Final answer:
To calculate the molarity of a concentrated solution, the mass of the solute is converted into moles and then divided by the final volume of the solution in liters. Based on the initial concentration of 0.200% (m/v) and the volumes provided, the correct molarity is not among the given options.
Step-by-step explanation:
You want to determine the molarity of a sodium nitrate (NaNO₃) solution that has been concentrated by evaporation. To do this, you need to first figure out how much solute is in the original solution and then calculate the molarity based on the new volume.
Initially, you have 755 mL of a 0.200% (m/v) NaNO₃ solution. The percentage means you have 0.200 grams of NaNO₃ in every 100 mL of solution, so first calculate the total mass of NaNO₃:
- Total mass of NaNO₃ = 0.200% of 755 mL = (0.200/100) × 755
- Total mass of NaNO₃ = 1.51 grams
Molarity (M) is defined as moles of solute per liter of solution. To find the molarity after evaporation:
- Convert the mass of NaNO₃ to moles (molecular weight of NaNO₃ = 85.0 g/mol)
- Divide the moles of NaNO₃ by the new volume in liters (462 mL = 0.462 liters)
- Moles of NaNO₃ = 1.51 grams / 85.0 g/mol = 0.0178 moles
- M = 0.0178 moles / 0.462 liters = 0.0385 M
However, none of the given options match this result. Please double-check the values provided, as the calculation based on the given starting concentration and volumes does not result in one of the four provided multiple-choice answers.