Question

The amount of sugar $ {(C_{12}H_{22}O_{11})}$ required to prepare $2\, L$ of its $0.1\, M$ aqueous solution is :

• A. 68.4 g
• B. 17.1 g
• C. 34.2g
• D. 136.8 g

Answer 1

The Correct Option is A

To solve this problem, we need to find out how much sugar (sucrose, C_{12}H_{22}O_{11}) is required to prepare 2 liters of a 0.1 M aqueous solution.

First, we will find the number of moles of sucrose needed:

1. The molarity (M) is defined as the number of moles of solute per liter of solution. Hence, M = \frac{\text{moles of solute}}{\text{volume of solution in liters}}.
2. We are preparing 2 L of a 0.1 M solution.
3. Using the formula for molarity: 0.1 = \frac{\text{moles of sucrose}}{2}
4. Solving for the moles of sucrose: \text{moles of sucrose} = 0.1 \times 2 = 0.2 moles.

Next, we will convert moles to grams using the molar mass of sucrose:

1. The molecular formula of sucrose is C_{12}H_{22}O_{11}.
2. The molar mass of sucrose is calculated as follows:
   1. Carbon (C): 12 atoms × 12 g/mol = 144 g/mol
   2. Hydrogen (H): 22 atoms × 1 g/mol = 22 g/mol
   3. Oxygen (O): 11 atoms × 16 g/mol = 176 g/mol
   4. Total: 144 + 22 + 176 = 342 \, \text{g/mol}
3. Grams of sucrose needed: \text{grams} = \text{moles} \times \text{molar mass} = 0.2 \times 342 = 68.4 \, \text{g}

Thus, the correct answer is 68.4 g, which is the amount of sugar required to prepare 2 liters of a 0.1 M sucrose solution. Therefore, the correct option is:

68.4 g