Final answer:
To find the molarity of a 50.0% ammonium nitrate solution with a density of 1.22 g/mL, convert the percentage to mass, then to moles using the molar mass, and divide by the volume of the solution in liters. The calculation yields a molarity of 7.62 M.
Step-by-step explanation:
The question asks for the molarity of an ammonium nitrate (NH₄NO₃) solution, given that the solution is 50.0% NH₄NO₃ by mass and has a density of 1.22 g/mL at 25°C. To calculate molarity, which is moles of solute per liter of solution (mol/L), we'll need to use the molar mass of NH₄NO₃ and the density of the solution.
First, we calculate the mass of NH₄NO₃ in 1 liter of solution. As the density is 1.22 g/mL, 1 liter (1000 mL) would have a mass of 1220 grams. Since the solution is 50.0% NH₄NO₃ by mass, 50.0% of 1220 grams is dedicated to NH₄NO₃, which is 610 grams.
Now, using the molar mass of NH₄NO₃, which is 80.06 g/mol, we convert the mass of NH₄NO₃ to moles: 610 grams ÷ 80.06 g/mol = 7.618 moles. Finally, since we've calculated the moles in 1 liter of solution, this is also the molarity. Therefore, the molarity is 7.618 M, which rounds to 7.62 M to three significant figures.