Which of the following solutions at the same temperature will be isotonic?

Options

A. 3.42 g of cane sugar in one litre water and 0.18 g of glucose in one litre water.
B. 3.42 g of cane sugar in one litre water and 0.18 g of glucose in 0.1 litre water.
C. 3.42 g of cane sugar in one litre water and 0.585 g of NaCl in one litre water.
D. 3.42 g of cane sugar in one litre water and 1.17 g of NaCl in one litre water.

Answer

To determine which of the given solutions are isotonic at the same temperature, we need to compare their osmotic pressures. Isotonic solutions have equal osmotic pressures. The osmotic pressure (π) can be calculated using the formula:

\[ \pi = iCRT \]

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

Since \( R \) and \( T \) are constant for all solutions, we only need to focus on the van't Hoff factor (\( i \)) and the concentration (\( C \)) of each solution.

### Step-by-Step Solution:

1. **Identify the Solutions**:
We have two solutions to compare:
- Solution A: Cane sugar (3.42 g in 1 L)
- Solution B: Glucose (0.18 g in 0.1 L)

2. **Calculate Molar Mass**:
- For Cane Sugar (C12H22O11):
\[ \text{Molar mass} = 12 \times 12 + 22 \times 1 + 11 \times 16 = 342 \, \text{g/mol} \]
- For Glucose (C6H12O6):
\[ \text{Molar mass} = 6 \times 12 + 12 \times 1 + 6 \times 16 = 180 \, \text{g/mol} \]

3. **Calculate Concentration (C)**:
- For Cane Sugar:
\[ C = \frac{3.42 \, \text{g}}{342 \, \text{g/mol}} = 0.01 \, \text{mol/L} \]
- For Glucose:
\[ C = \frac{0.18 \, \text{g}}{180 \, \text{g/mol}} = 0.001 \, \text{mol/L} \]
Since the volume is 0.1 L:
\[ C = \frac{0.001}{0.1} = 0.01 \, \text{mol/L} \]

4. **Determine Van't Hoff Factor (i)**:
- Cane Sugar: Non-electrolyte, \( i = 1 \)
- Glucose: Non-electrolyte, \( i = 1 \)

5. **Calculate Osmotic Pressure**:
- For Cane Sugar:
\[ \pi = iCRT = 1 \times 0.01 \times RT = 0.01RT \]
- For Glucose:
\[ \pi = iCRT = 1 \times 0.01 \times RT = 0.01RT \]

6. **Compare Osmotic Pressures**:
Both solutions have the same osmotic pressure of \( 0.01RT \), indicating they are isotonic.

### Conclusion:
The correct answer is that the solutions containing 3.42 g of cane sugar in 1 L and 0.18 g of glucose in 0.1 L are isotonic.