Final answer:
The molality of a 10.0% by mass NaCl solution is calculated by finding the mass of NaCl and water, determining the moles of NaCl using its molar mass, and then dividing by the mass of the water in kilograms, yielding approximately 1.90 m (mol/kg).
Step-by-step explanation:
Calculating Molality of a NaCl Solution
To calculate the molality of a 10.0% by mass NaCl solution, we first determine the mass of NaCl and water from the given percentage. In a 100 g solution, there would be 10.0 g of NaCl and 90.0 g (or 0.090 kg) of water (the solvent). Next, we use the molar mass of NaCl, which is 58.44 g/mol, to find the number of moles of NaCl.
Number of moles of NaCl = Mass of NaCl / Molar mass of NaCl = 10.0 g / 58.44 g/mol
This calculation yields approximately 0.171 moles of NaCl.
Finally, molality (m) is defined as moles of solute divided by kilograms of solvent. Therefore, the molality of the NaCl solution is:
Molality (m) = Moles of NaCl / Kilograms of water
Molality (m) = 0.171 moles / 0.090 kg = approximately 1.90 m (mol/kg)