The molarity of 20% by mass `H_(2)SO_(4)` solution of density `1.02 g cm^(-3)` is :

Options

A. a.2.08 M
B. b.1.56 M
C. c.1M
D. d.5 M

Explanation

To find the molarity of a 20% by mass H₂SO₄ solution with a density of 1.02 g/cm³, follow these steps:

### Step 1: Understand the Definition of Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution.

### Step 2: Calculate the Mass of H₂SO₄ in the Solution
Given that the solution is 20% by mass H₂SO₄, this means there are 20 grams of H₂SO₄ in 100 grams of the solution.

### Step 3: Calculate the Molar Mass of H₂SO₄
The molar mass of H₂SO₄ can be calculated as follows:
- Hydrogen (H) = 1 g/mol, and there are 2 H atoms → 2 × 1 = 2 g/mol
- Sulfur (S) = 32 g/mol
- Oxygen (O) = 16 g/mol, and there are 4 O atoms → 4 × 16 = 64 g/mol

Adding these together:
\[ \text{Molar mass of H₂SO₄} = 2 + 32 + 64 = 98 \text{ g/mol} \]

### Step 4: Calculate the Number of Moles of H₂SO₄
Using the molar mass, calculate the number of moles of H₂SO₄:
\[ \text{Number of moles} = \frac{\text{mass of H₂SO₄}}{\text{molar mass of H₂SO₄}} = \frac{20 \text{ g}}{98 \text{ g/mol}} \approx 0.2041 \text{ moles} \]

### Step 5: Calculate the Volume of the Solution
Using the density of the solution, we can find the volume. The formula for density is:
\[ \text{Density} = \frac{\text{mass}}{\text{volume}} \]
Rearranging gives us:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} \]
Substituting the values:
\[ \text{Volume} = \frac{100 \text{ g}}{1.02 \text{ g/cm}^3} \approx 98.04 \text{ cm}^3 \]

### Step 6: Convert Volume to Liters
To convert cm³ to liters:
\[ \text{Volume in liters} = \frac{98.04 \text{ cm}^3}{1000} \approx 0.09804 \text{ L} \]

### Step 7: Calculate the Molarity
Now, we can calculate the molarity:
\[ \text{Molarity} = \frac{\text{number of moles}}{\text{volume in liters}} = \frac{0.2041 \text{ moles}}{0.09804 \text{ L}} \approx 2.0816 \text{ M} \]

### Final Answer
The molarity of the 20% by mass H₂SO₄ solution is approximately **2.0816 M**.

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