The molality of `1 L` solution with `x% H_(2)SO_(4)` is equal to 9. The weight of the solvent present in the solution is `910 g`. The value of `x` is:

Options

A. 90
B. 80.3
C. 40.13
D. 9

Explanation

To solve the problem, we need to find the value of \( x \) in the context of a solution of sulfuric acid (H₂SO₄) with a given molality and the weight of the solvent. Here’s the step-by-step solution:

### 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:
\[ \text{Molality} = \frac{\text{Number of moles of solute}}{\text{Weight of solvent (kg)}} \]

### Step 2: Convert the Weight of Solvent to Kilograms
Given that the weight of the solvent is 910 grams, we convert this to kilograms:
\[ \text{Weight of solvent (kg)} = \frac{910 \text{ g}}{1000} = 0.910 \text{ kg} \]

### Step 3: Calculate the Number of Moles of Solute
We know the molality is 9, so we can rearrange the formula to find the number of moles of solute:
\[ \text{Number of moles of solute} = \text{Molality} \times \text{Weight of solvent (kg)} = 9 \times 0.910 = 8.19 \text{ moles} \]

### Step 4: Calculate the Mass of H₂SO₄
Next, we need to find the mass of H₂SO₄ using the number of moles and its molar mass. The molar mass of H₂SO₄ is calculated as follows:
\[ \text{Molar mass of H₂SO₄} = (2 \times 1) + 32 + (4 \times 16) = 98 \text{ g/mol} \]
Now, we can find the mass of H₂SO₄:
\[ \text{Mass of H₂SO₄} = \text{Number of moles} \times \text{Molar mass} = 8.19 \times 98 = 803.28 \text{ g} \]

### Step 5: Calculate the Mass of the Solution
The mass of the solution can be calculated as the sum of the mass of the solute (H₂SO₄) and the mass of the solvent:
\[ \text{Mass of solution} = \text{Mass of solute} + \text{Mass of solvent} = 803.28 \text{ g} + 910 \text{ g} = 1713.28 \text{ g} \]

### Step 6: Calculate the Percentage of H₂SO₄ in the Solution
The percentage \( x \) of H₂SO₄ in the solution is given by:
\[ x\% = \left( \frac{\text{Mass of H₂SO₄}}{\text{Mass of solution}} \right) \times 100 \]
Substituting the values we found:
\[ x\% = \left( \frac{803.28}{1713.28} \right) \times 100 \approx 46.9\% \]

### Final Answer
Thus, the value of \( x \) is approximately **46.9**.

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