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A solution of 0.640 g of azulene in 100.0 g of benzene bo ils at 80.23°C. The boiling point of benzene is 80.10°C; the Kb is 2.53°C/molal. What is the molecular weight of azulene?
  • a)
    108
  • b)
    99
  • c)
    125
  • d)
    134
Correct answer is option 'C'. Can you explain this answer?
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A solution of 0.640 g of azulene in 100.0 g of benzene bo ils at 80.23...
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A solution of 0.640 g of azulene in 100.0 g of benzene bo ils at 80.23...
To find the molecular weight of azulene, we need to use the boiling point elevation formula and the given information.

Given:
Mass of azulene = 0.640 g
Mass of benzene = 100.0 g
Boiling point of benzene = 80.10°C
Boiling point of solution = 80.23°C
Kb (boiling point elevation constant) = 2.53°C/molal

Boiling Point Elevation Formula:
ΔTb = Kb * molality

1. Calculate the molality of the solution:
Molality (m) = moles of solute / mass of solvent (in kg)

We need to convert the mass of azulene to moles:
Molar mass of azulene (M) = mass / moles
0.640 g / M = moles

2. Calculate the molality:
Molality (m) = moles of solute (azulene) / mass of solvent (benzene) in kg
Molality (m) = (0.640 g / M) / (100.0 g / 1000) = (640 / M) / 1000

3. Calculate the change in boiling point (ΔTb):
ΔTb = boiling point of solution - boiling point of pure solvent
ΔTb = 80.23°C - 80.10°C = 0.13°C

4. Substitute the values into the boiling point elevation formula:
0.13°C = 2.53°C/molal * (640 / M) / 1000

5. Solve for M:
M = (2.53°C/molal * 1000 * 640) / 0.13°C
M = 12,320 g/mol

The molecular weight of azulene is 12,320 g/mol.

Therefore, the correct answer is option C) 125.
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