To calculate the molecular weight of a substance from its vapor density, we can use the following formula:
Molecular weight = (RT/P) x d
where:
R is the gas constant (0.0821 L atm/mol K)
T is the temperature in Kelvin
P is the pressure in atm
d is the vapor density (in g/L) of the substance
First, we need to calculate the vapor density of the substance using the given information. We can use the ideal gas law to find the number of moles of the substance in the flask:
PV = nRT
where:
P is the pressure (687 mmHg = 0.903 atm)
V is the volume (100 mL = 0.1 L)
n is the number of moles of gas
R is the gas constant (0.0821 L atm/mol K)
T is the temperature in Kelvin (45°C = 318 K)
Solving for n, we get:
n = PV/RT = (0.903 atm)(0.1 L)/(0.0821 L atm/mol K)(318 K) = 0.00372 mol
Next, we can use the mass and volume information to find the density of the substance:
density = mass/volume = 1.22 g/0.1 L = 12.2 g/L
Since the vapor density is half of the density of the substance in the liquid state, we can calculate the vapor density:
vapor density = density/2 = 6.1 g/L
Finally, we can use the formula above to find the molecular weight:
Molecular weight = (RT/P) x d
Molecular weight = (0.0821 L atm/mol K)(318 K)/(0.903 atm) x 6.1 g/L
Molecular weight = 92.2 g/mol
Therefore, the molecular weight of the substance is 92.2 g/mol.