A student determines the freezing point of a solution of 1.96g of naphthalene in 25.64g of paradichlorobenzene(PDB). The following temperature-time reading are recorded.

PDB/Napthalene
Time(Min) 0 0.5 1.5 2 2.5 3 3.5 4 4.5
Temp(°C) 59.7 58.0 54.8 53.4 52.1 50.9 49.5 49.6 49.5

a) Estimate the freezing Point of the solution from the above data_________°C

b) Taking the Kf for PDB to be 7.10, calculate the molecular weight of the solid. Assume 53°C to be the freezing point of pure PDB. MW______________________________
0 following

I would take 49.5 as the freezing point or you could use 49.5, 49.6 and 49.5, take the average as 49.53 which rounds to 49.5.

For #2, what is the solid? Is that Naphthalene (by the way, note the spelling) or is that the mixture of PDB and naphthalene.

To estimate the freezing point of the solution, we need to find the temperature at which the solution starts to freeze. This can be determined by looking at the temperature-time readings and identifying the point at which the temperature starts to decrease steadily.

From the given data, we can see that the temperature decreases steadily from 59.7°C to 49.5°C. Therefore, the freezing point of the solution is approximately 49.5°C.

Now, to calculate the molecular weight of the solid, we can use the formula:

∆T = Kf * m * i

Where:
∆T = change in freezing point
Kf = cryoscopic constant
m = molality of the solution
i = Van't Hoff factor

Since we are given the Kf value of PDB as 7.10, and assuming the solution is a 1 molal solution (1 mol of solute per kg of solvent), we can rearrange the formula to solve for the molecular weight (MW):

MW = (∆T / (Kf * m * i))

From the data, we know that the freezing point depression (∆T) is 53°C - 49.5°C = 3.5°C. The molality (m) of the solution can be calculated by first finding the moles of naphthalene:

moles of naphthalene = mass of naphthalene / molar mass of naphthalene

mass of naphthalene = 1.96g
molar mass of naphthalene = 128.17 g/mol

moles of naphthalene = 1.96g / 128.17 g/mol

Next, we calculate the molality (m) using the formula:

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

mass of PDB = 25.64g

mass of solvent (in kg) = 25.64g / 1000

Now, we can substitute the values into the formula to calculate the molecular weight (MW):

MW = (3.5°C / (7.10 * m * i))

where
∆T = 3.5°C
Kf = 7.10
m = moles of solute / mass of solvent (in kg)
i = 1 (since we assume no dissociation)

Substitute the values and solve for MW.