Calculate mole fraction of a 2.4 m aqueous solution of citric acid (C₆H₈O₇).

• A. 0.96
• B. 0.041
• C. 0.55
• D. 0.024

Answer: (B)

Verified step by step guidance

1. Understand that the mole fraction is the ratio of the moles of solute to the total moles of solute and solvent. In this case, the solute is citric acid (C6H8O7) and the solvent is water.
2. Recognize that a 2.4 m (molal) solution means there are 2.4 moles of citric acid per 1 kg of water.
3. Calculate the moles of water. Since the molar mass of water (H2O) is approximately 18.015 g/mol, convert 1 kg of water to moles: \( \text{moles of water} = \frac{1000 \text{ g}}{18.015 \text{ g/mol}} \).
4. Determine the total moles in the solution by adding the moles of citric acid to the moles of water: \( \text{total moles} = 2.4 + \text{moles of water} \).
5. Calculate the mole fraction of citric acid using the formula: \( \text{mole fraction of citric acid} = \frac{\text{moles of citric acid}}{\text{total moles}} \).