A `5.8%` solution of `NaCI` has vapour pressure closest to:

Options

A. `5.8%` solution of urea
B. 2m solution of glucose
C. 1m solution of urea
D. `5.8%` solution of glucose

Explanation

To determine the vapor pressure of a 5.8% NaCl solution, we will follow these steps:

### Step 1: Understand the Meaning of a 5.8% Solution
A 5.8% NaCl solution means that there are 5.8 grams of NaCl in 100 mL of solution.

### Step 2: Calculate the Molar Mass of NaCl
The molar mass of NaCl (sodium chloride) can be calculated as follows:
- Sodium (Na) = 23 g/mol
- Chlorine (Cl) = 35.5 g/mol
- Molar mass of NaCl = 23 + 35.5 = 58.5 g/mol

### Step 3: Calculate the Number of Moles of NaCl
To find the number of moles of NaCl in the solution:
\[ \text{Number of moles} = \frac{\text{mass of solute}}{\text{molar mass}} = \frac{5.8 \text{ g}}{58.5 \text{ g/mol}} \approx 0.099 \text{ moles} \]

### Step 4: Calculate the Molality of the Solution
Since we are considering a 5.8% solution, we can assume the density of the solution is close to that of water (1 g/mL). Thus, 100 mL of solution weighs approximately 100 g, and the mass of the solvent (water) can be estimated as:
\[ \text{Mass of solvent} = 100 \text{ g (solution)} - 5.8 \text{ g (NaCl)} = 94.2 \text{ g} = 0.0942 \text{ kg} \]
Now, we can calculate the molality (m) of the solution:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} = \frac{0.099 \text{ moles}}{0.0942 \text{ kg}} \approx 1.05 \text{ mol/kg} \]

### Step 5: Determine the Van't Hoff Factor for NaCl
NaCl dissociates into two ions in solution:
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
Thus, the Van't Hoff factor (i) for NaCl is 2.

### Step 6: Calculate the Effective Concentration
The effective concentration of particles in solution can be calculated as:
\[ \text{Effective molality} = i \times \text{molality} = 2 \times 1.05 \approx 2.1 \]

### Step 7: Compare with Glucose Solution
For comparison, a 2 molal solution of glucose has a Van't Hoff factor of 1 (since glucose does not dissociate). Therefore, the vapor pressure of the 5.8% NaCl solution will be closest to that of a 2 molal glucose solution.

### Final Answer
The vapor pressure of a 5.8% NaCl solution is closest to that of a 2 molal glucose solution.

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