The number of pairs of the solutions having the same value of the osmotic pressure from the following is. `0.500M C_2H_5OH` (aq) and `0.25 M KBr` (aq)
B. `0.100 M K_4[Fe(CN)_6]` (aq) and `0.100 M FeSO_4(NH_4)_2SO_4` (aq)
C. `0.05 M K_4[Fe(CN)_6]` (aq) and `0.25 M NaCl (aq)`
D. `0.15MNaCl` (aq) and `0.01MBaCl_(2)(aq)`
E. `0.02MKCl*MgCl_(2)*6H_(2)O(aq)` and `0.05MKCl(aq)`

Answer

To determine the number of pairs of solutions having the same value of osmotic pressure, we will use the formula for osmotic pressure (π):

\[ \pi = iCRT \]

Where:
- \( \pi \) = osmotic pressure
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = molarity (concentration of the solution)
- \( R \) = ideal gas constant (constant for our calculations)
- \( T \) = temperature (constant for our calculations)

Since \( R \) and \( T \) are constant, we can compare \( iC \) for different solutions. Let's analyze each pair:

### Pair A:
- **0.500 M C₂H₅OH**:
- \( i = 1 \) (does not dissociate)
- \( iC = 1 \times 0.500 = 0.500 \)

- **0.25 M KBr**:
- \( i = 2 \) (dissociates into K⁺ and Br⁻)
- \( iC = 2 \times 0.25 = 0.500 \)

**Conclusion**: Both have the same osmotic pressure (0.500).

### Pair B:
- **0.100 M K₄[Fe(CN)₆]**:
- \( i = 5 \) (dissociates into 4 K⁺ and 1 [Fe(CN)₆]⁴⁻)
- \( iC = 5 \times 0.100 = 0.500 \)

- **0.100 M FeSO₄(NH₄)₂SO₄**:
- \( i = 5 \) (dissociates into 1 Fe²⁺, 2 NH₄⁺, and 2 SO₄²⁻)
- \( iC = 5 \times 0.100 = 0.500 \)

**Conclusion**: Both have the same osmotic pressure (0.500).

### Pair C:
- **0.05 M K₄[Fe(CN)₆]**:
- \( i = 5 \)
- \( iC = 5 \times 0.05 = 0.250 \)

- **0.25 M NaCl**:
- \( i = 2 \)
- \( iC = 2 \times 0.25 = 0.500 \)

**Conclusion**: Different osmotic pressures (0.250 vs 0.500).

### Pair D:
- **0.15 M NaCl**:
- \( i = 2 \)
- \( iC = 2 \times 0.15 = 0.300 \)

- **0.01 M BaCl₂**:
- \( i = 3 \) (dissociates into Ba²⁺ and 2 Cl⁻)
- \( iC = 3 \times 0.01 = 0.030 \)

**Conclusion**: Different osmotic pressures (0.300 vs 0.030).

### Pair E:
- **0.02 M KCl·MgCl₂·6H₂O**:
- \( i = 5 \) (dissociates into 1 K⁺ and 2 Cl⁻ and 1 Mg²⁺)
- \( iC = 5 \times 0.02 = 0.100 \)

- **0.05 M KCl**:
- \( i = 2 \)
- \( iC = 2 \times 0.05 = 0.100 \)

**Conclusion**: Both have the same osmotic pressure (0.100).

### Summary of Pairs with Same Osmotic Pressure:
- Pair A: Same (0.500)
- Pair B: Same (0.500)
- Pair C: Different
- Pair D: Different
- Pair E: Same (0.100)

### Final Count of Pairs with Same Osmotic Pressure:
Total pairs with the same osmotic pressure = 4 (A, B, E).

### Final Answer:
The number of pairs of solutions having the same value of osmotic pressure is **4**.

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