100 ml 20% (by mass) H_(2)SO_(4)` (density=1.2 gm/ml) and 100 ml 40% (by mass) H_(2)SO_(4)` (density=1.4 gm/ml) are mixed together. Which are the correct concentration terms for this mixture ?

Options

A. Molality=2.54
B. Molarity=2.04
C. Molality=4.54
D. Molarity=4.08

Answer

To solve the problem, we need to find the molality and molarity of the mixture of two sulfuric acid solutions. Here’s a step-by-step breakdown of the solution:

### Step 1: Calculate the mass of each solution
1. **For 20% H₂SO₄:**
- Volume = 100 mL
- Density = 1.2 g/mL
- Mass = Density × Volume = 1.2 g/mL × 100 mL = 120 g

2. **For 40% H₂SO₄:**
- Volume = 100 mL
- Density = 1.4 g/mL
- Mass = Density × Volume = 1.4 g/mL × 100 mL = 140 g

### Step 2: Calculate the mass of H₂SO₄ in each solution
1. **For 20% H₂SO₄:**
- Mass of H₂SO₄ = 20% of 120 g = (20/100) × 120 g = 24 g

2. **For 40% H₂SO₄:**
- Mass of H₂SO₄ = 40% of 140 g = (40/100) × 140 g = 56 g

### Step 3: Calculate the total mass of H₂SO₄ and the total mass of the solution
- Total mass of H₂SO₄ = 24 g + 56 g = 80 g
- Total mass of the solution = 120 g + 140 g = 260 g

### Step 4: Calculate the mass of the solvent
- Mass of solvent = Total mass of solution - Mass of solute
- Mass of solvent = 260 g - 80 g = 180 g

### Step 5: Calculate molality (m)
Molality is defined as the number of moles of solute per kilogram of solvent.
1. **Calculate moles of H₂SO₄:**
- Molar mass of H₂SO₄ = 2(1) + 32 + 4(16) = 98 g/mol
- Moles of H₂SO₄ = Mass of H₂SO₄ / Molar mass = 80 g / 98 g/mol = 0.816 mol

2. **Calculate molality:**
- Molality (m) = Moles of solute / Mass of solvent (kg)
- Mass of solvent in kg = 180 g / 1000 = 0.180 kg
- Molality = 0.816 mol / 0.180 kg ≈ 4.53 mol/kg

### Step 6: Calculate molarity (M)
Molarity is defined as the number of moles of solute per liter of solution.
1. **Total volume of the solution:**
- Total volume = 100 mL + 100 mL = 200 mL = 0.200 L

2. **Calculate molarity:**
- Molarity (M) = Moles of solute / Volume of solution (L)
- Molarity = 0.816 mol / 0.200 L ≈ 4.08 mol/L

### Final Results
- **Molality ≈ 4.53 mol/kg**
- **Molarity ≈ 4.08 mol/L**