Freezing-point depression can be used to determine the molecular mass of a compound. Suppose that 1.28 g of an unknown molecule were added to 19.9 g of water and the freezing point of the solution determined. If the new freezing point of water were found to be -1.50°C, what would you predict to be the molecular mass of the compound?

To determine the molecular mass of the compound using freezing-point depression, we need to calculate the change in freezing point.

The formula to calculate the change in freezing point is given by:

ΔTf = Kf * m

Where:
ΔTf = Change in freezing point
Kf = Cryoscopic constant for the solvent (water)
m = Molality of the solution

First, let's calculate the molality of the solution:

Molality (m) = moles of solute / mass of solvent (in kg)

Given that the mass of water (solvent) is 19.9 g and the mass of the unknown molecule (solute) is 1.28 g, we can convert the mass of water to kg:

Mass of water (kg) = 19.9 g / 1000 = 0.0199 kg

Next, we need to calculate the moles of the unknown molecule:

Moles = Mass / Molecular mass

Given that the mass of the unknown molecule is 1.28 g, we can calculate the moles using the periodic table or other known information about the compound.

Finally, once we have the moles of the unknown molecule and the mass of the water, we can calculate the molality. Using this molality value, we can calculate the change in freezing point (ΔTf) using the cryoscopic constant for water.

ΔTf = Kf * m

Rearranging the formula to solve for Kf:

Kf = ΔTf / m

Now, we can insert the values into the formula. Given that the new freezing point of water is -1.50°C, and the initial freezing point of pure water is 0.00°C:

ΔTf = -1.50°C - 0.00°C = -1.50°C

Let's assume the molecular mass of the unknown compound is 'X' g/mol. Calculate the moles of the unknown compound using:

Moles = Mass / Molecular mass = 1.28 g / X g/mol

Now, we can calculate the molality:

Molality (m) = Moles of solute / Mass of solvent (kg) = (1.28 g / X g/mol) / 0.0199 kg

Finally, we can substitute the value of molality into the equation for ΔTf:

Kf = ΔTf / m = -1.50°C / ((1.28 g / X g/mol) / 0.0199 kg)

Now, we can solve for the molecular mass (X) by rearranging the equation:

X = (ΔTf / Kf) * (1.28 g / 0.0199 kg)

Plug in the values of ΔTf and Kf to calculate the molecular mass of the unknown compound.

To determine the molecular mass of a compound using freezing-point depression, you need to use the formula:

ΔT = Kf * m * i

Where:
ΔT is the change in freezing point,
Kf is the cryoscopic constant (unique to the solvent),
m is the molality of the solution,
and i is the van't Hoff factor, which represents the number of particles the compound dissociates into when it dissolves.

To apply this formula, we need to find the molality (m) and the change in freezing point (ΔT).

1. Finding molality (m):
Molality is defined as the number of moles of solute per kilogram of solvent. In this case, the solvent is water.

Step 1: Find the moles of the unknown compound.
To find the moles, we'll use the formula:

moles = mass / molar mass

Given that the mass of the unknown compound is 1.28 g, we need to know the molar mass of the compound to find the moles. Let's call the molar mass "M."

moles = 1.28 g / M

Step 2: Find the molality (m).
Since we need the molality, we also need the mass of the solvent (water).
Given that the mass of water is 19.9 g, we convert it to kilograms by dividing by 1000:

mass of water = 19.9 g / 1000 = 0.0199 kg

Now, we can calculate the molality:

m = moles of solute / mass of solvent
= (1.28 g / M) / 0.0199 kg
= (1.28 / M) / 0.0199
= 64.3216 / M

2. Finding the change in freezing point (ΔT):
The change in freezing point (ΔT) is the difference between the normal freezing point of the solvent (water) and the freezing point of the solution.

ΔT = (Freezing point of pure solvent) - (Freezing point of the solution)

Given that the new freezing point is -1.50°C and the freezing point of pure water is 0°C, we have:

ΔT = 0 - (-1.50)
= 1.50°C

Remember to convert the temperature to Kelvin because the cryoscopic constant (Kf) is typically given in units of K·kg/mol.

ΔT = 1.50 + 273.15
= 274.65 K

Now, we can use the formula:
ΔT = Kf * m * i

In this case, we assume i = 1 because we are considering a non-ionic compound.

Molecular mass (M) = Kf * (ΔT / m)

We'll need the cryoscopic constant (Kf) for water, which is 1.86 K·kg/mol (given).

Plugging in the values:
M = 1.86 * (274.65 K / 64.3216)
= 7.9423

The predicted molecular mass of the compound is approximately 7.9423 g/mol.