Which of the following pair of solutions can be expected to be isotonic at the same temperature ?

Options

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

Answer

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

\[ \pi = iCRT \]

Where:
- \(i\) = van't Hoff factor (number of particles the solute dissociates into)
- \(C\) = concentration of the solution
- \(R\) = universal gas constant
- \(T\) = temperature (which is constant for this problem)

Since \(R\) and \(T\) are constant, we can focus on the values of \(i\) and \(C\). If two solutions have the same concentration and the same van't Hoff factor, they will have the same osmotic pressure and thus will be isotonic.

Let's analyze each option:

### Option A: 0.1 molar urea and 0.1 molar NaCl
- **Urea** does not dissociate, so \(i = 1\).
- **NaCl** dissociates into Na\(^+\) and Cl\(^-\), so \(i = 2\).
- Since \(i\) values are different (1 for urea and 2 for NaCl), they are **not isotonic**.

### Option B: 0.1 molar NaCl and 0.1 molar Na2SO4
- **NaCl** has \(i = 2\).
- **Na2SO4** dissociates into 2 Na\(^+\) and 1 SO4\(^{2-}\), so \(i = 3\).
- Since \(i\) values are different (2 for NaCl and 3 for Na2SO4), they are **not isotonic**.

### Option C: 0.1 molar calcium nitrate and 0.1 molar sodium sulfate
- **Sodium sulfate** has already been calculated to have \(i = 3\).
- **Calcium nitrate** (Ca(NO3)2) dissociates into 1 Ca\(^{2+}\) and 2 NO3\(^-\), giving \(i = 3\).
- Both solutions have the same \(i\) value (3) and the same concentration (0.1 molar), therefore they are **isotonic**.

### Option D: 0.1 molar glucose and 0.1 molar MgCl2
- **Glucose** does not dissociate, so \(i = 1\).
- **MgCl2** dissociates into 1 Mg\(^{2+}\) and 2 Cl\(^-\), so \(i = 3\).
- Since \(i\) values are different (1 for glucose and 3 for MgCl2), they are **not isotonic**.

### Conclusion:
The only pair of solutions that can be expected to be isotonic at the same temperature is **Option C: 0.1 molar calcium nitrate and 0.1 molar sodium sulfate**.

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