3.20 g of unknown gas occupied 2.24 L at STP; Identify this gas from the following list: nitrogen, oxygen , hydrogen, methane CH4, of propane CH3CH2CH3.
One mole of any gas occupies 22.4 L @ STP so you have 2.24/224 = 0.1 mol of the gas. Then mol = grams/molar mass. Rearranging you get molar mass = grams/mols = 3.20/0.1 = 32
Which gas listed has a molar mass of 32?
To identify the gas from the given options, we need to calculate the number of moles of the gas using the ideal gas law equation:
PV = nRT
Where:
P = Pressure (STP = 1 atm)
V = Volume (2.24 L)
n = Number of moles (unknown)
R = Ideal gas constant (0.0821 L·atm/(mol·K))
T = Temperature in Kelvin (STP = 273 K)
Rearranging the equation to solve for n:
n = PV / RT
Substituting the given values into the equation:
n = (1 atm) * (2.24 L) / (0.0821 L·atm/(mol·K)) * (273 K)
n ≈ 0.100 mol
Now, we need to determine which gas has a molar mass close to 3.20 g / 0.100 mol ≈ 32 g/mol. Let's calculate the molar mass of each gas:
Nitrogen (N2) - 2 * 14.01 g/mol = 28.02 g/mol
Oxygen (O2) - 2 * 16.00 g/mol = 32.00 g/mol
Hydrogen (H2) - 2 * 1.01 g/mol = 2.02 g/mol
Methane (CH4) - 12.01 g/mol + 4 * 1.01 g/mol = 16.05 g/mol
Propane (C3H8) - 3 * 12.01 g/mol + 8 * 1.01 g/mol = 44.11 g/mol
From the molar masses, the gas with a molar mass closest to 32 g/mol is Oxygen (O2). Therefore, the unknown gas is most likely oxygen (O2).