in 100 g of naphthalene 2.423 g of s was dissolved. melting point of naphthalene=80.1C ∆Tf=661C Lf =35.7/g of naphthalerie molecular formula of sulphur added is

To find the molecular formula of sulfur added to naphthalene, we can use the data provided regarding the freezing point depression (∆Tf). The relationship between the freezing point depression, the molality of the solution, the freezing point depression constant (Kf), and the mass of the solute is given by the formula:

Understanding Freezing Point Depression

The formula for freezing point depression is expressed as:

∆Tf = Kf × m

Where:

• ∆Tf = change in freezing point (in °C)
• Kf = freezing point depression constant (in °C kg/mol)
• m = molality of the solution (in mol/kg)

Calculating the Molality

We know that:

• ∆Tf = 80.1°C - freezing point of the solution
• Initial freezing point of pure naphthalene = 80.1°C
• Final freezing point after adding sulfur = 80.1°C - ∆Tf = 80.1°C - 6.61°C = 73.49°C

Now, we can rearrange the formula to find the molality:

m = ∆Tf / Kf

Substituting the values:

m = 6.61°C / 35.7°C kg/mol

Calculating this gives:

m = 0.185 mol/kg

Finding the Moles of Sulfur

Next, we need to calculate the number of moles of sulfur that corresponds to this molality. Since we have 100 g of naphthalene, we first convert this mass into kilograms:

Mass of naphthalene = 100 g = 0.1 kg

Now, using the molality (m = moles of solute / kg of solvent), we can rearrange to find the moles of sulfur:

moles of sulfur = molality × kg of solvent

moles of sulfur = 0.185 mol/kg × 0.1 kg = 0.0185 moles

Calculating the Mass of Sulfur

The molar mass of sulfur (S) is approximately 32.07 g/mol. To find the mass of sulfur dissolved, we multiply the number of moles by the molar mass:

mass of sulfur = moles × molar mass

mass of sulfur = 0.0185 moles × 32.07 g/mol ≈ 0.592 g

Determining the Molecular Formula

Since the problem states that 2.423 g of sulfur was dissolved in naphthalene, it seems there might be a mistake in the interpretation or in the initial data. This calculation indicates that approximately 0.592 g of sulfur would cause that degree of freezing point depression.

To find the molecular formula of sulfur, we know that the most common form of sulfur is S8. Therefore, if we were to determine the molecular formula from the context of this scenario, we would recognize that sulfur typically exists as S8 in its molecular form.

Final Thoughts

To summarize, while our calculations suggest that a smaller mass of sulfur affects the freezing point of naphthalene as indicated, the molecular formula of sulfur itself is S8. If there are specifics to the experiment or data you need to clarify, please let me know!