A solution is prepared by dissolving 9.8 g of phosphoric acid (H3PO4) in 250 g of water. What is the molality of phosphoric acid in the solution?

• A. 0.10 mol/kg
• B. 0.25 mol/kg
• C. 0.40 mol/kg
• D. 0.80 mol/kg

Answer: (C)

Verified step by step guidance

1. Identify the given data: mass of phosphoric acid (H\3PO\4) is 9.8 g, and mass of water (solvent) is 250 g.
2. Calculate the number of moles of phosphoric acid using its molar mass. The molar mass of H\3PO\4 is calculated by summing the atomic masses: (3 \times 1.01) + (1 \times 30.97) + (4 \times 16.00). Then, use the formula: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\).
3. Convert the mass of water from grams to kilograms because molality is expressed in moles of solute per kilogram of solvent: \(\text{mass of water in kg} = \frac{250}{1000}\).
4. Calculate the molality using the formula: \(m = \frac{\text{moles of solute}}{\text{kilograms of solvent}}\).
5. Interpret the result to determine which of the given options matches the calculated molality.