text{Mass of } H₂SO₄ \]
\[ \text{Mass of water} = 1.8 \, \text{kg} - 1.764 \, \text{kg} = 0.036 \, \text{kg} \]

### Step 6: Calculate the Molality
Now we can calculate the molality using the formula:
\[ \text{Molality (m)} = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} \]
\[ \text{Molality (m)} = \frac{18 \, \text{moles}}{0.036 \, \text{kg}} = 500 \, \text{mol/kg} \]

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

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