The molality of a sulphuric acid solution is `0.2"mol"//"kg"` Calculate the total weight of the solution :

Options

A. `1000 mL`
B. `1098.6g`
C. `980.4g`
D. `1019.6g`

Explanation

To solve the problem, we need to calculate the total weight of the sulfuric acid solution given its molality. Here's a step-by-step breakdown of the solution:

### Step 1: Understand the Definition of Molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, the molality of the sulfuric acid solution is given as 0.2 mol/kg.

### Step 2: Calculate the Number of Moles of Sulfuric Acid
Since the molality is 0.2 mol/kg, this means that in 1 kg (1000 g) of solvent (water), there are 0.2 moles of sulfuric acid (H₂SO₄).

### Step 3: Calculate the Mass of Sulfuric Acid
To find the mass of sulfuric acid, we need to use its molar mass. The molar mass of H₂SO₄ is approximately 98 g/mol.

\[ \text{Mass of H₂SO₄} = \text{Number of moles} \times \text{Molar mass} \]
\[ \text{Mass of H₂SO₄} = 0.2 \, \text{mol} \times 98 \, \text{g/mol} = 19.6 \, \text{g} \]

### Step 4: Calculate the Total Weight of the Solution
The total weight of the solution is the sum of the mass of the solute (sulfuric acid) and the mass of the solvent (water).

\[ \text{Total weight of solution} = \text{Mass of solute} + \text{Mass of solvent} \]
\[ \text{Total weight of solution} = 19.6 \, \text{g} + 1000 \, \text{g} = 1019.6 \, \text{g} \]

### Conclusion
The total weight of the sulfuric acid solution is **1019.6 grams**.

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