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 determine the molar mass of the gas, we can use the ideal gas law equation, which relates pressure (P), volume (V), temperature (T), and molar mass (M) of a gas:
PV = nRT
Where:
P = pressure (in atm or cmHg)
V = volume (in liters or mL)
n = number of moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K or 62.36 cmHg.mL/mol.K)
T = temperature (in Kelvin)
First, we need to convert the given data to the appropriate units:
Pressure = 60. cm of Hg = 60. / 760. atm (since 1 atm = 760. cmHg)
Volume = 125 mL = 125 / 1000 L (since 1 L = 1000 mL)
Temperature = 25°C = 25 + 273.15 K (since temperature must be in Kelvin)
Now we can plug the values into the equation:
(60. / 760.) * (125 / 1000) = (n * 0.0821 * (25 + 273.15))
Simplifying the equation:
0.0158 = 0.0821 * (n * 298.15)
Rearranging the equation to solve for n (the number of moles):
n = 0.0158 / (0.0821 * 298.15)
n ≈ 0.00066 moles
Finally, we can calculate the molar mass by dividing the mass of the sample by the number of moles:
Mass of sample = 0.429 g
Molar mass (M) = Mass of sample / Moles
M ≈ 0.429 g / 0.00066 moles ≈ 651 g/mol
Therefore, the molar mass of the gas is approximately 651 g/mol.