The molality of a sulphuric acid solution is` 0.6` 'mol//kg'. The total weight of the solution which contains `1 kg` of solvent.

Options

A. 1000 g
B. 980.3 g
C. 1058.8 g
D. 1013.3 g

Answer

To find the total weight of the sulfuric acid solution, we can follow these steps:

### Step 1: Understand the definition of molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \]

### Step 2: Identify the given values
From the question, we know:
- Molality (m) = 0.6 mol/kg
- Mass of solvent = 1 kg

### Step 3: Calculate the number of moles of solute
Using the formula for molality, we can rearrange it to find the moles of solute:
\[ \text{moles of solute} = m \times \text{mass of solvent (kg)} \]
Plugging in the values:
\[ \text{moles of solute} = 0.6 \, \text{mol/kg} \times 1 \, \text{kg} = 0.6 \, \text{mol} \]

### Step 4: Calculate the mass of the solute
Next, we need to find the mass of the solute (sulfuric acid, \( \text{H}_2\text{SO}_4 \)). The molar mass of sulfuric acid is approximately 98 g/mol. Therefore, the mass of the solute can be calculated as:
\[ \text{mass of solute} = \text{moles of solute} \times \text{molar mass of solute} \]
\[ \text{mass of solute} = 0.6 \, \text{mol} \times 98 \, \text{g/mol} = 58.8 \, \text{g} \]

### Step 5: Calculate the total weight of the solution
The total weight of the solution is the sum of the mass of the solvent and the mass of the solute:
\[ \text{total weight of solution} = \text{mass of solvent} + \text{mass of solute} \]
\[ \text{total weight of solution} = 1000 \, \text{g} + 58.8 \, \text{g} = 1058.8 \, \text{g} \]

### Final Answer
The total weight of the solution is **1058.8 g**.

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