The molality of 15 % by wt solution of `H_2SO_4` is

Options

A. 18
B. 2.6
C. 1.2
D. 1.8

Answer

To find the molality of a 15% by weight solution of H₂SO₄, 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:
\[ \text{Molality} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

### Step 2: Determine the Amount of Solute and Solvent
Given that the solution is 15% by weight, this means that in 100 grams of the solution, there are 15 grams of H₂SO₄ (solute) and the remaining weight is the solvent (water).

- Mass of H₂SO₄ (solute) = 15 g
- Mass of solution = 100 g
- Mass of solvent (water) = 100 g - 15 g = 85 g

### Step 3: Convert the Mass of Solvent to Kilograms
Since molality is calculated using the mass of the solvent in kilograms, we need to convert grams to kilograms:
\[ \text{Mass of solvent} = 85 \text{ g} = 0.085 \text{ kg} \]

### Step 4: Calculate the Moles of H₂SO₄
To find the moles of H₂SO₄, we need to use its molar mass. The molar mass of H₂SO₄ is calculated as follows:
- H: 1 g/mol × 2 = 2 g/mol
- S: 32 g/mol × 1 = 32 g/mol
- O: 16 g/mol × 4 = 64 g/mol

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

Now, we can calculate the number of moles of H₂SO₄:
\[ \text{Moles of H₂SO₄} = \frac{\text{mass of H₂SO₄}}{\text{molar mass of H₂SO₄}} = \frac{15 \text{ g}}{98 \text{ g/mol}} \approx 0.153 \text{ moles} \]

### Step 5: Calculate the Molality
Now that we have the moles of solute and the mass of the solvent in kilograms, we can calculate the molality:
\[ \text{Molality} = \frac{0.153 \text{ moles}}{0.085 \text{ kg}} \approx 1.8 \text{ mol/kg} \]

### Final Answer
The molality of the 15% by weight solution of H₂SO₄ is approximately **1.8 mol/kg**.

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