Determine the mass of a nonvolatile, nonionizing compound that must be added to 4.68 kg of water to lower the freezing point to 98.70oC. The molar mass of the compound is 50.0 g/mol and the Kf for water is 1.86oC kg/mol. Ignore significant figures for this problem.
Answer
You need to proof this problem. I don't think the numbers are right. Freezing point of water is -1.86; I don't know how you can add a solvent to it to RAISE the freezing point.
To find the mass of the compound that needs to be added to water, we can use the formula for calculating the freezing point depression:
ΔTf = Kf * m
Where:
ΔTf is the change in freezing point (in degrees Celsius),
Kf is the freezing point depression constant for water (in degrees Celsius per mole per kilogram),
m is the molality of the compound in water (in moles of solute per kilogram of solvent).
In this problem, we are given the following information:
Initial freezing point of water (pure solvent): 0oC
Final freezing point of the solution: 98.70oC
Mass of water (solvent): 4.68 kg
Molar mass of the compound: 50.0 g/mol
Kf for water: 1.86oC kg/mol
We need to find the mass of the compound that causes a freezing point depression of ΔTf = 98.70oC - 0oC = 98.70oC.
First, we need to calculate the molality (m) of the compound in the water solution.
m = moles of solute / mass of solvent (in kg)
The mass of the solvent is given as 4.68 kg, and we need to find the moles of solute. We can use the molar mass to convert the mass of the compound to moles.
moles of solute = mass of compound / molar mass of compound
Since the molar mass of the compound is given as 50.0 g/mol, we can convert it to kg/mol by dividing by 1000.
Now, let's calculate the molality of the compound in the water solution:
m = (mass of compound / molar mass of compound) / mass of solvent
= (mass of compound / (50.0 g/mol / 1000)) / 4.68 kg
Simplifying the equation:
m = (mass of compound / 0.0500 kg/mol) / 4.68 kg
= (mass of compound / 0.0500) / 4.68
Now, we can substitute the values into the freezing point depression formula:
98.70oC = 1.86oC kg/mol * [(mass of compound / 0.0500) / 4.68]
To solve for the mass of the compound:
98.70oC * 4.68 = 1.86oC kg/mol * (mass of compound / 0.0500)
mass of compound = (98.70oC * 4.68 * 0.0500) / 1.86oC kg/mol
mass of compound ≈ 0.125 kg
Therefore, the mass of the compound that must be added to the water to lower the freezing point to 98.70oC is approximately 0.125 kg.