Which salt shows maximum osmotic pressure in its `1 m` solution.

Options

A. `AgNO_(3)`
B. `Na_(2)SO_(4)`
C. `(NH_(4))(3)PO_(4)`
D. `MgCl_(2)`

Explanation

To determine which salt shows maximum osmotic pressure in a 1 m solution, we can use the formula for osmotic pressure:

\[ \pi = iCRT \]

Where:
- \(\pi\) = osmotic pressure
- \(i\) = van 't Hoff factor (number of particles the solute dissociates into)
- \(C\) = molarity of the solution
- \(R\) = universal gas constant
- \(T\) = temperature in Kelvin

Since \(C\), \(R\), and \(T\) are constant for the same conditions, we can focus on the van 't Hoff factor \(i\). The higher the value of \(i\), the greater the osmotic pressure.

Now, let's analyze the dissociation of each salt:

1. **AgNO3**:
- Dissociation: \( \text{AgNO}_3 \rightarrow \text{Ag}^+ + \text{NO}_3^- \)
- Number of particles (\(i\)): 2

2. **Na2SO4**:
- Dissociation: \( \text{Na}_2\text{SO}_4 \rightarrow 2\text{Na}^+ + \text{SO}_4^{2-} \)
- Number of particles (\(i\)): 3

3. **NH4(PO4)**:
- Dissociation: \( \text{NH}_4\text{PO}_4 \rightarrow 3\text{NH}_4^+ + \text{PO}_4^{3-} \)
- Number of particles (\(i\)): 4

4. **MgCl2**:
- Dissociation: \( \text{MgCl}_2 \rightarrow \text{Mg}^{2+} + 2\text{Cl}^- \)
- Number of particles (\(i\)): 3

Now we can summarize the values of \(i\) for each salt:

- AgNO3: \(i = 2\)
- Na2SO4: \(i = 3\)
- NH4(PO4): \(i = 4\)
- MgCl2: \(i = 3\)

From the above calculations, we can see that the salt with the highest van 't Hoff factor \(i\) is **NH4(PO4)** with \(i = 4\).

Thus, the salt that shows maximum osmotic pressure in its 1 m solution is **NH4(PO4)**.