The mass of a sample of a liquid compound was found to be 0.534 g after the compound was vaporized in a containter placed in a boiling water bath at 100°C at 748 torr. The volume of the container was 286mL. Calculate the molecular mass of the compound.
PV = nRT and solve for n.
n = grams/molar mass
Solve for molar mass.
To calculate the molecular mass of the compound, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 100°C + 273.15
T(K) = 373.15 K
Next, let's convert the pressure from torr to atm (since the ideal gas constant R has units in atm):
1 atm = 760 torr
P(atm) = P(torr) / 760
P(atm) = 748 torr / 760
P(atm) ≈ 0.9842 atm
Now we can rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
Plugging in the values we have:
P = 0.9842 atm
V = 286 mL (convert to liters by dividing by 1000)
V = 286 mL / 1000
V = 0.286 L
R = 0.0821 L·atm/mol·K
T = 373.15 K
Now, let's calculate the number of moles (n):
n = (0.9842 atm * 0.286 L) / (0.0821 L·atm/mol·K * 373.15 K)
n ≈ 0.0121 mol
Next, we need to calculate the molar mass of the compound. We know that the mass of the compound is 0.534 g, and we now know the number of moles (n ≈ 0.0121 mol).
Molar mass = Mass / Moles
Molar mass = 0.534 g / 0.0121 mol
Molar mass ≈ 44.13 g/mol
Therefore, the molecular mass of the compound is approximately 44.13 g/mol.