Final answer:
The molarity of a magnesium nitrate solution prepared by dissolving 8.2 g of magnesium nitrate in 400.0 mL of solution is 0.138 M. This is found by first calculating the number of moles of magnesium nitrate and then dividing by the volume in liters.
Step-by-step explanation:
To calculate the molarity of a magnesium nitrate solution, we need to know the molar mass of magnesium nitrate and the volume of the solution. The molar mass of magnesium nitrate, Mg(NO3)2, is the sum of the atomic masses of magnesium (24.31 g/mol), nitrogen (14.01 g/mol), and oxygen (16.00 g/mol). Therefore, the molar mass is 24.31 g/mol + (2 × 14.01 g/mol) + (6 × 16.00 g/mol) = 148.31 g/mol. With 8.2 g of magnesium nitrate, we can calculate the number of moles:
Number of moles = mass (g) / molar mass (g/mol)
Number of moles = 8.2 g / 148.31 g/mol = 0.0553 moles
Since the volume of the solution is 400.0 mL, we convert it to liters by dividing by 1000 mL/L:
Volume in liters = 400.0 mL / 1000 mL/L = 0.4 L
Molarity is defined as the number of moles of solute per liter of solution:
Molarity (M) = moles of solute / liters of solution
Molarity (M) = 0.0553 moles / 0.4 L = 0.138 M