The molal freezing point constant for water is `1.86^(@)C//m`. Therefore, the freezing point of 0.1 M NaCl solution in water is expected to be:

Options

A. `-1.86^(@)C`
B. `-0.186^(@)C`
C. `-0.372^(@)C`
D. `+0.372^(@)C`

Answer

To find the freezing point of a 0.1 M NaCl solution in water, we can follow these steps:

### Step 1: Understand the Concept of Freezing Point Depression
The freezing point depression can be calculated using the formula:
\[ \Delta T_f = i \cdot K_f \cdot m \]
where:
- \(\Delta T_f\) = depression in freezing point
- \(i\) = Van't Hoff factor (number of particles the solute dissociates into)
- \(K_f\) = molal freezing point constant of the solvent (for water, \(K_f = 1.86 \, °C/m\))
- \(m\) = molality of the solution

### Step 2: Calculate the Van't Hoff Factor for NaCl
Sodium chloride (NaCl) dissociates in water into two ions:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
Thus, the Van't Hoff factor \(i\) for NaCl is:
\[ i = 2 \quad (\text{1 Na}^+ \text{ and } 1 \text{ Cl}^-) \]

### Step 3: Convert Molarity to Molality
Since the question provides the concentration in molarity (0.1 M), we need to convert it to molality. However, for dilute solutions, molarity and molality can be approximated to be equal when the solvent is water. Therefore, we can consider:
\[ m \approx 0.1 \, m \]

### Step 4: Calculate the Freezing Point Depression
Substituting the values into the freezing point depression formula:
\[ \Delta T_f = i \cdot K_f \cdot m = 2 \cdot 1.86 \, °C/m \cdot 0.1 \, m \]
\[ \Delta T_f = 2 \cdot 1.86 \cdot 0.1 = 0.372 \, °C \]

### Step 5: Determine the Freezing Point of the Solution
The freezing point of pure water is 0 °C. The freezing point of the solution can be calculated as:
\[ \text{Freezing Point of Solution} = \text{Freezing Point of Solvent} - \Delta T_f \]
\[ \text{Freezing Point of Solution} = 0 \, °C - 0.372 \, °C = -0.372 \, °C \]

### Final Answer
The freezing point of the 0.1 M NaCl solution in water is approximately:
\[ \text{Freezing Point} = -0.372 \, °C \]

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