At the same temperature, following solution will be isotonic

Options

A. 3.24 g of sucrose per litre of water and 0.18 gm glucose per litre of water
B. 3.42 gm of sucrose per litre and 0.18 gm glucose in 0.1 litre water
C. 3.24 gm of surcose per litre of water and 0.585 gm of sodium chloride per litre of water
D. 3.42 gm of sucrose per litre of water and 1.17 gm of sodium chloride per litre of water

Answer

To determine which solutions are isotonic, we need to compare the osmotic pressures of the given solutions. Isotonic solutions have equal osmotic pressure, which means their concentrations must be equal when expressed in terms of moles of solute per liter of solution.

### Step-by-Step Solution:

1. **Understand the Concept of Isotonic Solutions**:
- Isotonic solutions have the same osmotic pressure. This occurs when the concentration of solute particles is equal in both solutions.

2. **Use the Formula for Osmotic Pressure**:
- The osmotic pressure (π) can be calculated using the formula:
\[ \pi = CRT \]
where \( C \) is the molarity (moles of solute per liter of solution), \( R \) is the universal gas constant, and \( T \) is the temperature in Kelvin.

3. **Calculate Moles of Sucrose**:
- For the first option, we have 3.24 g of sucrose (C₁₂H₂₂O₁₁).
- The molar mass of sucrose is 342 g/mol.
- Calculate the number of moles:
\[ \text{Moles of sucrose} = \frac{3.24 \, \text{g}}{342 \, \text{g/mol}} \approx 0.0095 \, \text{mol} \]

4. **Calculate Moles of Glucose**:
- For the second option, we have 0.18 g of glucose (C₆H₁₂O₆).
- The molar mass of glucose is 180 g/mol.
- Calculate the number of moles:
\[ \text{Moles of glucose} = \frac{0.18 \, \text{g}}{180 \, \text{g/mol}} = 0.001 \, \text{mol} \]

5. **Compare Moles**:
- The moles of sucrose (0.0095 mol) and glucose (0.001 mol) are not equal, so these solutions are not isotonic.

6. **Calculate Moles for NaCl**:
- For the second option, we have 3.42 g of sucrose.
- Calculate the moles:
\[ \text{Moles of sucrose} = \frac{3.42 \, \text{g}}{342 \, \text{g/mol}} \approx 0.01 \, \text{mol} \]
- For NaCl, we have 0.585 g.
- The molar mass of NaCl is 58.5 g/mol.
- Calculate the moles:
\[ \text{Moles of NaCl} = \frac{0.585 \, \text{g}}{58.5 \, \text{g/mol}} = 0.01 \, \text{mol} \]

7. **Compare Moles for Isotonic Condition**:
- The moles of sucrose (0.01 mol) and NaCl (0.01 mol) are equal, indicating that these solutions are isotonic.

8. **Conclusion**:
- The second option (3.42 g of sucrose and 0.585 g of NaCl) is isotonic because the number of moles of solute in both solutions is equal.