An aqueous solution of ethanol has density `1.025 g// mL` and it is 2 M. What is the molality of this solution ?

Options

A. `1.79`
B. `2.143`
C. `1.951`
D. None of these

Answer

To find the molality of the ethanol solution, we can follow these steps:

### Step 1: Understand the Definitions
- **Molarity (M)** is defined as the number of moles of solute per liter of solution.
- **Molality (m)** is defined as the number of moles of solute per kilogram of solvent.

### Step 2: Gather Given Information
- Density of the solution = 1.025 g/mL
- Molarity of the solution = 2 M (which means 2 moles of ethanol per liter of solution)

### Step 3: Convert Molarity to Mass of Solution
Since molarity is given as 2 M, we know that in 1 liter (1000 mL) of solution, there are 2 moles of ethanol.

### Step 4: Calculate the Mass of Ethanol
- Molar mass of ethanol (C2H5OH) = 2(12) + 6(1) + 16 = 46 g/mol
- Mass of ethanol in 1 L of solution = 2 moles × 46 g/mol = 92 g

### Step 5: Calculate the Mass of the Solution
- The density of the solution is 1.025 g/mL, so the mass of 1 L (1000 mL) of solution = 1.025 g/mL × 1000 mL = 1025 g

### Step 6: Calculate the Mass of the Solvent (Water)
- Mass of solvent (water) = Mass of solution - Mass of solute (ethanol)
- Mass of solvent = 1025 g - 92 g = 933 g

### Step 7: Convert Mass of Solvent to Kilograms
- Mass of solvent in kg = 933 g ÷ 1000 = 0.933 kg

### Step 8: Calculate Molality
- Molality (m) = moles of solute / kg of solvent
- Moles of solute (ethanol) = 2 moles (from the molarity)
- Molality = 2 moles / 0.933 kg ≈ 2.14 mol/kg

### Final Answer
The molality of the ethanol solution is approximately **2.14 mol/kg**.

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