1. Understand Molality
Molality (m) is a concentration unit that expresses the moles of solute per kilogram of solvent. In this case:
* Solute: NaCl (sodium chloride)
* Solvent: Water (H₂O)
2. Calculate Moles of NaCl
* Find the molar mass of NaCl: Na (22.99 g/mol) + Cl (35.45 g/mol) = 58.44 g/mol
* Calculate the moles of NaCl: (292.5 g NaCl) / (58.44 g/mol) = 5.00 mol NaCl
3. Determine the Mass of Water
* We know the desired molality is 0.25 m, meaning 0.25 moles of NaCl per 1 kg of water.
* Since we have 5.00 moles of NaCl, we need to find the mass of water that corresponds to that many moles at a 0.25 m concentration:
* (5.00 mol NaCl) / (0.25 mol NaCl/kg H₂O) = 20 kg H₂O
4. Convert to Grams
* 1 kg = 1000 g
* 20 kg H₂O * 1000 g/kg = 20000 g H₂O
Answer: You would need 20,000 grams of water to dissolve 292.5 g of NaCl and create a 0.25 m aqueous solution.
