The molality of a 1 L solution with x % `H_2SO_4` is 9. The weight of solvent present in the solution is 910 grams. The value of x is :

Answer

To solve the problem step by step, we need to calculate the percentage concentration \( x \) of \( H_2SO_4 \) in a solution given its molality and the weight of the solvent.

### Step 1: Understand the given data
- Molarity (molality) of the solution = 9 mol/kg
- Weight of the solvent = 910 grams = 0.910 kg (since 1 kg = 1000 grams)
- Volume of the solution = 1 L

### Step 2: Calculate the number of moles of solute
Using the formula for molality:
\[ \text{Molality} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]
We can rearrange this to find the number of moles of solute:
\[ \text{Number of moles of solute} = \text{Molality} \times \text{Mass of solvent in kg} \]
Substituting the values:
\[ \text{Number of moles of solute} = 9 \, \text{mol/kg} \times 0.910 \, \text{kg} = 8.19 \, \text{moles} \]

### Step 3: Calculate the mass of \( H_2SO_4 \)
To find the mass of \( H_2SO_4 \), we use the formula:
\[ \text{Mass of solute} = \text{Number of moles} \times \text{Molar mass} \]
The molar mass of \( H_2SO_4 \) is approximately 98 g/mol. Therefore:
\[ \text{Mass of } H_2SO_4 = 8.19 \, \text{moles} \times 98 \, \text{g/mol} = 802.62 \, \text{grams} \]

### Step 4: Calculate the mass of the solution
The mass of the solution is the sum of the mass of the solute and the mass of the solvent:
\[ \text{Mass of solution} = \text{Mass of solute} + \text{Mass of solvent} \]
Substituting the values:
\[ \text{Mass of solution} = 802.62 \, \text{grams} + 910 \, \text{grams} = 1712.62 \, \text{grams} \]

### Step 5: Calculate the percentage concentration \( x \)
The percentage concentration \( x \) can be calculated using the formula:
\[ x = \left( \frac{\text{Mass of solute}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values:
\[ x = \left( \frac{802.62 \, \text{grams}}{1712.62 \, \text{grams}} \right) \times 100 \approx 46.87\% \]

### Final Answer
The value of \( x \) is approximately **46.87%**.

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