Here's the explanation:
1. Molality vs. Molarity
- Molality (m) is defined as the number of moles of solute per kilogram of _solvent_.
- Molarity (M) is defined as the number of moles of solute per liter of _solution_.
2. Calculations
- Let's consider 1 kg of solvent (water) for both solutions.
- 1 molal urea solution:
- Molar mass of urea (CH₄N₂O) = 60 g/mol
- 1 molal solution means there is 1 mole of urea dissolved in 1 kg of water.
Therefore, 1 molal urea solution contains 60 grams of urea in 1 kg of water.
- 0.5 NaCl solution:
- Molar mass of NaCl (sodium chloride) = 58.45 g/mol
- A 0.5 M NaCl solution means there are 0.5 moles of NaCl dissolved in 1 liter of solution. To find the mass of NaCl in 1 kg of water:
Mass of NaCl = (0.5 moles) x (58.45 g/mol) = 29.225 grams
Therefore, a 0.5 M NaCl solution contains 29.23 grams of NaCl in 1 kg of water.
3. Comparison
- The mass of urea in a 1 molal urea solution (60 grams) is different from the mass of NaCl in a 0.5 M NaCl solution (29.23 grams) when both solutions are made using 1 kg of water.
- Therefore, 1 molal urea solution is _not equal_ to 0.5 M NaCl solution in terms of concentration or composition.