If 500 . g of water is added to 75 \(\mathrm{g}\) of a \(2.5-m\) NaCl solution, what is the mass percent of \(\mathrm{NaCl}\) in the diluted solution?

To find the initial amount of NaCl in the 75 g NaCl solution, we can use the definition of molality. Molality is defined as the number of moles of solute per kilogram of solvent in the solution: \(molality = \frac{moles \, of \, solute}{mass \, of \, solvent (kg)}\) First, we need to convert the 75 g solution mass to the mass of the solvent (water): Since NaCl is completely dissociated in water, so the mass of solvent (water) can be found using the following formula: \(mass \, of \, solvent = mass\_total\_solution - mass \, of \, NaCl\) Next, we can rearrange the molality formula to find the moles of solute (NaCl): \(moles \, of \, NaCl = molality × mass \, of \, solvent (kg) \) Finally, we can convert the moles of NaCl into the initial mass of NaCl: \(mass \, of \, NaCl = moles \, of \, NaCl × molar \, mass \, of \, NaCl\) where the molar mass of NaCl is approximately 58.44 g/mol.

To find the mass of the diluted solution, we will add the mass of the solute (NaCl) and the mass of the solvent (water): \(mass \, of \, diluted \,solution = mass \, of \, NaCl + mass \, of \, added \,water + mass \, of \, initial \,water \)

Now that we have the mass of NaCl and the total mass of the diluted solution, we can calculate the mass percent of NaCl: \(mass \,percent \, of \, NaCl = \frac{mass \, of \, NaCl}{mass \, of \, diluted \, solution} × 100\% \) Now plug in the values obtained from Steps 1 and 2 to calculate the mass percent of NaCl.