Calculate the molality and molarity of a solution made by mixing equal volumes of `30%` by weight of `H_(2)SO_(4)` (density`=1.20g//ml`) and `70%` by weight of `H_(2)SO_(4)` (density`=1.60g//mL`)

Explanation

To calculate the molality and molarity of a solution made by mixing equal volumes of `30%` by weight of `H₂SO₄` (density `= 1.20 g/mL`) and `70%` by weight of `H₂SO₄` (density `= 1.60 g/mL`), we can follow these steps:

### Step 1: Calculate the mass of each solution

1. **For 30% H₂SO₄ solution:**
- Volume = 100 mL
- Density = 1.20 g/mL
- Mass = Density × Volume = 1.20 g/mL × 100 mL = 120 g

2. **For 70% H₂SO₄ solution:**
- Volume = 100 mL
- Density = 1.60 g/mL
- Mass = Density × Volume = 1.60 g/mL × 100 mL = 160 g

### Step 2: Calculate the total mass of the mixed solution

- Total mass of the solution = Mass of 30% solution + Mass of 70% solution
- Total mass = 120 g + 160 g = 280 g

### Step 3: Calculate the mass of H₂SO₄ in each solution

1. **For 30% H₂SO₄:**
- Mass of H₂SO₄ = (30/100) × Mass of solution = (30/100) × 120 g = 36 g

2. **For 70% H₂SO₄:**
- Mass of H₂SO₄ = (70/100) × Mass of solution = (70/100) × 160 g = 112 g

### Step 4: Calculate the total mass of H₂SO₄

- Total mass of H₂SO₄ = Mass from 30% solution + Mass from 70% solution
- Total mass of H₂SO₄ = 36 g + 112 g = 148 g

### Step 5: Calculate the number of moles of H₂SO₄

- Molar mass of H₂SO₄ = 98 g/mol
- Number of moles of H₂SO₄ = Mass / Molar mass = 148 g / 98 g/mol ≈ 1.51 moles

### Step 6: Calculate the mass of the solvent (water)

- Mass of solvent = Total mass of solution - Mass of H₂SO₄
- Mass of solvent = 280 g - 148 g = 132 g

### Step 7: Calculate the molality of the solution

- Molality (m) = Number of moles of solute / Mass of solvent (kg)
- Mass of solvent in kg = 132 g / 1000 = 0.132 kg
- Molality = 1.51 moles / 0.132 kg ≈ 11.44 molal

### Step 8: Calculate the total volume of the mixed solution

- Total volume = Volume of 30% solution + Volume of 70% solution
- Total volume = 100 mL + 100 mL = 200 mL

### Step 9: Calculate the molarity of the solution

- Molarity (M) = Number of moles of solute / Volume of solution (L)
- Volume of solution in L = 200 mL / 1000 = 0.2 L
- Molarity = 1.51 moles / 0.2 L = 7.55 M

### Final Answers:
- **Molality** = 11.44 molal
- **Molarity** = 7.55 M

---