Calcualate the molarity and molality of 20% aqueous ehtanol `(C_(5) H_(5) OH)` solution by volume. (density of solution `= 0.96 g mL^(-1)`)

Explanation

To calculate the molarity and molality of a 20% aqueous ethanol (C2H5OH) solution by volume, we will follow these steps:

### Step 1: Understand the given data
- **Volume percentage of ethanol**: 20% (by volume)
- **Density of the solution**: 0.96 g/mL

### Step 2: Calculate the volume of ethanol and water in 100 mL of solution
Since the solution is 20% ethanol by volume, in 100 mL of the solution:
- Volume of ethanol (C2H5OH) = 20 mL
- Volume of water = 100 mL - 20 mL = 80 mL

### Step 3: Calculate the mass of the solution
Using the density of the solution:
- Mass of the solution = Volume × Density
- Mass of the solution = 100 mL × 0.96 g/mL = 96 g

### Step 4: Calculate the mass of ethanol
To find the mass of ethanol in the solution, we need to use the mass of the solution and the mass of water:
- Mass of water = Volume of water × Density of water (1 g/mL)
- Mass of water = 80 mL × 1 g/mL = 80 g

Now, we can find the mass of ethanol:
- Mass of ethanol = Mass of solution - Mass of water
- Mass of ethanol = 96 g - 80 g = 16 g

### Step 5: Calculate the number of moles of ethanol
To find the number of moles of ethanol, we need its molar mass:
- Molar mass of ethanol (C2H5OH) = 2(12) + 6(1) + 16 = 46 g/mol

Now we can calculate the number of moles:
- Number of moles of ethanol = Mass of ethanol / Molar mass of ethanol
- Number of moles of ethanol = 16 g / 46 g/mol ≈ 0.348 moles

### Step 6: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
- Molarity = Number of moles of ethanol / Volume of solution in liters
- Volume of solution = 100 mL = 0.1 L
- Molarity = 0.348 moles / 0.1 L = 3.48 M

### Step 7: Calculate the molality of the solution
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
- Mass of solvent (water) = 80 g = 0.08 kg
- Molality = Number of moles of ethanol / Mass of solvent in kg
- Molality = 0.348 moles / 0.08 kg = 4.35 m

### Final Answers
- **Molarity**: 3.48 M
- **Molality**: 4.35 m