To calculate the molecular weight of a substance, we can use the ideal gas law, which relates the pressure (P), volume (V), number of moles (n), and temperature (T) of a gas:
PV = nRT
where R is the gas constant. Rearranging this equation gives:
n = PV / RT
We can use this equation to calculate the number of moles of the substance in the vapor phase. Then, we can use the definition of molecular weight, which is the mass of one mole of the substance, to calculate the molecular weight.
First, let's convert the temperature and pressure to SI units:
Temperature: 45°C = 318.15 K
Pressure: 687 mmHg = 91.6 kPa
Next, let's calculate the number of moles of the substance in the vapor phase. We know that 1.22 g of the substance was vaporized in a 100 mL flask, which is equivalent to 0.1 L. Therefore, the concentration of the substance in the vapor phase is:
c = 1.22 g / 0.1 L = 12.2 g/L
We can convert this concentration to units of pressure using the ideal gas law:
PV = nRT
n/V = P/RT
n/V = (91.6 kPa) / (8.314 J/mol K * 318.15 K) = 0.0361 mol/L
Therefore, the number of moles of the substance in the vapor phase is:
n = (0.0361 mol/L) * 0.1 L = 0.00361 mol
Finally, we can calculate the molecular weight using the definition of molecular weight:
molecular weight = mass / moles
mass = 1.22 g
moles = 0.00361 mol
molecular weight = 1.22 g / 0.00361 mol = 337.4 g/mol
Therefore, the molecular weight of the substance is approximately 337.4 g/mol.