If 0.1 molar solution of glucose (Molecular weight `=180`) is separated from 0.1 molar solution of cane sugar (Molecular weight `=242`) by a semi -permeable membrane, then which one of the following statements is correct?

Options

A. Water will flow from glucose solution into cane sugar solution.
B. Cane sugar will flow across the mebrane into glucose solution.
C. Glucose will flow across the membrane into cane sugar solution.
D. There will be no net movement across the semi-permeable membrane.

Explanation

To solve the problem, we need to analyze the situation involving two solutions separated by a semi-permeable membrane. The solutions in question are:

1. A 0.1 molar solution of glucose (Molecular weight = 180 g/mol)
2. A 0.1 molar solution of cane sugar (Molecular weight = 242 g/mol)

### Step 1: Understand the concept of osmotic pressure
Osmotic pressure is the pressure required to prevent the flow of solvent into a solution via osmosis. It can be calculated using the formula:
\[ \Pi = i \cdot M \cdot R \cdot T \]
where:
- \( \Pi \) = osmotic pressure
- \( i \) = Van't Hoff factor (number of particles the solute dissociates into)
- \( M \) = molarity of the solution
- \( R \) = universal gas constant
- \( T \) = temperature in Kelvin

### Step 2: Determine the Van't Hoff factor for both solutes
For both glucose and cane sugar:
- Glucose does not dissociate in solution, so \( i = 1 \).
- Cane sugar also does not dissociate in solution, so \( i = 1 \).

### Step 3: Calculate the osmotic pressure for both solutions
Since both solutions have the same molarity (0.1 M) and the same Van't Hoff factor (1), we can conclude:
- Osmotic pressure of glucose solution:
\[ \Pi_{glucose} = 1 \cdot 0.1 \cdot R \cdot T \]
- Osmotic pressure of cane sugar solution:
\[ \Pi_{cane\ sugar} = 1 \cdot 0.1 \cdot R \cdot T \]

Thus, both solutions have the same osmotic pressure.

### Step 4: Determine the implications of equal osmotic pressure
When two solutions have the same osmotic pressure, they are said to be isotonic. In an isotonic solution, there is no net movement of solvent across the semi-permeable membrane.

### Step 5: Evaluate the provided statements
Now, let's analyze the statements given in the question:
- **Statement A**: Water will flow from glucose solution into cane sugar. (Incorrect, as there is no net flow)
- **Statement B**: Cane sugar will flow across the membrane. (Incorrect, solutes do not cross the semi-permeable membrane)
- **Statement C**: Glucose will flow across the membrane. (Incorrect, solutes do not cross the semi-permeable membrane)
- **Statement D**: There will be no net movement across the semi-permeable membrane in isotonic solution. (Correct)

### Conclusion
The correct answer is **Statement D**: There will be no net movement across the semi-permeable membrane in isotonic solution.

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