An aqueous solution of glucose is `10%` in strength ,The volume in which `1`g mole of it dissolved will be

Options

A. 18 litre
B. 9 litre
C. 0.9 litre
D. 1.8 litre

Explanation

To solve the problem of how much volume will 1 gram mole of glucose dissolve in a 10% aqueous solution, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the meaning of 10% weight by volume solution**:
- A 10% weight by volume (w/v) solution means that there are 10 grams of solute (glucose) in 100 mL of solution.

2. **Determine the molar mass of glucose**:
- The molecular formula of glucose is C₆H₁₂O₆.
- To calculate its molar mass:
- Carbon (C): 12 g/mol × 6 = 72 g/mol
- Hydrogen (H): 1 g/mol × 12 = 12 g/mol
- Oxygen (O): 16 g/mol × 6 = 96 g/mol
- Total molar mass = 72 + 12 + 96 = 180 g/mol.

3. **Calculate the volume of solution for 1 mole of glucose**:
- Since 1 mole of glucose weighs 180 grams, we need to find out how much volume of the solution contains 180 grams of glucose.
- From the 10% solution, we know that 10 grams of glucose is present in 100 mL of solution.
- We can set up a proportion to find the volume (V) that contains 180 grams of glucose:
\[ \frac{10 \text{ g}}{100 \text{ mL}} = \frac{180 \text{ g}}{V} \]

4. **Cross-multiply and solve for V**:
- Cross-multiplying gives:
\[ 10 \text{ g} \cdot V = 180 \text{ g} \cdot 100 \text{ mL} \]
- Simplifying:
\[ 10V = 18000 \]
- Dividing both sides by 10:
\[ V = 1800 \text{ mL} \]

5. **Convert mL to liters**:
- Since the answer is typically required in liters, convert 1800 mL to liters:
\[ V = \frac{1800 \text{ mL}}{1000} = 1.8 \text{ L} \]

### Final Answer:
The volume in which 1 gram mole of glucose is dissolved is **1.8 liters**.

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