Which among the following will show maximum osmotic pressure ?

Options

A. 1 M NaCl
B. `1M MgCl_(2)`
C. `1M (NH_(4))_(3)PO_(4)`
D. `1M Na_(2)SO_(4)`

Explanation

To determine which substance will show the maximum osmotic pressure, we can follow these steps:

### Step 1: Understand the formula for osmotic pressure
The osmotic pressure (π) is given by the formula:
\[ \pi = i \cdot C \cdot R \cdot T \]
Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = concentration of the solution
- \( R \) = gas constant
- \( T \) = temperature

### Step 2: Identify constants
In this case, we are told that:
- The concentration (C) is 1 molar for all options.
- The temperature (T) is constant.
- The gas constant (R) is also constant.

Since C, R, and T are constants, we can simplify the equation to:
\[ \pi \propto i \]
This means that osmotic pressure is directly proportional to the van 't Hoff factor \( i \).

### Step 3: Determine the van 't Hoff factor (i) for each option
The van 't Hoff factor \( i \) is determined by the number of ions produced when the solute dissociates in solution.

1. **NaCl**:
- Dissociates into \( Na^+ \) and \( Cl^- \).
- \( i = 2 \) (1 Na+ + 1 Cl-)

2. **MgCl2**:
- Dissociates into \( Mg^{2+} \) and 2 \( Cl^- \).
- \( i = 3 \) (1 Mg2+ + 2 Cl-)

3. **\( NH_4)_3PO_4 \)**:
- Dissociates into 3 \( NH_4^+ \) and 1 \( PO_4^{3-} \).
- \( i = 4 \) (3 NH4+ + 1 PO4^3-)

4. **Na2SO4**:
- Dissociates into 2 \( Na^+ \) and \( SO_4^{2-} \).
- \( i = 3 \) (2 Na+ + 1 SO4^2-)

### Step 4: Compare the values of \( i \)
Now we can compare the values of \( i \) for each option:
- NaCl: \( i = 2 \)
- MgCl2: \( i = 3 \)
- \( (NH_4)_3PO_4 \): \( i = 4 \)
- Na2SO4: \( i = 3 \)

### Step 5: Determine which has the maximum osmotic pressure
Since osmotic pressure \( \pi \) is directly proportional to \( i \), the substance with the highest \( i \) will have the maximum osmotic pressure.

From our calculations, \( (NH_4)_3PO_4 \) has the highest \( i \) value of 4.

### Conclusion
Therefore, the substance that will show the maximum osmotic pressure is:
\[ \text{Option 3: } (NH_4)_3PO_4 \]

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