Which one of the following pairs of solution can we expect to be isotonic at the same temperature

Options

A. `0.1M` urea and `0.1M NaCI`
B. `0.1M` urea dn `0.2M MgCI_(2)`
C. `0.1M NaCI` and `0.1M Na_(2)SO_(2)`
D. `0.1M Ca(NO_(3))_(2)` and `0.1M Na_(2)SO_(4)`

Explanation

To determine which pair of solutions can be expected to be isotonic at the same temperature, we need to calculate the osmotic pressure of each solution. The osmotic pressure (\( \pi \)) can be calculated using the formula:

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

Where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( C \) = molarity (concentration in mol/L)
- \( R \) = ideal gas constant (0.0821 L·atm/(K·mol))
- \( T \) = temperature in Kelvin (not needed for comparison since it's constant for all solutions)

### Step-by-Step Solution:

1. **Identify the Solutions**: We have the following pairs of solutions to analyze:
- Option 1: 0.1 mol urea and 0.1 mol NaCl
- Option 2: 0.1 mol urea and 0.1 mol MgCl2
- Option 3: 0.1 mol urea and 0.1 mol KCl
- Option 4: 0.1 mol Na2SO4 and 0.1 mol CaCl2

2. **Calculate Osmotic Pressure for Each Pair**:
- **Option 1**:
- Urea: \( i = 1 \) (does not dissociate)
- NaCl: \( i = 2 \) (dissociates into Na⁺ and Cl⁻)
- Osmotic Pressure for Urea: \( \pi_{urea} = 1 \cdot 0.1 = 0.1 \)
- Osmotic Pressure for NaCl: \( \pi_{NaCl} = 2 \cdot 0.1 = 0.2 \)

- **Option 2**:
- Urea: \( i = 1 \)
- MgCl2: \( i = 3 \) (dissociates into Mg²⁺ and 2 Cl⁻)
- Osmotic Pressure for Urea: \( \pi_{urea} = 0.1 \)
- Osmotic Pressure for MgCl2: \( \pi_{MgCl2} = 3 \cdot 0.1 = 0.3 \)

- **Option 3**:
- Urea: \( i = 1 \)
- KCl: \( i = 2 \) (dissociates into K⁺ and Cl⁻)
- Osmotic Pressure for Urea: \( \pi_{urea} = 0.1 \)
- Osmotic Pressure for KCl: \( \pi_{KCl} = 2 \cdot 0.1 = 0.2 \)

- **Option 4**:
- Na2SO4: \( i = 3 \) (dissociates into 2 Na⁺ and SO₄²⁻)
- CaCl2: \( i = 3 \) (dissociates into Ca²⁺ and 2 Cl⁻)
- Osmotic Pressure for Na2SO4: \( \pi_{Na2SO4} = 3 \cdot 0.1 = 0.3 \)
- Osmotic Pressure for CaCl2: \( \pi_{CaCl2} = 3 \cdot 0.1 = 0.3 \)

3. **Compare the Osmotic Pressures**:
- Option 1: \( \pi_{urea} = 0.1 \), \( \pi_{NaCl} = 0.2 \) (not isotonic)
- Option 2: \( \pi_{urea} = 0.1 \), \( \pi_{MgCl2} = 0.3 \) (not isotonic)
- Option 3: \( \pi_{urea} = 0.1 \), \( \pi_{KCl} = 0.2 \) (not isotonic)
- Option 4: \( \pi_{Na2SO4} = 0.3 \), \( \pi_{CaCl2} = 0.3 \) (isotonic)

### Conclusion:
The only pair of solutions that can be expected to be isotonic at the same temperature is **Option 4: 0.1 mol Na2SO4 and 0.1 mol CaCl2**.