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

Options

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

Answer

To find the molality of \( H_2SO_4 \) given its molarity and density, we can follow these steps:

### Step 1: Understand the given values
- Molarity (\( M \)) of \( H_2SO_4 \) = 18 M
- Density (\( d \)) of \( H_2SO_4 \) = 1.8 g/cm³

### Step 2: Use the formula for molality
The formula to convert molarity to molality is:
\[ m = M \times \frac{1000}{d \times 1000 - M \times M_m} \]
where:
- \( m \) = molality
- \( M \) = molarity
- \( d \) = density
- \( M_m \) = molar mass of the solute

### Step 3: Calculate the molar mass of \( H_2SO_4 \)
The molar mass (\( M_m \)) of \( H_2SO_4 \) can be calculated as follows:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Sulfur (S): 32 g/mol × 1 = 32 g/mol
- Oxygen (O): 16 g/mol × 4 = 64 g/mol

Adding these together:
\[ M_m = 2 + 32 + 64 = 98 \text{ g/mol} \]

### Step 4: Substitute the values into the formula
Now, substitute \( M = 18 \), \( d = 1.8 \), and \( M_m = 98 \) into the molality formula:
\[ m = 18 \times \frac{1000}{1.8 \times 1000 - 18 \times 98} \]

### Step 5: Calculate the denominator
Calculate \( 1.8 \times 1000 \):
\[ 1.8 \times 1000 = 1800 \text{ g} \]
Now calculate \( 18 \times 98 \):
\[ 18 \times 98 = 1764 \text{ g} \]
Now, subtract:
\[ 1800 - 1764 = 36 \text{ g} \]

### Step 6: Calculate molality
Now substitute back into the equation for molality:
\[ m = 18 \times \frac{1000}{36} \]
Calculating this gives:
\[ m = 18 \times 27.78 \approx 500 \text{ mol/kg} \]

### Final Answer
Thus, the molality of \( H_2SO_4 \) is **500 mol/kg**.