The density of 2.0 M solution of a solute is `1.2 g mL^(-1)`. If the molecular mass of the solute is `100 g mol^(-1)`, then the molality of the solution is

Options

A. 2.0 m
B. 1.2 m
C. 1.0 m
D. 0.6 m

Explanation

To find the molality of a solution given its molarity, density, and molecular mass of the solute, we can follow these steps:

### Step 1: Understand the given data
- Molarity (M) = 2.0 M
- Density of the solution = 1.2 g/mL
- Molecular mass of the solute = 100 g/mol

### Step 2: Calculate the mass of the solution
Since molarity is defined as the number of moles of solute per liter of solution, we can determine the number of moles of solute in 1 liter (1000 mL) of solution.

\[ \text{Number of moles of solute} = \text{Molarity} \times \text{Volume of solution (L)} = 2.0 \, \text{mol/L} \times 1 \, \text{L} = 2 \, \text{mol} \]

Now, we can calculate the mass of the solution using its density:

\[ \text{Mass of solution} = \text{Density} \times \text{Volume} = 1.2 \, \text{g/mL} \times 1000 \, \text{mL} = 1200 \, \text{g} \]

### Step 3: Calculate the mass of the solute
Using the number of moles of solute and its molecular mass, we can find the mass of the solute:

\[ \text{Mass of solute} = \text{Number of moles} \times \text{Molecular mass} = 2 \, \text{mol} \times 100 \, \text{g/mol} = 200 \, \text{g} \]

### Step 4: Calculate the mass of the solvent
The mass of the solvent can be calculated by subtracting the mass of the solute from the mass of the solution:

\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} = 1200 \, \text{g} - 200 \, \text{g} = 1000 \, \text{g} \]

### Step 5: Convert the mass of the solvent to kilograms
Since molality is defined as the number of moles of solute per kilogram of solvent, we convert the mass of the solvent from grams to kilograms:

\[ \text{Mass of solvent in kg} = \frac{1000 \, \text{g}}{1000} = 1 \, \text{kg} \]

### Step 6: Calculate the molality of the solution
Now we can calculate the molality (m):

\[ \text{Molality} (m) = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} = \frac{2 \, \text{mol}}{1 \, \text{kg}} = 2 \, \text{m} \]

### Final Answer
The molality of the solution is **2 m**.

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