Calculate the normal freezing point of a sample of sea water containing 3.8% NaCl and 0.12 % `MgCl_(2)` by mass .(`k_(f)` for water ` = 1.86 km^(-1)`).

Explanation

To calculate the normal freezing point of a sample of seawater containing 3.8% NaCl and 0.12% MgCl₂ by mass, we will follow these steps:

### Step 1: Determine the mass of solutes
Given the percentages, we can assume we have 100 g of seawater. Thus:
- Mass of NaCl = 3.8 g
- Mass of MgCl₂ = 0.12 g

### Step 2: Calculate the number of moles of each solute
1. **For NaCl:**
- Molar mass of NaCl = 58.5 g/mol
- Moles of NaCl = mass / molar mass = 3.8 g / 58.5 g/mol = 0.065 moles

2. **For MgCl₂:**
- Molar mass of MgCl₂ = 24.3 (Mg) + 2 × 35.5 (Cl) = 95.3 g/mol
- Moles of MgCl₂ = mass / molar mass = 0.12 g / 95.3 g/mol = 0.00126 moles

### Step 3: Determine the Van't Hoff factors (i)
- For NaCl, it dissociates into Na⁺ and Cl⁻, so i = 2.
- For MgCl₂, it dissociates into Mg²⁺ and 2 Cl⁻, so i = 3.

### Step 4: Calculate the total number of moles of particles in solution
Using the Van't Hoff factors:
- Total moles from NaCl = 0.065 moles × 2 = 0.130 moles
- Total moles from MgCl₂ = 0.00126 moles × 3 = 0.00378 moles

Total moles of particles = 0.130 + 0.00378 = 0.1338 moles

### Step 5: Calculate the mass of the solvent (water)
Assuming 100 g of seawater:
- Mass of water = 100 g - (mass of NaCl + mass of MgCl₂)
- Mass of water = 100 g - (3.8 g + 0.12 g) = 96.08 g

### Step 6: Convert mass of water to kilograms
- Mass of water in kg = 96.08 g / 1000 = 0.09608 kg

### Step 7: Calculate molality (m)
Molality (m) = moles of solute / mass of solvent (kg)
- m = 0.1338 moles / 0.09608 kg = 1.39 molal

### Step 8: Calculate the depression in freezing point (ΔTf)
Using the formula:
ΔTf = Kf × m
- Kf for water = 1.86 °C kg/mol
- ΔTf = 1.86 °C kg/mol × 1.39 molal = 2.59 °C

### Step 9: Calculate the new freezing point (Tf)
The normal freezing point of pure water is 0 °C, so:
- Tf = 0 °C - ΔTf = 0 °C - 2.59 °C = -2.59 °C

### Final Answer
The normal freezing point of the seawater sample is **-2.59 °C**.

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