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______________________________
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To estimate the freezing point of the solution, we need to identify the temperature at which the solution starts to freeze. This can be determined by looking for a significant drop in temperature over time.

Based on the given data, we can see that the temperature decreases gradually over time. However, there is a noticeable drop in temperature between 2.5 minutes and 3 minutes. The temperature drops from 52.1°C to 50.9°C during this period. This significant drop suggests that the solution is starting to freeze.

Therefore, we can estimate the freezing point of the solution to be around 52.1°C.

Now, let's move on to calculating the molecular weight of the solid. The formula for calculating the freezing point depression is:

ΔT = Kf * m

where:
ΔT is the change in freezing point (in °C)
Kf is the cryoscopic constant of the solvent (in this case, PDB)
m is the molality of the solute (in this case, naphthalene)

In this problem, we are given the Kf value for PDB as 7.10 and the weight of naphthalene as 1.96g. We need to find the molality (m) of naphthalene.

Molality (m) can be calculated using the formula:

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

First, we need to convert the weight of naphthalene from grams to kilograms:

1.96g = 0.00196kg

Next, we need to calculate the moles of naphthalene. To do this, we divide the weight of naphthalene by its molar mass (which is 128.17 g/mol):

moles = (0.00196kg) / (128.17 g/mol) = 0.0000153 mol

Now, we can calculate the molality:

m = (0.0000153 mol) / (25.64g of PDB / 1000g) = 0.000598 mol/kg

Finally, we can calculate the change in freezing point (ΔT) by substituting the values into the freezing point depression equation:

ΔT = (7.10)(0.000598 mol/kg) = 0.00425°C

The change in freezing point (ΔT) is the difference between the freezing point of the pure solvent and the freezing point of the solution. In this case, the freezing point of pure PDB is given as 53°C. Therefore, the freezing point of the solution can be calculated as:

Freezing Point of Solution = Freezing Point of Pure Solvent - ΔT
Freezing Point of Solution = 53°C - 0.00425°C

Therefore, the freezing point of the solution is approximately 52.99575°C.

To summarize:

a) The estimated freezing point of the solution is approximately 52.1°C.

b) The molecular weight (MW) of the solid is calculated to be approximately 128.17 g/mol (the molar mass of naphthalene).