After you preform your experiment, you determine that the Kf value for naphthalene is 6.9 . You are using 10g of naphthalene and added 1.0 g of your unknown. The the freezing point of the solvent decreased by 4.42 when the unknown was added. Knowing this information, determine the molar mass of the unknown

delta T = Kf*m

Solve for m

m = moles/kg solvent
Solve for moles

moles = grams/molar mass
Solve for molar mass.

To determine the molar mass of the unknown substance, we can use the equation:

ΔT = Kf * m * i

Where:
ΔT = change in freezing point
Kf = cryoscopic constant
m = molality of the solution
i = van 't Hoff factor (which is the number of particles the solute breaks into in the solution)

We can rearrange the equation to solve for molality (m):

m = ΔT / (Kf * i)

In this case, we know the following information:
Kf for naphthalene = 6.9 °C/m
ΔT (change in freezing point) = 4.42 °C
Mass of naphthalene (solvent) = 10 g
Mass of unknown (solute) = 1.0 g

First, let's calculate the molality of the solution using the mass of the solvent:

molality = moles of solute / mass of solvent (in kg)

To find moles of solute, we need to use the given mass of the unknown substance and its molar mass, which we need to calculate.

To calculate the molar mass of the unknown, we can use the formula:

Molar mass = (n * M_solute) / m_solute

Where:
n = moles of solute
M_solute = molar mass of solute
m_solute = mass of solute

Rearranging this equation, we can solve for n:

n = (m_solute * Molar mass) / M_solute

Now, let's calculate the molality using the given data:

molality = moles of solute / mass of solvent (in kg)

First, we need to convert the masses to kg:

mass of solvent = 10 g = 0.01 kg

Next, let's calculate the moles of solute:

moles of solute = (mass of unknown / molar mass of unknown)

Since we don't know the molar mass of the unknown yet, we'll keep it as a variable, M.

moles of solute = (1.0 g / M)

Finally, we can calculate the molality:

molality = (moles of solute) / (mass of solvent)
= ((1.0 g / M) / 0.01 kg)
= (1.0 g / (0.01 kg * M))
= 100 / (M) mol/kg

Now we can substitute this expression for molality into the first equation mentioned above:

ΔT = Kf * m * i
4.42 °C = (6.9 °C/m) * (100 / M) mol/kg * i

Since naphthalene does not dissociate in the solution (i = 1), we can simplify the equation to:

4.42 °C = (690 / M) mol/kg

Now we can solve for M, the molar mass of the unknown substance:

4.42 °C * M = 690 mol/kg
M = (690 mol/kg) / 4.42 °C

M ≈ 156.1 g/mol

Therefore, the molar mass of the unknown substance is approximately 156.1 g/mol.