Final answer:
To find the molality of the ammonia solution, convert the density to kg/L, use the molarity to find moles of NH3, subtract the mass of NH3 from the total mass to get the mass of water, and divide moles of NH3 by the mass of water in kg. However, the correct answer of 5.70 mol/kg does not match any of the options provided.
Step-by-step explanation:
To calculate the molality of an aqueous solution of ammonia, given that the solution's concentration is 5.0 molarity (5.0 M) and the solution's density (ρsol) is 962 g/L, follow these steps:
- First, convert the density from g/L to kg/L by dividing by 1000, so 962 g/L is 0.962 kg/L.
- Since the solution is 5.0 M, we know this is 5.0 moles of NH3 per liter of solution.
- To find the mass of 1 liter of solution, multiply the density (0.962 kg/L) by the volume (1 L), which equals 0.962 kg.
- Now, subtract the mass of NH3 (molar mass = 17.03 g/mol) in moles from the total mass of the solution to get the mass of the water.
- 5.0 moles × 17.03 g/mol = 85.15 g or 0.08515 kg. Subtract this from the total mass of the solution (0.962 kg) to get the mass of the water, which is 0.962 kg - 0.08515 kg = 0.87685 kg.
- Finally, molality is moles of solute per kg of solvent (water). So, divide the moles of NH3 by the mass of the water in kg: 5.0 moles / 0.87685 kg = 5.70 mol/kg.
The molality of the solution to two decimal places is 5.70 mol/kg, which is not in the given options, so either the question contains an error, or additional information is required to match one of the provided options.