A 0.429-g sample of gas occupies 125 mL at 60. cm of Hg and 25°C.
The molar mass of the gas is ________ g/mol?
To find the molar mass of the gas, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, let's convert the given measurements to the appropriate units for the equation:
Given:
Mass of gas = 0.429 g
Volume of gas = 125 mL (convert to L by dividing by 1000) = 0.125 L
Pressure = 60. cm Hg (convert to atm by dividing by 760) = 0.0789 atm
Temperature = 25°C (convert to Kelvin by adding 273.15) = 298.15 K
Now, we can rearrange the equation to solve for the number of moles:
n = (PV) / (RT)
n = (0.0789 atm * 0.125 L) / (0.0821 L.atm/mol.K * 298.15 K)
n = 0.00103 moles
Now that we know the number of moles, we can calculate the molar mass:
Molar mass = (Mass of gas) / (Number of moles)
Molar mass = 0.429 g / 0.00103 moles
Molar mass ≈ 416.5 g/mol
Therefore, the molar mass of the gas is approximately 416.5 g/mol.