The molarity of 20% by mass `H_(2)SO_(4)` solution of density `1.28 g cm^(-3)` is :

Options

A. 2.56 M
B. 1.56 M
C. 1M
D. 5 M

Explanation

To find the molarity of a 20% by mass \( H_2SO_4 \) solution with a density of \( 1.28 \, \text{g/cm}^3 \), we can follow these steps:

### Step 1: Calculate the mass of the solution
Assume we have 100 g of the solution (this makes calculations easier).

### Step 2: Calculate the mass of the solute
Since the solution is 20% by mass \( H_2SO_4 \):
\[ \text{Mass of } H_2SO_4 = 20\% \text{ of } 100 \, \text{g} = 20 \, \text{g} \]

### Step 3: Calculate the mass of the solvent
The mass of the solvent (water) can be calculated as:
\[ \text{Mass of solvent} = \text{Total mass of solution} - \text{Mass of solute} = 100 \, \text{g} - 20 \, \text{g} = 80 \, \text{g} \]

### Step 4: Calculate the volume of the solution
Using the density of the solution, we can find the volume:
\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}} = \frac{100 \, \text{g}}{1.28 \, \text{g/cm}^3} = 78.125 \, \text{cm}^3 \]
Convert this volume to liters:
\[ \text{Volume in liters} = \frac{78.125 \, \text{cm}^3}{1000} = 0.078125 \, \text{L} \]

### Step 5: Calculate the number of moles of \( H_2SO_4 \)
The molar mass of \( H_2SO_4 \) is calculated as follows:
\[ \text{Molar mass of } H_2SO_4 = 2 \times 1 + 32 + 4 \times 16 = 98 \, \text{g/mol} \]
Now, calculate the number of moles of \( H_2SO_4 \):
\[ \text{Number of moles} = \frac{\text{Mass of solute}}{\text{Molar mass}} = \frac{20 \, \text{g}}{98 \, \text{g/mol}} \approx 0.2041 \, \text{mol} \]

### Step 6: Calculate the molarity
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{Number of moles}}{\text{Volume in liters}} = \frac{0.2041 \, \text{mol}}{0.078125 \, \text{L}} \approx 2.61 \, \text{M} \]

### Final Answer
The molarity of the 20% by mass \( H_2SO_4 \) solution is approximately **2.61 M**.

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