The molarity of 90% `H_(2)SO_(4)` solution is [density = 1.8 gm/ml]

Options

A. `1.8`
B. `48.4`
C. `91.83`
D. `94.6`

Explanation

To find the molarity of a 90% \( H_2SO_4 \) solution with a density of 1.8 g/mL, we can follow these steps:

### Step 1: Calculate the mass of the solution in 1 liter
The density of the solution is given as 1.8 g/mL. To find the mass of 1 liter (1000 mL) of the solution, we can use the formula:

\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]

\[ \text{Mass of solution} = 1.8 \, \text{g/mL} \times 1000 \, \text{mL} = 1800 \, \text{g} \]

### Step 2: Calculate the mass of \( H_2SO_4 \) in the solution
Since the solution is 90% \( H_2SO_4 \) by mass, we can calculate the mass of \( H_2SO_4 \) in the 1800 g of solution:

\[ \text{Mass of } H_2SO_4 = 90\% \times 1800 \, \text{g} = 0.90 \times 1800 \, \text{g} = 1620 \, \text{g} \]

### Step 3: Calculate the number of moles of \( H_2SO_4 \)
To find the number of moles of \( H_2SO_4 \), we need its molar mass. The molar mass of \( H_2SO_4 \) is approximately 98 g/mol. We can calculate the number of moles using the formula:

\[ \text{Number of moles} = \frac{\text{Mass}}{\text{Molar mass}} \]

\[ \text{Number of moles of } H_2SO_4 = \frac{1620 \, \text{g}}{98 \, \text{g/mol}} \approx 16.53 \, \text{mol} \]

### Step 4: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution. Since we have calculated the number of moles of \( H_2SO_4 \) and we are considering 1 liter of solution, the molarity is:

\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume of solution in liters}} \]

\[ \text{Molarity} = \frac{16.53 \, \text{mol}}{1 \, \text{L}} = 16.53 \, \text{M} \]

### Final Answer
The molarity of the 90% \( H_2SO_4 \) solution is approximately **16.53 M**.

---