Lowering of vapour pressures of equimolar solution of glucose, sodium chloride and barium nitrate are in the order.

Options

A. Glucose `gt NaCl gt Ba (NO_(3))_(2)`
B. Glucose `= NaCl = Ba(NO_(3))_(2)`
C. `Ba(NO_(3))_(2)gt NaCl gt` Glucose
D. `NaCl gt Ba(NO_(3))_(2)gt` Glucose

Explanation

To determine the order of lowering of vapor pressures of equimolar solutions of glucose, sodium chloride, and barium nitrate, we can follow these steps:

### Step 1: Understand the Concept of Vapor Pressure Lowering
The lowering of vapor pressure of a solution is related to the number of solute particles in the solution. The relative lowering of vapor pressure can be expressed as:
\[ \frac{P_0 - P}{P_0} = x_2 \]
where \(P_0\) is the vapor pressure of the pure solvent, \(P\) is the vapor pressure of the solution, and \(x_2\) is the mole fraction of the solute.

### Step 2: Identify the Type of Solutes
- **Glucose**: A non-electrolyte that does not dissociate in solution. Therefore, it contributes 1 particle per formula unit (n = 1).
- **Sodium Chloride (NaCl)**: An electrolyte that dissociates into two ions (Na\(^+\) and Cl\(^-\)). Therefore, it contributes 2 particles per formula unit (n = 2).
- **Barium Nitrate (Ba(NO₃)₂)**: An electrolyte that dissociates into three ions (Ba\(^{2+}\) and two NO₃\(^-\)). Therefore, it contributes 3 particles per formula unit (n = 3).

### Step 3: Calculate the Van't Hoff Factor (i)
The Van't Hoff factor (i) is defined as the number of particles the solute produces in solution:
- For glucose: \(i = 1\)
- For NaCl: \(i = 2\)
- For barium nitrate: \(i = 3\)

### Step 4: Relate Vapor Pressure Lowering to the Van't Hoff Factor
The lowering of vapor pressure is directly proportional to the number of solute particles:
\[ P_0 - P \propto i \]
Thus, we can conclude:
- Glucose: \(P_0 - P \propto 1\)
- NaCl: \(P_0 - P \propto 2\)
- Barium Nitrate: \(P_0 - P \propto 3\)

### Step 5: Determine the Order of Lowering of Vapor Pressure
From the above analysis, we can establish the order of lowering of vapor pressure:
\[ \text{Barium Nitrate} > \text{Sodium Chloride} > \text{Glucose} \]

### Final Answer
The order of lowering of vapor pressures of equimolar solutions of glucose, sodium chloride, and barium nitrate is:
\[ \text{Barium Nitrate} > \text{Sodium Chloride} > \text{Glucose} \]