Correct increasing order of osmotic pressure for the following is

Options

A. Sucrose (0.1 M) `lt` glucose (0.5 M)`lt `urea(1M) `lt` NaCl(2M)
B. Glucose(0.5 M)`lt` urea (1M)` lt `NaCl(2M)`lt`Sucrose(0.1 M)`
C. Urea(1 M)`lt`NaCl(2M)`lt`glucose(0.5 M)`lt Sucrose(0.1 M)`
D. NaCl(2M)`lt` sucrose(0.1 M)`lt` glucose(0.5 M)`lt `urea(1M)

Answer

To determine the correct increasing order of osmotic pressure for the substances sucrose, glucose, urea, and NaCl, we will use the formula for osmotic pressure:

\[ \pi = I \cdot C \cdot R \cdot T \]

Where:
- \(\pi\) = osmotic pressure
- \(I\) = Van't Hoff factor (number of particles produced from the solute)
- \(C\) = concentration of the solution (in molarity)
- \(R\) = gas constant (which remains constant)
- \(T\) = temperature (which also remains constant)

### Step 1: Calculate the Van't Hoff factor (I) for each solute

1. **Sucrose**:
- Does not dissociate in solution.
- \(I = 1\)

2. **Glucose**:
- Also does not dissociate in solution.
- \(I = 1\)

3. **Urea**:
- Does not dissociate in solution.
- \(I = 1\)

4. **NaCl**:
- Dissociates into Na\(^+\) and Cl\(^-\).
- \(I = 2\)

### Step 2: Calculate the osmotic pressure for each solute

1. **Sucrose**:
- Concentration \(C = 0.1 \, \text{M}\)
- \(\pi = I \cdot C \cdot R \cdot T = 1 \cdot 0.1 \cdot R \cdot T = 0.1RT\)

2. **Glucose**:
- Concentration \(C = 0.5 \, \text{M}\)
- \(\pi = I \cdot C \cdot R \cdot T = 1 \cdot 0.5 \cdot R \cdot T = 0.5RT\)

3. **Urea**:
- Concentration \(C = 1 \, \text{M}\)
- \(\pi = I \cdot C \cdot R \cdot T = 1 \cdot 1 \cdot R \cdot T = 1RT\)

4. **NaCl**:
- Concentration \(C = 2 \, \text{M}\)
- \(\pi = I \cdot C \cdot R \cdot T = 2 \cdot 2 \cdot R \cdot T = 4RT\)

### Step 3: Compare the osmotic pressures

- Sucrose: \(0.1RT\)
- Glucose: \(0.5RT\)
- Urea: \(1RT\)
- NaCl: \(4RT\)

### Step 4: Arrange in increasing order of osmotic pressure

From the calculated osmotic pressures, we can arrange them in increasing order:

1. Sucrose: \(0.1RT\)
2. Glucose: \(0.5RT\)
3. Urea: \(1RT\)
4. NaCl: \(4RT\)

### Final Answer

The correct increasing order of osmotic pressure is:

**Sucrose < Glucose < Urea < NaCl**