Consider the following solutions:
I.1 M sucrose , II. 1 M KCl
III.1 M benzoic acid in benzene
IV.`1 M (NH_(3))_(3)PO_(4)`
Which of the following is/are true?

Options

A. All solutions are isotonic.
B. III is hypotonic of I,II, and IV.
C. I,II, and III are hypertonic of IV.
D. IV is hypertonic of I,II, and III.

Answer

To determine which of the given solutions are isotonic, we need to analyze the van 't Hoff factor (i) for each solution, as it affects the osmotic pressure (π) of the solutions. The osmotic pressure is given by the formula:

\[ \pi = iCRT \]

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

### Step-by-Step Solution:

1. **Identify the Solutions and Their Properties:**
- **I. 1 M Sucrose**: Sucrose is a non-electrolyte and does not dissociate in solution. Therefore, \( i = 1 \).
- **II. 1 M KCl**: KCl is an electrolyte that dissociates completely into K\(^+\) and Cl\(^-\). Therefore, \( i = 2 \).
- **III. 1 M Benzoic Acid in Benzene**: Benzoic acid can dimerize in non-polar solvents like benzene, leading to \( i < 1 \). For simplicity, we can assume \( i \approx 0.5 \) for this case.
- **IV. 1 M (NH\(_3\))\(_3\)PO\(_4\)**: Ammonium phosphate dissociates into 4 ions (3 NH\(_4^+\) and 1 PO\(_4^{3-}\)). Therefore, \( i = 4 \).

2. **Calculate the Effective Concentration for Each Solution:**
- For **I**: \( \pi_1 = i \cdot C = 1 \cdot 1 = 1 \)
- For **II**: \( \pi_2 = i \cdot C = 2 \cdot 1 = 2 \)
- For **III**: \( \pi_3 = i \cdot C \approx 0.5 \cdot 1 = 0.5 \)
- For **IV**: \( \pi_4 = i \cdot C = 4 \cdot 1 = 4 \)

3. **Compare the Osmotic Pressures:**
- \( \pi_1 = 1 \)
- \( \pi_2 = 2 \)
- \( \pi_3 = 0.5 \)
- \( \pi_4 = 4 \)

4. **Determine Isotonic Solutions:**
- Solutions are isotonic if they have the same osmotic pressure. Here, the osmotic pressures are different:
- **IV** is hypertonic (highest pressure).
- **II** is hypertonic compared to I and III.
- **I** is isotonic with II but hypertonic to III.
- **III** is hypotonic (lowest pressure).

### Conclusion:
- The solutions are not isotonic as they have different osmotic pressures. Therefore, the statement "all solutions are isotonic" is false.

### Final Answer:
None of the solutions are isotonic.

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