Calculate the molecular mass of sulphur if 35.5 g of sulphure dissolves in 100 g of CS2 to produce a solution that has a boiling point of 49.48 c.
It would have been an act of kindness to include the boiling point elevation constant as well as the normal boiling point of CS2. I looked them up on the web. Make sure that the numbers I'm using are the same as you are using for Kb and b.p.
The boiling point elevation constant, kb, for CS2 is 2.3 o^C (degrees Celsius) and its boiling point is 46.3 o^C (degrees Celsius).Aug 28, 2018
delta T = Kb*molality
delta T = 49.48 - 46.3 = 3.18
Kb = 2.3
molality = mols/kg solvent = mols/0.1 kg CS2
mols = grams/molar mass = 35.5 g/molar mass.
molar mass CS2 = ???. Solve for this.
Substitute those values into the above and solve for molar mass. molar mass is the only unknown. Post your work if you get stuck.
i asked for the molar mass for the Sulphur ......However you give me the given for calculating the molar mass for it and it is 257.2g/mol
To calculate the molecular mass of sulfur, we can use the ideal gas law and the concept of boiling point elevation.
Step 1: Find the number of moles of sulfur dissolved in CS2.
Using the given data, we can determine the moles of sulfur using the formula:
moles of solute = mass of solute / molar mass of solute
The molar mass of sulfur (S) is approximately 32 g/mol.
moles of sulfur = 35.5 g / 32 g/mol
moles of sulfur = 1.109 mol
Step 2: Find the molality of the solution.
Molality (m) is defined as the number of moles of solute divided by the mass of the solvent in kilograms.
molality = moles of sulfur / mass of CS2 solvent
mass of CS2 solvent = 100 g = 0.1 kg
molality = 1.109 mol / 0.1 kg
molality = 11.09 mol/kg
Step 3: Calculate the boiling point elevation (∆Tb) using the formula:
∆Tb = Kb * m
where Kb is the molal boiling point elevation constant for CS2, which is 2.42 °C·kg/mol.
∆Tb = 2.42 °C·kg/mol * 11.09 mol/kg
∆Tb = 26.85 °C
Step 4: Calculate the boiling point of the solution.
The boiling point of the solution is the sum of the boiling point of the pure solvent (CS2) and the boiling point elevation (∆Tb) caused by the dissolved solute (sulfur).
boiling point of solution = boiling point of solvent + ∆Tb
boiling point of solution = 49.48 °C + 26.85 °C
boiling point of solution = 76.33 °C
Step 5: Use the boiling point elevation formula and the freezing point depression formula to calculate the molecular mass of sulfur.
The boiling point elevation (∆Tb) can be calculated using the formula:
∆Tb = Kb * m = R * molality
where R is the gas constant, which is 8.314 J/(mol·K).
Rearranging the equation, we can solve for the molecular mass (M):
M = ∆Tb / (Kb * m)
M = 76.33 °C / (2.42 °C·kg/mol * 11.09 mol/kg)
M ≈ 2.583 g/mol
Therefore, the molecular mass of sulfur is approximately 2.583 g/mol.
To calculate the molecular mass of sulfur, we need to use the concept of colligative properties, specifically boiling point elevation.
Boiling point elevation occurs when a solute is dissolved in a solvent, thereby raising the boiling point of the liquid. The change in boiling point is directly proportional to the molality of the solute.
First, we need to determine the molality of the solute (sulfur) in the solution. Molality (m) is defined as the moles of solute divided by the mass of the solvent in kilograms.
Given:
Mass of sulfur = 35.5 g
Mass of CS2 (solvent) = 100 g
First, let's convert the masses to moles using the molar masses of sulfur (32.06 g/mol) and CS2 (76.14 g/mol).
Moles of sulfur = mass of sulfur / molar mass of sulfur
= 35.5 g / 32.06 g/mol
= 1.108 mol
Moles of CS2 = mass of CS2 / molar mass of CS2
= 100 g / 76.14 g/mol
= 1.313 mol
Next, we calculate the molality using the moles of sulfur and the mass of the solvent in kilograms.
Molality (m) = moles of sulfur / mass of CS2 (in kg)
= 1.108 mol / 0.1 kg
= 11.08 mol/kg
Now, we need to calculate the boiling point elevation (∆Tb) using the formula:
∆Tb = Kb * m
where Kb is the molal boiling point elevation constant, which is 2.53 °C/molal for CS2.
∆Tb = 2.53 °C/molal * 11.08 mol/kg
= 28.00 °C
Finally, we can calculate the boiling point of the solution using the formula:
Boiling point of solution = boiling point of pure solvent + ∆Tb
Boiling point of solution = 49.48 °C + 28.00 °C
= 77.48 °C
Now, we use the boiling point elevation formula to solve for the molecular mass of sulfur.
∆Tb = (Kb * m) / (M * Kb)
28.00 °C = (2.53 °C/molal) / (M * 2.53 °C/molal)
28.00 = 1 / M
M = 1 / 28.00
M ≈ 0.0357
The molecular mass of sulfur is approximately 0.0357 kg/mol.
Note: It's important to note that the boiling point elevation method assumes ideal behavior, meaning no interactions between solute and solvent molecules. In reality, there might be some deviations from the ideal behavior, but for this calculation, we consider ideal conditions.