What mass of water (in grams) is needed to dissolve 28.7 g of ammonium nitrate NH4NO3 in order to prepare a 0.452 m (molal) solution?

Molal is the number of moles per kg of solvent (not solution).

or molal = moles/(kg of water)

thus mass needed (in kg) =
(moles NH4NO3)/0.452

calculate (moles NH4NO3) from the data in the question then use the expression above to find the kg of water needed. Hence convert kg to g as asked for in the question.

793.4 g

To calculate the mass of water needed to dissolve a certain amount of ammonium nitrate and prepare a specific molal solution, you can use the formula:

molality = moles of solute / mass of solvent in kg

First, convert the given mass of ammonium nitrate to moles using its molar mass:

molar mass of NH4NO3 = 14.01 g/mol (N) + 1.01 g/mol (H) x 4 + 14.01 g/mol (N) + 3O16.00 g/mol
= 80.04 g/mol

moles of NH4NO3 = 28.7 g / 80.04 g/mol
≈ 0.3584 mol

Next, calculate the mass of water required using the molality formula:

0.452 m (molal) = 0.3584 mol / mass of water (in kg)

Rearranging the formula to solve for the mass of water:

mass of water (in kg) = 0.3584 mol / 0.452 m
≈ 0.792 kg

Finally, convert the mass of water from kg to grams:

mass of water (in grams) = 0.792 kg x 1000 g/kg
= 792 g

Therefore, approximately 792 grams of water is needed to dissolve 28.7 grams of ammonium nitrate in order to prepare a 0.452 m (molal) solution.

To find the mass of water needed to dissolve the given mass of ammonium nitrate, we need to understand the concept of molality. Molality (m) is defined as the number of moles of solute per kilogram of solvent.

First, let's calculate the number of moles of ammonium nitrate (NH4NO3) using the given mass and its molar mass. The molar mass of NH4NO3 is:
NH4NO3 = (1 * 14.01 g/mol) + (1 * 1.01 g/mol) + (3 * 16.00 g/mol)
= 80.04 g/mol

Number of moles of NH4NO3 = Mass of NH4NO3 / Molar mass of NH4NO3
= 28.7 g / 80.04 g/mol
= 0.3585 mol

Next, we convert the given molality (0.452 m) to moles of solute per kilogram of solvent. Since we want to solve for the mass of water, we assume that the mass of the solvent is 1 kg (1000 g).

Molality (m) = Moles of solute / Mass of solvent (in kg)
0.452 m = 0.3585 mol / (Water mass in kg)

Rearranging the equation to solve for water mass:
Water mass in kg = Moles of solute / Molality
= 0.3585 mol / 0.452 m
= 0.7927 kg

Finally, we convert the mass of water from kilograms to grams:
Water mass in grams = 0.7927 kg * 1000 g/kg
= 792.7 g

Therefore, approximately 792.7 grams of water is needed to dissolve 28.7 grams of ammonium nitrate to prepare a 0.452 m (molal) solution.