Calculate the molecular mass of sulphur if 35.5 g of sulphure dissolves in 1 00 g of CS2 to produce a solution that has a boiling point of 49.48 c.
To calculate the molecular mass of sulfur, we need to use the concept of boiling point elevation, which depends on the concentration of the solution.
The boiling point elevation (ΔTb) can be calculated using the equation:
ΔTb = Kbp * molality
Where:
ΔTb = change in boiling point
Kbp = boiling point elevation constant specific to the solvent
molality = moles of solute / mass of solvent in kg
First, we need to calculate the molality (m) of the solution. The moles of sulfur dissolved in CS2 can be determined using the molar mass of sulfur:
Moles of Sulfur = mass of sulfur / molar mass of sulfur
Given:
Mass of sulfur = 35.5 g
Mass of CS2 (solvent) = 100 g
Next, we need to convert the mass of CS2 into kilograms:
Mass of CS2 (solvent) = 100 g = 0.1 kg
Now, we can calculate the molality:
Moles of Sulfur = 35.5 g / molar mass of sulfur
Moles of Sulfur = 35.5 g / molar mass of sulfur
Molality (m) = Moles of Sulfur / mass of CS2 (solvent) in kg
Lastly, we can use the boiling point elevation equation to calculate the molecular mass of sulfur. The boiling point elevation constant (Kbp) for CS2 is 2.4 °C/molal:
ΔTb = Kbp * molality
Given:
ΔTb (change in boiling point) = 49.48 °C
Kbp (boiling point elevation constant) = 2.4 °C/molal
Molality (m) = calculated in the previous step
Now, rearrange the equation to solve for the molecular mass of sulfur:
Molar mass of sulfur = ΔTb / (Kbp * molality)
Substitute the given values:
Molar mass of sulfur = 49.48 °C / (2.4 °C/molal * molality)
Finally, plug in the value of molality and solve for the molecular mass of sulfur.