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

Options

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

Answer

To determine which pair of solutions can be expected to be isotonic at the same temperature, we need to calculate the osmotic pressure for each pair using the formula:

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

Where:
- \(\pi\) is the osmotic pressure,
- \(i\) is the Van't Hoff factor (number of particles the solute dissociates into),
- \(C\) is the concentration of the solution,
- \(R\) is the gas constant,
- \(T\) is the temperature.

### Step-by-Step Solution

1. **Identify the pairs of solutions**:
- A: 0.1 M urea and 0.1 M NaCl
- B: 0.1 M urea and 0.2 M MgCl₂
- C: 0.1 M NaCl and 0.1 M Na₂SO₄
- D: 0.1 M calcium nitrate and 0.1 M sodium sulfate

2. **Calculate osmotic pressure for each pair**:

**Pair A: 0.1 M urea and 0.1 M NaCl**
- Urea (non-electrolyte): \(i = 1\)
\[ \pi_{\text{urea}} = 1 \cdot 0.1 \cdot R \cdot T = 0.1RT \]
- NaCl (dissociates into Na⁺ and Cl⁻): \(i = 2\)
\[ \pi_{\text{NaCl}} = 2 \cdot 0.1 \cdot R \cdot T = 0.2RT \]
- **Conclusion**: Not isotonic (0.1RT ≠ 0.2RT)

**Pair B: 0.1 M urea and 0.2 M MgCl₂**
- Urea: \(i = 1\)
\[ \pi_{\text{urea}} = 0.1RT \]
- MgCl₂ (dissociates into Mg²⁺ and 2Cl⁻): \(i = 3\)
\[ \pi_{\text{MgCl₂}} = 3 \cdot 0.2 \cdot R \cdot T = 0.6RT \]
- **Conclusion**: Not isotonic (0.1RT ≠ 0.6RT)

**Pair C: 0.1 M NaCl and 0.1 M Na₂SO₄**
- NaCl: \(i = 2\)
\[ \pi_{\text{NaCl}} = 2 \cdot 0.1 \cdot R \cdot T = 0.2RT \]
- Na₂SO₄ (dissociates into 2Na⁺ and SO₄²⁻): \(i = 3\)
\[ \pi_{\text{Na₂SO₄}} = 3 \cdot 0.1 \cdot R \cdot T = 0.3RT \]
- **Conclusion**: Not isotonic (0.2RT ≠ 0.3RT)

**Pair D: 0.1 M calcium nitrate and 0.1 M sodium sulfate**
- Calcium nitrate (dissociates into Ca²⁺ and 2NO₃⁻): \(i = 3\)
\[ \pi_{\text{Ca(NO₃)₂}} = 3 \cdot 0.1 \cdot R \cdot T = 0.3RT \]
- Sodium sulfate (dissociates into 2Na⁺ and SO₄²⁻): \(i = 3\)
\[ \pi_{\text{Na₂SO₄}} = 3 \cdot 0.1 \cdot R \cdot T = 0.3RT \]
- **Conclusion**: Isotonic (0.3RT = 0.3RT)

3. **Final Answer**: The correct option is **D: 0.1 M calcium nitrate and 0.1 M sodium sulfate** as they have the same osmotic pressure and are therefore isotonic.