# What is the molecular weight of sulfur if 35.5 grams of sulfur dissolve in 100.0 grams of CS2 to produce a solution that has a boiling point of 49.48°C?

The molecular mass of sulfur is 256 u.

As you might have guessed, this is a boiling point elevation problem. The formula for boiling point elevation is

We need to look up the values of

We can use this information to calculate the molality

We have 100.0 g or 0.1000 kg of CS₂. So we can calculate the moles of sulfur.

Molality =

Moles of solute = molality× kilograms of solvent = 1.38 mol·kg⁻¹ × 0.1000 kg = 0.138 mol

So 35.5 g of sulfur = 0.138 mol

∴ Molar mass of sulfur =

∴ The experimental molecular mass of sulfur is 257 u (The actual molecular mass of S₈ is 256 u).

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The molecular weight of sulfur can be calculated using the formula for boiling point elevation:

ΔT = K_b * m

Where: ΔT = change in boiling point (in °C) K_b = ebullioscopic constant (for CS2, K_b = 2.42 °C/m) m = molality of the solution

First, we need to calculate the molality of the solution:

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

The mass of CS2 solvent is (100.0 g - 35.5 g) = 64.5 g

Converting this to kilograms: 64.5 g / 1000 = 0.0645 kg

Now, we need to find the moles of sulfur:

moles of sulfur = mass of sulfur / molar mass of sulfur

The molar mass of sulfur is approximately 32.06 g/mol.

moles of sulfur = 35.5 g / 32.06 g/mol = 1.107 moles

Now, we can calculate the molality:

molality (m) = 1.107 moles / 0.0645 kg = 17.14 mol/kg

Now, we can use the boiling point elevation formula:

ΔT = K_b * m

Substitute the values:

ΔT = 2.42 °C/m * 17.14 mol/kg = 41.49 °C

The change in boiling point is 49.48°C - initial boiling point (CS2 = 46.2°C) = 3.28°C.

Therefore, 41.49°C = 3.28°C

Now, we can find the molecular weight of sulfur using the formula:

ΔT = K_b * m

Rearranging the formula to solve for molecular weight:

molecular weight (M) = ΔT / K_b

Substitute the values:

M = 3.28°C / 2.42°C/m = 1.36 mol

The molecular weight of sulfur is approximately 1.36 * 32.06 g/mol = 43.61 g/mol.

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