Final answer:
To create a solution with a freezing point of -6.0 °C, you would need to add 1590 g of NaCl to 1.6 kg of water.
Step-by-step explanation:
In order to calculate the mass of NaCl needed to create a solution with a freezing point of -6.0 °C, we need to use the freezing point depression equation. The equation is: ΔT = Kf imes m imes i, where ΔT is the freezing point depression, Kf is the cryoscopic constant, m is the molality of the solution, and i is the van't Hoff factor. The van't Hoff factor for NaCl is 2 because it dissociates into two ions (Na+ and Cl-) in water.
Given that the freezing point depression is 3.7 °C, we can rearrange the equation to solve for the molality of the solution: m = ΔT / (Kf imes i) = 3.7 °C / (1.86 °C kg water/mol ion imes 2) = 0.993 mol/kg.
Now, we can use the molality to calculate the mass of NaCl needed. The molality is defined as the number of moles of solute (NaCl) per kilogram of solvent (water). We know that the mass of water is 1.6 kg, so the mass of NaCl needed is: mass = molality imes mass of water = 0.993 mol/kg imes 1.6 kg = 1.59 kg = 1590 g.