a student puts 1.25 kg of ice in an ice cream maker with 350 g of rock salt. All the ice eventually becomes liquid water as the rock salt dissolves. Solve for the molality of the solution, then for its new freezing temperature.

delta T = i*Kf*m

We need i, Kf, m.
i = 2 for NaCl
Kf we know for water is 1.86 c/m
1.25 kg ice eventually becomes 1.25 kg water.
So we need m. m = mols/kg solvent. We have kg solvent so we need mols.

mols NaCl = grams/molar mass. You know grams and molar mass, solve for mols NaCl. Use that to solve for m and use that to solve for delta T.
Then new freezing point is 0-delta T.

To solve for the molality of the solution, we first need to calculate the number of moles of solute (rock salt) and the mass of the solvent (water).

1. Calculate the number of moles of rock salt:
Given that the student uses 350 g of rock salt, we need to convert this mass to moles using the molar mass of rock salt. The molar mass of NaCl (rock salt) is approximately 58.44 g/mol.

Number of moles of rock salt = mass / molar mass
Number of moles of rock salt = 350 g / 58.44 g/mol

2. Calculate the mass of the solvent (water):
The ice completely dissolves, and since ice is just solid water, we can consider the total mass to be the mass of the solvent. The student starts with 1.25 kg of ice, which is equivalent to 1250 g of water.

Mass of solvent (water) = 1250 g

3. Calculate the molality of the solution:
Molality (m) is defined as the moles of solute per kilogram of solvent.

Molality (m) = moles of solute / mass of solvent (kg)
Molality (m) = (moles of rock salt) / (mass of solvent / 1000)

Before substituting the values, we need to convert the mass of the solvent to kilograms:

Mass of solvent (water) = 1250 g / 1000 = 1.25 kg

Now, we can substitute the values:

Molality (m) = (350 g / 58.44 g/mol) / 1.25 kg

Solve this equation to find the molality.

To calculate the new freezing temperature, we need to use the equation for the cryoscopic constant (K_f) and the van't Hoff factor (i).

The equation for the new freezing temperature is:
ΔT = K_f * m * i

In this case, the van't Hoff factor (i) for NaCl is 2 since it dissociates into Na+ and Cl- ions in water.

You would need to know the cryoscopic constant (K_f) for water to calculate the freezing point depression. The cryoscopic constant varies depending on the solvent used. For water, K_f is approximately 1.86 °C/m.

Substitute the values into the equation to find the freezing point depression:

ΔT = 1.86 °C/m * (molality) * (van't Hoff factor)

Solve this equation to find the new freezing temperature.